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1706 worked questions from the practitioner guides — each one a figure that moves, and the reason it moves.
These are the calculations that get stated as conclusions elsewhere: what a recovery is worth once you account for what it is paid in, how a catch-up is solved rather than looked up, why a promote can go to nothing on a five percent move in exit values. Every figure below is a live formula in one of the free companion workbooks.
Companion workbooks: /distressed
A worked capital structure at three enterprise values. The break migrates from the first lien to the subordinated notes without a single document changing.
Composition and time do more damage to a recovery than the headline number suggests. Two arithmetic steps most screens skip.
Reading a distressed bond price as a view on enterprise value: the formula, the return it needs, and the two claims the shortcut forgets.
A worked rights offering with a backstop premium: the value of the right, the dilution of those who decline, and what happens below plan value.
A worked Chapter 7 liquidation analysis: proceeds by asset class, the costs most models forget, and the best interests test for the first lien.
A non-pro-rata uptier on a $500M first-lien term loan, worked through the waterfall at five enterprise values against the same new money lent pro rata.
The allowed claim of an unsecured noteholder worked from the indenture: accrued coupon, unamortised OID, no postpetition interest, and what each error does to the return.
A priming DIP and a 1:1 roll-up run through the waterfall at five enterprise values, with the transfer between first lien lenders priced.
Plan value fixes the percentages, the market fixes the recoveries: the reorganised equity split worked down the waterfall, with the valuation fight priced.
Accept or hold out, priced as two scenarios and a break-even probability of default, with participation and enterprise value as the levers that move it.
Section 506(b) worked as arithmetic: the cushion, the monthly accrual, the month it runs out, and the cents it takes from the unsecured creditors.
Section 506(a) splits an undersecured claim in two. The split decides the lender's recovery, and it quietly sets the bondholders' too.
Three break-evens for one bond: getting your money back, earning the target return, and how many months the case can run before the target is gone.
The two-thirds test is measured on claims that vote, so the blocking stake depends on who else turns up, and buying a third of the class usually overpays.
Senior on the cover is not senior in the waterfall: a holding company bond ranks behind every creditor of the company that owns the assets, unless a guarantee lets it in.
The price sits between the risk-free value and the recovery, and where it sits is the default probability, once you fix what default pays.
A cramdown pays the secured class in full on paper; the discount rate decides how much of that is real.
Professional fees come off the top of the waterfall, so the whole bill lands on the fulcrum class, and it grows with every month the case runs.
The quoted margin on a debtor-in-possession loan says little about its return. The fee stack, earned over a short and uncertain case, does most of the work.
Bid protections come out of the sale proceeds, so a topping bid is worth far less to creditors than its headline suggests.
Companion workbooks: /fundcontroller
Most write-ups state the catch-up formula then hardcode the answer. Set it as a solve and it moves on its own when the carry rate does.
Five findings in one quarter-end close, and not one of them was a modelling error. Every one was a control that did not exist.
A subsequent close worked from the capital calls: the contribution, the interest, the fee catch-up, and what the rate actually transfers.
The hypothetical liquidation worked tier by tier, and why the accrual moves faster than NAV in the catch-up band.
The fee step-down worked year by year on one agreement, the three readings of the base, and the write-down that gets left in.
Three numbers that look alike, the portfolio value, the fund NAV and the limited partners' NAV, and the bridge from each to the next, with the carry accrual that separates the last two.
One investor's calls, distributions and NAV run through XIRR, quarterly IRR and annual IRR, with the Excel formulas and the date errors that move the answer.
Translating a euro investment in a dollar fund, splitting the gain two ways, and keeping the quarterly split consistent with the cumulative one.
The exit of a portfolio company worked through the fund's books: net proceeds, escrow, the reversal of the prior mark, the journal entries and the escrow true-up.
Why the undrawn commitment in the quarterly report overstates what a fund can still invest, and the five deductions that turn it into a budget.
Shared costs by commitments, deal costs by participation, vehicle costs to the vehicle: why one allocation key moves money between two groups of investors.
One quarter's capital call on an illustrative buyout fund, sized from the uses of cash and allocated investor by investor.
One distribution on an illustrative $200m buyout fund, run investor by investor through a European waterfall.
Rerun the whole fund through one waterfall, with the preferred return compounded in time, and compare it with what the general partner was actually paid.
Fees, carry, closing date and currency are set investor by investor, so the fund's reported net IRR is nobody's return in particular.
A subscription line is leverage on time: it magnifies whatever the investment does relative to its cost, and the IRR can move either way.
A transfer in the middle of a quarter forces the fund to split one quarter's results between two investors. The two accepted methods can give very different answers.
Vested points times a value per point. The carry plan decides the vesting step, the leaver category and which value applies, and the range is wide.
When a fund sells part of a holding it bought in tranches, the cost it relieves decides the realised gain, the realised multiple and, under a deal-by-deal waterfall, when carry is paid.
A reserve for late claims keeps the fund alive and the LPs' cash idle. Both have a price, and it belongs next to the chance of a recall.
Companion workbooks: /pere
Net of fees, core earns 6.56% and opportunistic 15.15%: the 12.50-point gross spread shrinks to 8.59.
Carried interest is not proportional to performance near the hurdle. It is a step function, and $2m of headroom is what stands between a promote and none.
The same deals, the same total profit, two calculation orders — and a $9M promise to repay that is only as good as the entity that made it.
Leverage multiplies value changes by a fixed factor and income by a spread that can turn negative. Both are one line of arithmetic.
The coupon is the smallest part of the comparison. Compounding, the term and what each instrument does to the senior loan decide it.
The compounding clause is worth millions on paper and nothing at all in most outcomes. The band where it bites can be computed.
The formula is one division; the useful part is seeing when the loan that is meant to lift the return pushes it down instead.
The promote is paid on the investors' capital but lands on the sponsor's small cheque, which is why the sponsor's IRR moves so much faster than the deal's.
The two IRRs come from the same property and two different cash-flow rows, and the gap between them is set by one comparison: the property's return against the all-in cost of the debt.
The weighted average of the layers is two lines of arithmetic; what it tells you is how much of the project's income is spoken for before the common equity sees a dollar.
An equity multiple without a holding period is half a number; solve it backwards from the IRR you need and the answer changes with every year of hold.
Return on cost and value per dollar for an apartment interior programme, with the downtime and vacancy the quick version leaves out.
Current pay, compounding accrual and a minimum multiple, on a $10 million preferred equity position, year by year.
A six-year value-add hold run with and without a year-three cash-out refinance, and the cost of the extra debt that decides the result.
Exit proceeds paid down a four-layer stack at each layer's claim on the exit date, and the cushion that accrued interest quietly removes.
A fee on the gross sale price is paid entirely from the equity, so the debt in the deal magnifies it. Here is the arithmetic at four levels of leverage.
The order in which a JV applies interim distributions, and why it only matters when the preferred return does not compound.
Two tests, not one: leverage is negative on cash yield when the interest rate beats the cap rate, and negative on IRR only when it beats the unlevered IRR.
Below replacement cost is one of the most quoted lines in a real estate investment memo. Built properly, it gives two discounts and a test of how far rents must rise before anyone builds competing supply.
A ground lease is a layer of capital: price it, compare it with the equity it replaces, and find the rent, exit cap and leverage at which it stops paying.
Companion workbooks: /familyoffice
A five-person office costs the same $2,442,000 at $100m as at $2bn. Against a tiered multi-family schedule the two curves cross exactly once.
Volatility drag, not expected return, decides whether a founder's family should pay tax to diversify, and it can be computed to the year.
Commitment pacing turns an allocation into an annual commitment, and shows why committing the target once never reaches it.
A family spending policy worked per heir rather than per family: the formula, what familiar rates do over three generations, and what moves the answer.
The fees saved, the cost of the team and the quality gap put on one scale, giving the programme size at which a family office should go direct.
Why a family with private fund commitments needs a reserve sized on capital calls in a stress, and how to test whether its bonds and cash would cover them.
A year-by-year simulation of income tax, realised gains and deferral, and why turnover, not the tax rate, is the part of the drag a family office controls.
The annuity that zeroes out the gift, the remainder year by year, and why the result depends on volatility more than on the rate.
The formula with every layer of tax, the comparison with Treasuries and corporates, and the bracket at which munis stop winning.
An installment sale to a grantor trust freezes the value of an asset in the estate at the note, and passes everything it earns above the interest rate to the next generation.
The 5 per cent minimum distribution looks modest until fees and inflation are added to it; then it sets a return hurdle most portfolios do not clear.
A term-of-years CRAT worked from the annuity factor: the charitable deduction, the 10 per cent remainder test, the maximum payout and what the family gives up.
A break-even worked from the load, the annual policy charges and the tax drag of the strategy it wraps, with the cases where PPLI never pays.
The annuity that zeroes out the gift, the remainder the family receives, what the 7520 rate and the trust's return do to it, and the back-loaded variant.
The trust against outright bequests, generation by generation, why the saving compounds to far more than 40 per cent, and what growth, payouts and GST exemption do to it.
The saving comes from two valuation discounts applied in sequence, and it lasts only as long as the partnership is run as a real one.
A foundation's cost is mostly fixed, a donor-advised fund's is a sliding percentage, and the asset given can matter more than either.
The comparison is not interest rate against tax rate. It is two balance sheets at death, and the biggest line is the growth on shares the seller no longer owns.
Family offices that invest directly increasingly pay their teams carry. Its cost depends on the outcome, the catch-up and the pooling, and all three can be priced.
The year-one tax saving is mostly a loan from the tax authority. What is left after the lower cost basis is taxed, and the two cases where harvesting is worth much more.
Companion workbooks: /investorrelations
7.12 per cent, 18.04 per cent, or 1.323 times the public market — one fund, one set of flows. The eleven-point gap is the valuation, and it is not cash.
A successor fund's pipeline weighted two ways, the probability of each milestone, and where the gap between them sits.
The re-up rate in dollars and in heads, the new money a target implies, and why retention beats prospecting at the margin.
One fund ranked against nineteen vintage peers on IRR, TVPI and DPI, with both Excel quartile methods, and why a top-quartile claim can rest on a formula choice.
Three loss ratios from one twelve-deal record, realised against unrealised, and why a threshold measure jumps when a large deal sits near 1.0x.
Fully realised, partially realised and unrealised: how to define the buckets, why each must be pooled, and what the split tells an investor that the blended figure hides.
Why DPI has to be read against the fund's age and its own TVPI, and how three funds with the same IRR can show very different DPIs at year eight.
A fund size target built bottom-up from deal pace, cheque size, reserves and the share of commitments that is never invested.
A fundraising timeline worked week by week from conversion, meeting capacity and the lag between first meeting and signed commitment.
Run the waterfall for the pool, date the payments, discount them and apply vesting: a points offer is a deferred option on the whole fund, not a number.
IRR measures the speed of money, not the amount: test it against the hurdle, the index and the peers, and always read it with the multiple.
One final close, $630m of demand for $362m of room, and three allocation policies worked LP by LP, with the minimum ticket and the gross-up problem.
Count hours, not names: tier the LP base, add the fixed reporting load, and size the team for the fundraising year rather than the quiet one.
Two LP bases with the same expected re-up rate, computed outcome by outcome, and why the concentrated one needs a bigger pipeline of new investors.
Value the first commitment, then the re-ups. More than half of what an LP is worth comes from funds it has not yet agreed to.
A line-by-line fundraising budget, with the organisational expenses cap and the placement fee offset applied to show who really pays.
The distribution rate for an LP report, the three ways it is computed, and what it says about when DPI reaches 1.0x.
A spin-out raises its first fund on a record earned elsewhere. The selection of deals moves the IRR more than the deals themselves.
The question every LP asks about a predecessor fund during a fundraise, and the shortcut that says the portfolio could even fall in value and still get there.
Subtract the firm's budget from the percentage fee year by year, give back the carry, and check the fund size before agreeing to it.
Companion workbooks: /vc
Holding pro rata to the Series D costs $14.76m per company. A $40m reserve defends 2.71 of forty — and 61 per cent of the cost is the last round.
Where the pool is topped up decides who pays for it. Four lines of cap table arithmetic, and why the higher headline valuation can be the worse offer.
The stake on the term sheet is not the stake on the exit waterfall. Project the dilution first, then ask whether the company can return the fund.
Post-money SAFE conversion worked share by share: the cap price, the discount price, which one wins, and the pre-money at which they swap.
The formula prices only the money raised below the old price, spread across the whole capitalisation, which is why it costs founders a point where a ratchet costs six.
The textbook formula divides by churn, and when cohorts expand churn is negative: the answer then depends entirely on the horizon or the rate you choose, so state it.
The venture capital method worked on one Series A cheque: from exit value to target multiple, then the step most people skip, the dilution still to come.
A three-round cap table worked line by line, with the option pool created before each round, and the founders' stake after every step.
The interest converts too, the cap and the discount never both apply, and whether the Series A pre-money counts the note shares decides who pays for it.
Divide cash by net burn for the headline, then run the months forward: growing costs shorten it, and the fundraise has to start long before the last month.
Two ways to rank the same 1x non-participating preferences, worked across a range of exits, and the band where the choice moves real money.
A vertical SaaS market sized from countable clinics, a real price and a hiring plan, and the test a VC should run against the result.
A venture deal funnel run backwards from the fund's plan, stage by stage, to the calls each associate has to take every week.
The coupon, the fees, the final payment and the warrants on one schedule, and the exit prices at which the loan is cheaper than equity.
The scorecard method worked on one seed deal, what each rating is worth in money, and why the comparable average matters more than any of them.
A worked down round, full ratchet against broad-based weighted average, and why the size of the new round does not matter to the ratchet.
A worked down round in which one Series A investor takes its allocation and the other does not, with the exit waterfall run for both.
The pool on the term sheet is a rule of thumb. A hiring plan with grant bands, forfeitures and a horizon gives the number to negotiate with.
The commission in the terms of service is not the take rate, and a margin quoted on revenue hides how thin each order really is.
A repayment cap is a dollar fee on an amortising loan, so its rate depends on how fast revenue grows.
Companion workbooks: /money
£81.53 leaves the account and £20.46 reaches the debt. On minimums alone the set clears in 258 months and repays 1.78 times what was borrowed.
The 50/30/20 rule worked on one household's actual bills, and the take-home pay below which it cannot be followed at all.
Sizing an emergency fund on the bills that keep arriving, not on salary, and counting the months it takes to fill.
Run month by month on four illustrative debts, the two methods finish on the same day, and the price of the snowball's early wins can be stated in pounds.
Fee against interest, month by month: when a 0 per cent transfer saves money, and the one payment figure to work out before you apply.
The average daily balance method worked through one statement cycle, with what the timing of a payment is worth.
The amortising loan formula worked by hand and in Excel, where each payment goes, and what a longer term or a small overpayment really does.
Nominal rate against effective yield, worked on a savings balance at five compounding frequencies, with the Excel functions and a three-account comparison.
A consolidation loan lowers the rate and usually the payment; the rate saves money, and the longer term can take all of it back.
Paying off a debt earns its interest rate with certainty and without tax; investing has to beat that rate after tax, with room to spare for the risk.
The payoff-time formula and Excel's NPER on one card, checked month by month, with the payment that clears it in one, two or three years.
The two APR conventions on one small loan, why a shorter loan shows a higher APR, and what the same £300 costs on a credit card.
One division, two ratios, and the reason clearing the right debt can raise what a lender will let you borrow by more than the debt itself.
Overall and per card, what it takes to get under 30 and 10 per cent, and the two moves that raise the ratio without adding a penny of debt.
The monthly amount is the easy half. The half people miss is the balance the fund must already hold on the day you start, which depends on when the bills fall.
Zero per cent finance is rarely free when a cash price is on offer. Turn the lost discount into an interest rate and compare it with what your money earns or a loan costs.
A longer term makes the payment fit; the interest and the years of negative equity are what it costs.
Twenty-six half-payments make thirteen monthly payments a year. The thirteenth does the work; the two-week rhythm is worth very little.
The early withdrawal penalty is a fixed cost and the higher rate is a monthly gain, so the answer depends on how long the old CD has left to run.
Points prepay interest for a smaller payment later; whether they pay depends on how long the loan really lasts.
Companion workbooks: /investing
One point on the annual charge turns 738,846 into 567,961 over forty years — 23 per cent of the pot, and 2.43 of wealth lost per 1 of fee.
The compound interest formula for a monthly investment, worked once, with the range of results across returns and horizons.
Investing a sum at once or over twelve months, priced in expectation and on three price paths, with the argument about average cost taken apart.
Ten years of contributions made early beat thirty years made late, but only above a return you can calculate, and the reason sits in the last decade.
The compound interest formula turned around: solve for the payment, then see how horizon, return and fees move it.
The shortcut against the exact doubling formula, rate by rate, and what it shows about fees and inflation over a working life.
The exact formula, the shortcut and why it drifts, and a forty-year savings pot restated in today's money at five inflation rates.
The compound annual growth rate worked from a five-year record, the volatility drag that separates it from the average, and the Excel formulas for both.
The 4 per cent rule turns a spending figure into a target pot in one division; the order in which returns arrive decides whether it holds.
Losses are measured on the bigger base and recoveries on the smaller one, which punishes the seller and quietly rewards the saver who keeps buying.
Price return against total return on one lump sum, with the dividends taken as cash and reinvested, over four horizons and three yields.
The trade formula on one portfolio after a good year, rebalancing with new money instead of selling, a 5-point band, and what rebalancing did through a 30 per cent fall.
One division gives the capital, a second turns it into years of saving, and the yield you assume moves both more than anything else.
Your savings rate decides both how fast the pot grows and how big it has to be, which is why it matters more than your income.
The average cost of shares or fund units bought at different prices, what averaging down does to your break-even, and why the cost method changes the gain you report on a sale.
How to calculate the price-to-earnings ratio and the earnings yield, and how to turn any P/E into the growth rate the price is assuming.
The price chart shows half of what a dividend-paying share earned; the other half has to be added, and dated.
The formula, a worked holding over twenty years, and why the figure describes your past purchase rather than the return you can earn today.
The PEG scales the P/E by growth in one division, and in doing so assumes a share's multiple should rise in proportion to its growth rate.
Each missed day removes a multiplier on the whole balance, which is why ten days out of twenty years can take more than a third of the result.
Companion workbooks: /evergreen
A drawdown fund advertising 13.25 per cent ties an evergreen netting 8.64. On committed rather than called capital, 78.7 per cent of the edge vanishes.
Project the quarters at the redemption cap, net of what the portfolio still distributes, and solve for the opening sleeve.
When redemption requests exceed the quarterly cap, the fill ratio, not the cap, decides how fast an investor gets its money back.
A worked year-by-year ledger of the performance fee in a semi-liquid fund: the high-water mark, the hurdle, the catch-up, and who rides free.
A semi-liquid fund can pay a steady distribution whatever it earns. The coverage ratio and the NAV line show what the payout is made of.
Who pays the cost of deploying new money or selling private assets to meet redemptions: the investors who deal, or the ones who stay.
One portfolio, two prices: the order of operations that keeps each share class paying its own fees and the class NAVs tying to the fund.
An evergreen fund that buys LP interests at a discount and marks them to the manager's NAV books the discount as return on day one. The arithmetic, and who gains at whose expense.
Monthly dealing on quarterly appraisals lets new money buy at last quarter's price. The transfer is one formula, and it runs both ways.
The soft lock on a semi-liquid fund is small in percentage terms and large in annualised ones, and it is paid to the investors who stay, not to the manager.
A fast-growing evergreen fund carries a second cash balance on top of its liquidity sleeve: the money it has taken but not yet invested. Its cost is a simple product.
Why a single fund-level high-water mark lets new money ride free after a drawdown, what a depreciation deposit collects, and who bears the difference.
The quarterly hurdle and catch-up of a semi-liquid private credit fund worked line by line, and why an income fee can take a third of a year's total return.
Both wrappers around the same asset, the fee drag per year of capital at work, the return at which the ranking flips, and what the liquidity sleeve does to the answer.
How a DRIP prices new shares in an evergreen fund, the dilution when it reinvests below NAV, who pays it, and why the real benefit is the sales load it avoids.
An expense cap moves a new fund's costs in time, from its first investors to the ones who arrive later.
A fixed monthly charge on a growing NAV falls hardest on the investors who arrived first.
The static ratio divides liquidity by unfunded commitments and stops. The test that matters adds the calls, the redemptions and the distributions a bad year brings.
Same evergreen fund, same fees, two share classes. The accumulating version wins only through tax deferral, and only in regimes that allow it.
Two classes of the same semi-liquid fund, run through the full fee formula: what an early investor gains, why the gain shrinks when returns are low, and what the manager gives up.
Companion workbooks: /secondaries
The seller’s floor and the buyer’s ceiling are one formula at two rates. At equal required returns the zone is exactly zero — here it is 11.02 points apart.
The bid percentage is fixed on the reference NAV; the cheque, and the real discount, move with every call, distribution and mark until closing.
Split the profit at NAV, then split the IRR at par: the two answers differ, and the gap tells you where the risk in a secondary sits.
A discount to NAV is earned once and spread over the hold, so duration, not the headline percentage, decides the return.
Rolling is a decision to buy the asset again at the deal price, so measure it on the cash you give up, after the new fees and carry.
The buyer of an LP interest also buys the obligation to fund future calls at par, and that obligation has a present value of its own.
Secondaries do not make the J-curve shallower, they make it shorter, and the arithmetic shows by how much and when the effect disappears.
A secondary bid is the sum of company-level present values, not a discount applied to the manager's NAV, and the difference shows up in where the price comes from.
A stapled commitment is a cash flow, not goodwill: discount it at the return the buyer's capital must earn and take it off the price.
Price a tail-end interest on its net distributions, with the fund's costs in absolute amounts, and a large part of the discount turns out to be structure.
A deferred purchase price is an interest-free loan from seller to buyer. Priced at both sides' rates, it explains why headline secondary prices rise while effective prices fall.
Secondary bids are quoted on a reference NAV that is months old. Rolling it forward for cash and for markets shows what discount the buyer is really paying.
Acquisition debt on an LP interest is repaid from the first distributions, so it is outstanding for less than two years and adds far less return than the multiple suggests.
A preferred equity deal lets an LP raise cash without selling at a discount. It keeps the upside and, less visibly, all of the downside.
A continuation vehicle is a sale, so the old fund's waterfall runs at the transfer price: the GP crystallises carry on assets it still manages, and in the catch-up zone the price is its money one for one.
A secondary sale converts the whole residual value into distributions at once, so DPI jumps by the price and TVPI falls by the discount times RVPI; the real cost is the return the buyer earns on the cash flows you hand over.
The allocation schedule decides what the buyer loses when a GP exercises its right of first refusal or refuses consent on one line.
The discount to NAV makes the tail look twice as expensive. Measured against what the seller gives up, the gap is small and can reverse.
A NAV loan sits ahead of every LP in the fund. A secondary buyer has to price the interest on the assets and the debt, not on the reported NAV.
The holder of the right knows the portfolio better than the bidder, so the deals it lets through are the weaker ones. That selection, not the delay, is most of the cost.
Companion workbooks: /loanagreement
233,192 against 2,602,535 on the same breach. The ratio is 1/(k·c) — it ignores the size of the decline and turns on two terms the borrower negotiates.
The formula, the Excel one-liner, the two discounting errors and how the premium moves with rates and remaining term.
Quarter by quarter, the excess cash a sweep applies to the loan, the paydown the trigger requires, and why the cure time explodes as the decline deepens.
The definitions that turn net operating income into covenant cash flow, the assumed amortisation that inflates debt service, and the Excel to check both.
The bondholders get exactly the cash they were promised, so the price of leaving is set by the Treasury curve, not by a negotiated penalty.
An extension option is only as good as its conditions, and the cheque that satisfies them can be computed months before the test date.
The default rate looks like a modest percentage. The base it applies to, the whole principal for every day of default, is what makes it expensive.
A different test binds for different properties, so the release price has to be computed asset by asset, in the order the business plan sells them.
The cure for a failed loan-to-value test is a two-line sum, but the second line depends on how the agreement counts cash collateral.
The cash management clauses decide who is paid first every month; run numbers through them and the borrower's margin turns out much thinner than the covenant suggests.
The formula is simple; the definition is not, and the same prepayment costs anything from $959,464 to $2,265,000 depending on four words.
Which schedule an act sits in matters more than the act: the same default costs the guarantor 19.3 times more if it springs full recourse.
The same building, the same loan, the same test date: one ratio looks back and passes, the other looks forward and fails.
The thresholds in a burn-down are the part everyone negotiates. The NOI definition and the consecutive-quarter rule are what set the release date.
Upfront deposit, monthly collection, cap and major-tenant sweep are four numbers in the loan agreement. They only work if they are sized together against the rent roll.
The sponsor's personal financial statement says the guarantee is comfortably covered; the loan agreement's definitions say it is already in breach.
The monthly deposit is the easy part; the closing deposit depends on the bill calendar and on whether the reserves are pooled.
The cap in the loan agreement is what the lender wanted. What the sweep collects depends on the building's cash and when the trigger springs.
A carry guarantee is expected to be called: the lease-up produces the shortfall, and the release test decides how long it runs.
The measurement window in the NOI definition can decide a covenant breach before the covenant level does.
Companion workbooks: /limitedpartner
37 basis points, and a 22.8 per cent total-loss rate erases it. At the usual per-deal cap a single failure is 37 per cent of the annual cohort.
Overcommitment is a liquidity calculation: the ceiling is set by the year in which capital calls continue and distributions stop.
A denominator breach is three movements, not one: the public fall, the lag in private marks, and the net cash flows that keep arriving.
The J-curve that matters to a limited partner is cash, not reported IRR: how deep the hole gets, when it bottoms, and when it closes.
Correlation between funds sets a floor under portfolio risk, and the number of funds only decides how fast you approach it.
Turn the fee question around: solve for the underlying multiple at which the second layer disappears, then test the manager against it.
Performance persistence in private equity, turned into an expected multiple for the successor fund and a budget for what to concede at re-up.
Stack one vintage a year, add calls and distributions across vintages, and find the year the programme pays for itself. Then see what commitment growth does to that year.
A secondary sale shrinks the private book and, through the discount, the whole portfolio. The formula, the cost, and why selling to the top of the band halves it.
A fund's IRR is earned on capital while it is invested. The LP's return is earned on everything it set aside, including the years that money waits for calls.
A two-asset optimisation worked by hand: the weight that maximises the Sharpe ratio, why smoothed NAVs inflate it, and why liquidity sets the final number.
Fee savings per unit of commitment against costs that do not shrink with size: the minimum mandate at which an SMA beats the commingled fund, and what erases it.
Diversification, manager exposure across re-ups, share of the fund and the cost of monitoring each set a limit; the commitment is the one that binds.
The fee saving, what carry takes back, the IRR it adds, and the break-even probability at which the option to wait for the final close is worth more.
The carry cost of rolling forwards, the cash a dollar rally demands while the NAV gain stays illiquid, how little volatility the hedge removes, and the NAV-lag trap.
Funds of the same year share an entry market and an exit window. Two correlations, not one, show what pacing is worth.
A short record is a small sample from a noisy distribution. Test it against the market's dispersion before reading the story.
Negotiating capital is limited. Pricing each concession through the waterfall, at more than one gross return, shows which terms deserve it.
Headcount from the pacing plan, the manager funnel and the monitoring book: why ticket size and re-up mix move the answer more than the budget.
An annex fund is offered as extra exposure on cheap terms. The price at which it buys into the existing companies decides whether declining is neutral or a gift to the LPs who invest.
Companion workbooks: /growthequity
Defending costs 1.25 times the initial cheque across two rounds, not more in each — and below a 521 exit the follow-on dollars come back worth less than they cost.
The formula is one addition. The definitions decide the answer, and the same company can pass by five points or fail by fifteen.
One series on its own is a simple choice. A stack of series is a small game, and the junior rounds convert later than their price suggests.
Net revenue retention measures the growth a customer base produces on its own, and it is only as good as the cohort definition and the concentration behind it.
CAC payback tells a growth investor how long each new dollar of recurring revenue drains cash, and the same quarter can report four different answers.
The burn multiple says how much cash a company spends to add one unit of recurring revenue, and the definition decides which side of a band it lands on.
Working backwards from the exit is how a growth equity investor turns a target multiple into the highest price it can sign, and dilution is the step most often skipped.
The payout curve of a capped participating preference, the flat zone nobody models, and what the cap is really worth to common.
The compounding formula both ways, a cohort of 1,000 customers month by month, and the LTV error that hides in the annual version.
The standard version, the five variants a data room will offer, and why the magic number and CAC payback are the same ratio.
Net new ARR says how much a company grew; the quick ratio says whether the growth came from a sound base or from a sales engine refilling a leaking one.
The extra shares lower the IPO price they are counted at, so the share count has to be solved, not divided. Worked on an illustrative 100.0 growth round.
Entry at a high revenue multiple is a bet on growth outrunning the fall in that multiple: the formula, the growth it demands, and what a strong plan returns once the multiple halves.
Most growth rounds mix new shares for the company with existing shares bought from founders and early holders: the blended entry price, the ownership it buys, and the downside the cheaper common shares carry.
A cumulative dividend on non-participating preferred, worked across exits: where it pays, where it is worth nothing, and the one clause that changes everything.
The redemption amount, the instalment schedule, the investor's real IRR and whether the company can actually pay, worked on one illustrative minority deal.
T2D3 is the growth yardstick in every SaaS board deck. In numbers it is a 72-fold increase, a sales budget above opening ARR, and a fragile return for whoever pays for it.
Milestone tranching gives the investor a free option on the company's progress. Here is how to price it, from both sides of the table.
A sales capacity model turns a top-down ARR target into the account executives who must already be in seat. Ramp time and attainment decide whether the plan is possible.
The ARR formula, the six adjustments a growth investor makes to management ARR, and the revenue test that catches what does not belong.
Companion workbooks: /odd
Three of twelve managers carry a terminal flaw and the average approves all three. Splitting eight domains into sixteen makes it easier to hide, not harder.
The policy usually says 'fairly'. The fair amount is a calculation, and the gap between policy and practice shows up in the dead-deal log.
Every manager has a callback rule in its procedures. The expected loss shows why operational due diligence has to test whether it operates.
A valuation backtest on ten exits, with the reference mark that matters, the statistics to compute, and what a persistent uplift says about interim NAV.
A management company stress test for operational due diligence: fee income fund by fund, the investment-period cliff, and what a late successor fund does to the cash.
Why the percentage is the wrong test of alignment, and how operational due diligence turns a stated GP commitment into the partners' own cash at risk.
Single loss expectancy, rate of occurrence and the return on security spending, worked for a private equity manager's cyber register as an operational due diligence analyst would rebuild it.
An operational due diligence programme sized from initial reviews, tiered monitoring and event-driven work.
The expected value of an ODD review per manager, its break-even points, and why depth should scale with the ticket.
A key person clause is a probability, not a list of names. How many people it names and how many must leave decide how often it fires.
Audit adjustments are the cleanest evidence an operational due diligence analyst has on valuation. Their sign says more than their size.
Measuring whether two due diligence analysts rate managers the same way, with the chance correction that raw agreement leaves out.
Overall materiality, performance materiality and the clearly trivial threshold for a fund audit, and what a clean opinion can leave uncorrected in NAV, TVPI and carry.
Size the limit from the loss distribution, not the premium quote, and check the sublimit on the one scenario that carries half the expected loss.
Expected annual cost of three recovery tiers, the quarter-end outage that sets the real requirement, and the payment workaround that is cheaper than a faster tier.
Deposit insurance covers almost none of a fund's cash, so the operational question is whether the fund can still pay its next obligations if one bank stops paying.
Headcount turnover treats an associate and a founding partner as the same departure; the two weighted measures show what actually left the firm.
The GP sits on both sides of the price, and its economics in the two funds are not symmetrical. That is what a cross trade review has to measure.
A carry table with ten names can be a two-person firm. The Herfindahl index, the unallocated reserve and the deals each person leads show which.
A square-root rule sets the refresh interval for each manager from the review cost, the hazard of a deterioration and what finding it late costs.
Companion workbooks: /redebt
A 350 basis point margin advantage becomes 3.4 points of return on capital — and vanishes if the default estimate is 1.45 times out.
The exit test on a bridge loan, worked: debt yield, DSCR and LTV turned into required NOI, and the exit cap at which the refinancing fails.
Three ways to size the reserve, the closed form in Excel, and what a longer lease-up or a higher rate does to it.
Three sizing tests, three loan amounts, and the one that binds depends on the interest rate more than on the property.
The two LTVs that define a mezzanine position, and the value decline at which it actually starts to lose money.
The constant is what the debt costs the property's cash flow, and it sizes the loan as much as the interest rate does.
The balloon is fixed on the day the loan closes; the value it has to be refinanced against is not.
A five-year fixed-rate loan prepaid in each year, priced on a step-down schedule and on yield maintenance, with the treasury level at which they cross.
Interest-only and amortising versions of the same $30 million loan, month by month, and what the day count does to DSCR and the balloon.
Financing a whole loan on a repo line turns a high single-digit yield into a mid-teens return on equity. The same arithmetic multiplies the losses and adds a margin call.
A value-add bridge loan carries three loan-to-value figures and a loan-to-cost. Only one of them describes the lender's cushion if the plan stalls.
The in-balance test worked at one draw: the revised cost to complete, the retained contingency, the shortfall the sponsor must fund, and why loan-to-cost barely moves.
A floating-rate bridge loan whose cap expires before the extension: the Black-model cost of the replacement, why a 100 basis point move multiplies it by 5.7, and the monthly deposit that covers it.
Term sheets headline the debt yield test. The loan agreement usually adds an LTV test on a fresh appraisal, and on most cap rates that is the one that binds.
Crossing two loans does not add a cushion. It makes one property's fall coincide with the other's before the lender loses, and that is worth exactly as much as the assets are uncorrelated.
Mezzanine sits where most bad outcomes land, so its price is set by the value distribution, not by the senior spread.
Fees are struck on the commitment but earned on a balance that averages barely half of it.
A hotel's NOI falls two to two and a half times faster than its RevPAR, and faster still when the fall comes through rate.
Fixed or geared ground rent, a wasting head lease and a minimum unexpired term: how a lender turns a leasehold into a loan amount.
The intercreditor purchase option lets the mezzanine lender take control, but the price is set by the senior claim, not by the building.
Companion workbooks: /lease
5,788,000 becomes 807,365 once the over-market stream, the expiry dates and the cost of re-letting are priced — and nothing at all below a 43.7 per cent renewal rate.
Two caps with the same 5 per cent can bill a tenant very different amounts. The difference is set by the path of costs, and it can be computed year by year.
One division sets the breakpoint. What it implies for rent steps, sales risk and artificial breakpoints takes a few more lines.
The base year looks like a fixed number in the lease; it is in fact a measurement, and the gross-up clause decides what it measures.
The numerator is the tenant's own area and never in dispute; the whole negotiation sits in the denominator.
A gross rent and a triple net rent can be identical in year 1 and far apart by expiry, and the difference is a forecast of operating costs.
The payment formula behind an 'amortised over the term' clause, the balance at a break, and the valuation error it invites.
The load factor turns usable space into rentable space, and it decides which of two asking rents is really cheaper.
The contractual formula, the landlord's economic loss, and the gap between them that the option was worth.
Free rent and fixed bumps make reported rent and cash rent part company; the gap is a receivable that is only collected if the tenant stays.
The deposit is negotiated in months of rent; the exposure it is meant to cover is almost never written down beside it.
The percentage is only one of three words that set the bill: what it applies to, how part months are charged and whether damages follow matter as much.
The guarantee caps the guarantor at the notice period; what the landlord gets for the concession is its space back, empty and early.
A renewal at a percentage of market and a renewal at a fixed rent look alike in the lease. One is a discount, the other is an option, and they react to uncertainty in opposite ways.
The percentage in a profit-sharing clause gets negotiated; the definition of profit decides whether the landlord takes half the gain or twice it.
Tenants negotiate the 15 per cent. The money is in the definition of the base it applies to.
A sale resets the tax bill. The leases decide who pays it, and the price has to be solved, because the tax depends on the price.
A CAM audit is an investment decision. The lease sets what can be recovered, how far back, and who pays for the audit, and those decide whether it pays.
Monthly CAM is an estimate. The year-end reconciliation replaces it with the actual recoverable pool, and three lease definitions decide how big the true-up is.
A worked casualty abatement: the untenantable share, the definition of Rent, the end of the abatement period and who carries a long restoration.
Companion workbooks: /fundfinance
20 per cent becomes 38.41 on the same asset while the multiple falls. Two dollars of interest buys 18.4 points, and the longer the line runs the cheaper each point gets.
A borrowing base worked investor by investor, and why one exclusion costs more than the investor's own contribution.
The NAV facility loan-to-value worked from reported NAV to lending value, and why the asset that falls matters more than the size of the fall.
A subscription facility priced the way a CFO pays for it: per dollar actually drawn, at five levels of utilisation, and against a smaller line.
A fund borrows against its portfolio to return cash to investors. The two multiples, worked on the day of the draw and at repayment.
A NAV facility can sit comfortably inside its loan-to-value covenant and still run out of cash to pay its interest; the coverage test is where that shows.
Every dollar called from investors repays the subscription line and also removes the uncalled commitment that secured it.
The two limbs of a hybrid fund facility worked across a fund's life, with the year the NAV limb takes over, the year the facility size stops binding, and the stresses.
The two ways to raise liquidity against a private equity portfolio, priced over three years in five portfolio outcomes, with the fire sale a NAV loan's covenant can force.
The preferred return runs from the capital call, so a line that delays the call shrinks the hurdle. Whether that raises the carry depends on where the fund sits in the waterfall.
Distributions pay the interest first, the sweep takes its share of what is left, and the portfolio shrinks as it pays: three reasons the payoff is slower than the back of the envelope.
A secondary discount is a cost of capital in disguise: once it is annualised over the hold, the choice against a NAV loan turns on one break-even discount.
A management fee facility is repaid from what the management company keeps after paying its people, and that number is a fraction of the fee stream.
The structure, the cash waterfall year by year, what a 30 per cent NAV fall does to each tranche, and why a full sweep leaves the equity barely levered.
A multi-currency borrowing base revalued at spot, the dollar move that creates a deficiency, the capital call that cures it, and why borrowing in matching currencies removes the risk.
Lenders fund most of the partners' commitment to their own fund. For the partners, it is a leveraged and usually recourse position, and the arithmetic cuts both ways.
A secured currency forward priced the way a facility counts it, at inception and after an adverse year.
Paying interest in kind keeps cash in the fund, but the loan compounds while the collateral may not, so covenant headroom runs down by the calendar.
A private credit fund's SPV facility lends against the loans themselves. The base moves with every mark, default and concentration breach, and it is easy to overstate.
A subscription facility sized from the deal pipeline and the capital call cadence, with the stress case of two large deals closing in the same quarter.
Companion workbooks: /lpa
24 million recovers 13.20 net of tax and 7.20 is escrowed. The rule is e ≥ 1 − t, and every euro won on the tax clause lands uncollateralised.
Adding up a private fund's management fee from the rate, the base and the step-down, and the clause that moves it most.
The hurdle is a rate, so the multiple at which carried interest switches on depends on timing, and the band above it belongs to the manager.
A recycling clause lets the fund reinvest proceeds up to the fees it charged, so that the whole commitment goes to work. The gain has a one-line formula.
A year-by-year ledger of contributed capital and accrued preferred return, and the three shortcuts that misstate it by 7 to 10 units.
LPA default remedies priced as a present value, and compared with the routes an investor under liquidity stress actually has.
The catch-up rate decides how fast the manager reaches its carry share above the hurdle, not how much carry it earns when the fund does well.
A two-year extension looks like a formality. Priced against the NAV still in the fund, with carry on any further gain, it sets the return the last assets have to earn.
One definition in the waterfall, capital contributions or invested capital, decides whether the GP earns carry on the fees it charged. The cost is a fixed sum, and much larger near the hurdle.
Every investor asks for an MFN and most get one; its value is set by whose side letters it can elect from and what the exclusion list removes.
The percentage is what gets negotiated; the definition of invested underneath it moves the date by more than a year.
The no-fault divorce clause read as numbers: the vote, the fee tail, the carry the removed GP keeps, and what the replacement manager will want on top.
A 20 per cent single-company limit worked on one deal: the base, the follow-on, the bridge that fails to syndicate, and when the LPAC has to approve.
The clause that pays the general partner cash for tax on carry it has not yet received, worked year by year, and what happens if the fund then disappoints.
The LP giveback provision worked through a late indemnity claim: which distributions it reaches, which cap binds, and what one LP actually hands back.
The key person clause rarely forfeits anything outright; it changes the fee base, and the cost depends on when it bites and whether it is cured.
A consent threshold is a percentage of a defined base, and the base, not the percentage, decides who holds the veto.
The one-sentence clause in a deal-by-deal waterfall that decides how much of the GP's carry ends up as a clawback promise.
The percentage only binds in the first half of the fund's life. After 75 per cent is called, the uncalled leg takes over and shrinks with every capital call.
The overcall is the default clause that reaches the investors who paid, and its two limits bind at different points in the fund's life.
Companion workbooks: /euaml
Month 8, on a one-year window and a 14-week hiring lead time. The date is 12W − L/4.33 and holds for any portfolio size — the book only changes the euros.
Sizing customer due diligence refresh under the AMLR's one-year and five-year ceilings, tier by tier, in analyst-days rather than files.
The order of operations in an ownership chart decides whether a review finds two beneficial owners or none.
A weighted customer risk model, worked customer by customer, and the arithmetic reason every model needs overrides.
The ratio compliance teams report, the one statisticians mean, and the staffing that follows from both.
Article 55 sets a floor on the maximum, doubles the fixed amount for small institutions, and measures turnover at the top of the group.
A business-wide risk assessment reduces to one weighted number, and that number is built to hide the category that needs attention.
The AMLR occasional transaction threshold applied to four illustrative customers under four aggregation windows.
Above-the-line and below-the-line testing on an illustrative cash scenario, with the sample size the decision needs.
Many screening engines rank name matches with Jaro-Winkler or a close relative. Working one score by hand shows what a threshold can and cannot separate.
A KYC cost per customer is only meaningful by risk tier. The average hides a factor of seventeen between a simplified file and an enhanced one.
Sanctions ownership through a holding company, worked three ways: multiplied as for beneficial ownership, by the EU rule and by the OFAC rule.
A two-step test for smurfing on an illustrative year of cash deposits: the excess in the band under the threshold, then a binomial test per customer.
Rapid movement of funds is measured with three ratios, and the one most scenarios use on its own also flags every payroll and collection account in the bank.
An alert backlog clears at the rate capacity exceeds new alerts, which is why a team that looks almost big enough can take three years to catch up.
A first-digit test ranks customers whose amounts bunch below round limits; the statistic is the start of the review, not the alert.
The customers you want to find are the ones that distort the baseline, so the choice of mean or median decides who alerts.
The false positive rate says how noisy a monitoring system is. The detection rate says what it misses, and it can be estimated from SARs the bank already filed.
Enhanced due diligence asks for the source of wealth but not how to judge it. A year-by-year reconstruction gives a number a second reviewer can check.
A unit price test on an importer's shipments, the value that may have moved, and the mirror check against the exporter's own declaration.
Companion workbooks: /privatecredit
79 basis points of margin. The leverage covenant fails first, five basis points before the coverage covenant the chapter reports on, and 4.6 per cent of EBITDA is the whole cushion.
A worked unitranche: four coverage ratios for one borrower, the EBITDA cushion to a 1.10x covenant, and what a rate rise does to it.
The yield to three-year takeout worked on a direct loan, the five lives that change the answer, and OID against extra spread.
A worked first-out and last-out split: the formula, the sensitivity to size and price, and the loss the extra spread pays for.
A direct loan split into cash and paid-in-kind interest, worked quarter by quarter: the balance, the cash coupon, the leverage and the loss in default.
A direct lending fund at zero, one and two turns of leverage, worked from asset yield to net return, with the loss tolerance each turn gives up.
Yield by repayment year with and without a prepayment premium, the probability-weighted value, and what the premium actually compensates.
LTV, the equity cushion and the point at which a sponsor-backed loan starts to lose money, worked on one illustrative buyout.
A SOFR floor is a rate put the lender holds, and pricing it on the forward curve alone says it is worthless when it is not.
The borrower's all-in cost of one unitranche against a split first lien and second lien, with fees, agency costs and market flex priced on one illustrative buyout.
The ticking fee on a delayed draw term loan worked month by month, with the step-ups, the draw schedule and the lender's and borrower's reading of the result.
Default rate, recovery and the time it takes to collect: three inputs, and the one most loss rates leave out.
The regulatory leverage test of a business development company, worked from the balance sheet, with the markdown that breaks it and the borrowing it still allows.
The spread gap between a direct loan and a syndicated loan is a gross number; the premium an investor keeps is about half of it.
A recurring revenue loan is sized on ARR, but it is repaid from cash that the interest itself consumes, and the binding test is usually liquidity.
Adding loans removes the risk specific to each borrower, not the risk they share, and the second sets a floor no loan count can beat.
The covenant rarely stops a default. It puts the lender at the table early, and that is where the value is.
Lenders stress EBITDA as routine and check rates at today's print. Solving the covenant for the base rate shows how little room a levered floating-rate loan has.
Floating-rate loans pass every rate cut straight to the investor. How much of it lands depends less on leverage than on how the leverage is priced.
Weight each loan's rating factor by par, then read the result knowing that the factors climb steeply as credit quality falls.
Companion workbooks: /cbam
Carry and protection are both linear in the buffer, so the break-even probability is identical at 5 per cent and at 30 — and 2027 costs exactly twice 2026.
Embedded emissions minus the benchmark times the free allocation still retained, times the certificate price, year by year, and why the 2.5 per cent shortcut understates every year before 2034.
The annual mass threshold priced as a cliff: certificates on every tonne, a fixed cost of compliance, and the premium at which buying the last tonnes in the EU wins.
The Annex IV formula for a complex good is one line. The precursor carries almost all of the answer, and three easy errors take hundreds of tonnes off it.
For cement CBAM counts electricity too, and the clinker ratio does most of the work. Leaving out the indirect emissions under-declares almost a tenth.
CBAM ignores the smelter's electricity for aluminium, so a coal-powered and a hydro-powered profile declare the same figure. The product footprint is a different number.
For 2026 the price is fixed quarter by quarter and known before a single certificate can be bought. The quarter in which goods clear customs sets what they cost.
Fertilisers carry a two-level precursor chain and a gas 265 times stronger than CO2. Most of the result is decided upstream of the plant that ships the product.
For an electric arc furnace the carbon arrives in a dozen materials and leaves in three. The mass balance counts it at the door, not at the stack.
Hydrogen counts direct emissions only, so a reformer carries nearly nine tonnes a tonne and an electrolyser on a coal grid carries none.
The deduction follows the product benchmark, not the supplier's emissions, so every tonne above the benchmark is paid at the full certificate price from 2026.
The free allocation deduction does not grow with the emissions declared, so every tonne a default adds above actual data is a full certificate, and the mark-up grows each year.
Electricity is the CBAM good that pays in full from the first year. There is no free allocation to phase out, so the deduction that shrinks a steel bill in 2026 does not apply.
A surcharge clause that passes CBAM on to the buyer has to be invoiced before the certificate price is known, so it needs a formula, a provisional price and a true-up.
A supplier's carbon price reduces the certificates you surrender, but only after three haircuts, and never below zero.
How the Article 26 penalty is calculated, why it comes on top of the certificates, and why an under-declaration is costly from the first year.
A worked year-end for 2026 imports: the accrual on import, the CBAM left in closing stock, and the liability nobody has paid yet.
CBAM is paid on every tonne that crosses the border, including the offcuts that never reach the product. Standard costs built on the bill of materials miss them.
CBAM certificates cannot be bought forward, but their price follows EU ETS auctions, so the exposure can be hedged with allowance futures, imperfectly.
Companion workbooks: /coinvestment
0.019 turns under plain dilution, 0.285 under pay-to-play. The optimum is a property of the shareholders’ agreement, not of the portfolio.
Adverse selection and the fee saving are both real. The limit where one cancels the other is a number you can compute from the fund's own terms.
Fee savings arrive slowly and in small amounts; a write-off arrives at once. The ratio between them is a sizing rule.
Co-investment carry is charged vehicle by vehicle, with no netting of losers against winners, so the headline rate understates what the co-investor actually pays.
Late syndication at cost plus a carrying charge lowers the co-investor's multiple, yet often leaves its IRR above the fund's on the same deal.
A co-investment sold as no fee, no carry still pays the fees the sponsor charges the portfolio company, and unlike the fund's investors the co-investor gets none of them back.
The sponsor's model often shows equity before the management incentive plan, and the plan's structure, not its headline percentage, decides what the co-investor gives up.
Three scenarios, one expected multiple, and three different expected IRRs: which one belongs in the investment committee memo.
Four identical deals held once through a fund and once as co-investments: the interim IRR, the cash trough, and what a quarter of exposure in co-investments does to a programme.
The risk that matters is not losing money but doing worse than the fund you could have committed to, and it falls far more slowly with the deal count.
A co-investment is always a second helping of a company the investor already owns through the fund, so a single-name limit tested on the cheque alone is tested on the wrong number.
The break-even EBITDA of a leveraged co-investment, with debt paydown that shrinks as the business does, and why the exit multiple matters more than the downside case.
A co-investment budget is a deal-flow target in disguise: the funnel from offers to closed deals, the GP relationships it takes to fill it, and the team needed to review it.
Every co-investment carries a fixed bill for diligence, legal work, staff time and monitoring: the cheque size at which the fee and carry saving covers it, and the size at which it stops mattering.
Co-investment is sold on the fee saving. What a committee needs is its effect on the whole programme, weighted by the capital actually paid in.
Co-underwriting wins allocation and access. The bill arrives only when the sell-down fails, which is exactly when the deal is worth least.
A worked co-investment pacing model: deployment from a target NAV, the four-year ramp, and the cash the programme hands back once it is full.
Per-deal blockers tax every winner in full and give nothing back on the losers, which is why the co-investor's cost is higher than the fund's.
A GP offers a large LP either a management fee cut or priority on co-investments. Discount both to today and the answer turns on take-up, returns and deal selection.
A structured preferred offers a co-investor downside protection; the break-even against common equity is simpler than it looks.
Companion workbooks: /duediligence
Eighteen basis points is only the part that reaches the yield. Three of the four instruments never do, and the exercise is worth thirty-one.
A ten-year survey cost schedule turned into one price deduction, and why the items after your exit still come off your price.
Rent-free periods, stepped rents and an overstated rent, sorted into what is temporary and what is permanent, and priced accordingly.
The brochure yield is a set of conventions. Diligence replaces each with a verified figure, and the yield is where the replacements meet.
A Phase I flags a historic industrial use and the buyer has three weeks to exchange. The decision is an expected-value calculation, and the probability is the input nobody writes down.
The diligence budget for the deal you close is only part of the bill. The rest was spent on the deals you did not close, and it belongs in the same calculation.
The de minimis, the basket and the cap decide how much of what diligence finds can be recovered after completion, and each can be priced.
A retention tracks the actual cost of a defect found in diligence, so its size is a build-up, not a round number, and unused money goes back to the seller.
A share deal saves transfer tax but inherits an old tax base; the price turns on what that base costs over the buyer's hold, not on its face value.
A vendor's rent roll shows what a building can earn; diligence has to establish what it does earn, and which of the differences will last.
The rent proration is the small line; deposits, prepaid rent, the CAM reconciliation and unpaid leasing costs move more money at closing.
A default costs a void, a rent-free period and an early re-letting, capped by the lease expiry; priced that way, covenant risk is smaller and more specific than a yield add-on.
Fixtures in a commercial building carry tax relief to the buyer, but only if diligence secures the value before completion, and it is worth less than half its face amount.
VAT on a commercial property purchase is meant to be recoverable, but the stamp duty charged on it is not, and the funding gap costs money too.
A flood risk assessment gives return periods and damages; the price needs one number, built from the part insurance does not pay and the part the next buyer will deduct.
When the measured survey comes in below the particulars, the contracted rent does not move; the reviews, the re-lettings and the exit value do.
An unsettled review at sale is a bet on the tenant's surveyor. Price the odds, split the backdated rent and move the risk into a top-up clause.
The non-residential bands slice by slice, the shortcut, purchaser's costs, and the VAT and linked-purchase traps that change the figure at completion.
A restrictive covenant found in due diligence can be priced, insured or removed; the arithmetic says when the policy is the cheaper instrument, and what it must cover.
Under MEES an F or G unit is unlettable or an inherited compliance problem. Price the full cost of compliance, then gross it down for purchaser's costs.
Companion workbooks: /workout
463,000 euros of present value a month. No single error about enforcement, and no pair of errors, moves the indifference point from 58.7 cents to the 72 on the table.
The A note is the loan a market lender would hold today; the B note is an option on the building's recovery and should be valued as one.
The enforcement recovery a discounted payoff has to beat, built from forced-sale discount, costs, time and income, and the grid that sets the negotiating range.
Three present values and one division turn "extend and pretend" into a decision a credit committee can actually vote on.
Four haircuts, each simple, whose product takes a guarantee to about a third of its face.
Scenarios, probabilities and the effective rate: why the borrower's plan alone gives a provision of zero, and enforcement alone 33.18.
Same building, same timetable, two discount rates: the buyer's bid, the seller's hold value, and the gap that decides whether a loan sale clears.
A deed in lieu trades the guarantee and some cash for time and an orderly sale. Whether that trade pays is a present value calculation, not a matter of temperament.
Once the lender owns the building, the question changes from recovering a loan to running an equity investment, and the hurdle changes with it.
A workout that extends a loan and cuts its coupon changes the contractual cash flows, and IFRS 9 prices that change at the loan's original rate, not the market's.
A pay and accrual split restores cash coverage without conceding the contract rate; whether the lender has given anything away depends on the exit value.
The credit bid priced against the lender's REO plan, the guarantee on the deficiency and tax on the bid, with the outcome for every rival bid.
Two ways to enforce one defaulted loan, priced on the same basis, with a bridge of where the gap comes from and the liabilities that would close it.
A forced-sale discount is four separate things: a higher yield, a price chip, the costs of the process and the months it takes. Price each one.
A standstill while the borrower sells, priced against enforcing today: two branches, one probability, and the term that moves it most.
The same building priced two ways, with the forced-sale discount, costs, holding period and time value separated.
A protective advance priced as a decision: enforce the building as it stands, or fund the fit-out, wait for the letting and sell it stabilised.
The receiver's fee is on an invoice. The rent the borrower keeps and the value lost to unmanaged leases are not, and they are usually ten times larger.
The hedge sits in the same waterfall as the loan. Whether rates have fallen or risen since it was struck decides whether it takes from the recovery or adds to it.
Section 362(d)(3) prices a single-building Chapter 11 filing for the mortgage lender, and the base is the collateral value, not the claim.
Companion workbooks: /treasury
67.4567 per cent of the headroom, and it leaves at a fall in annual revenue of 8.4127 per cent — not the 13.3333 per cent the board deck implies.
One balance sheet, five correct answers, 214,000,000 down to 68,400,000 — and the definition alone is worth 0.3690 turns of leverage.
66,049,315 released, and leverage of 2.7622× or 3.1362× depending on which balance the test is asked of — the second is a breach at today's EBITDA.
Three components, 124,596,281 in total — and the double count that turns a margin of 27,403,719 into an apparent shortfall of -3,988,281.
An annualised 14.8980 per cent against a revolver at 4.50 per cent — worth 5,471,890 a year, and 0.3132 turns of reported leverage.
78.1818 per cent of gross debt fixed, and a net floating exposure after cash of -608,000.00 — the proportion, not the instrument.
A loss of 8,130,844.04 against spot, and the hedge did exactly what it was for — the break-even is the forward, not the spot.
361,824.00 between the best and worst yield, and 93,204,281.16 of the surplus already spoken for.
Nineteen lines, each with the covenant or limit it is measured against — and 27,403,718.84 without the revolver on every one of them.
Five subsidiary accounts priced on their own, swept into a physical pool and combined in a notional one, with who keeps the saving and why net cash is the wrong base.
Days cash on hand worked on one illustrative group, with the denominator built properly and the numerator read four ways, from reported cash to cash treasury can spend.
Withholding tax against the rate spread, worked on one subsidiary, and why waiting rarely avoids the tax.
A direct weekly forecast for one quarter, worked line by line, with the buffer for forecast error that a monthly view never shows.
Four subsidiaries, twelve intercompany payments a month, and the arithmetic that shows which part of the saving is real.
Two currency exposures, their volatilities and one correlation: the variance-covariance calculation a treasurer can defend, and the hedge ratio it points to.
The overlap cost of refinancing early, worked through, and the rise in yield it insures against.
An earnings credit pays bank fees, not interest, so the question is how much balance to leave in the analysed account and where the rest should sit.
The paper still needs the revolver behind it, and the commitment fee on the undrawn backstop takes most of the headline saving.
A rolling programme buys an average of forward rates, not a better rate. The worked case shows what that average costs and what it smooths.
Value the float at the company's own rate, cost the lockbox net of the work it removes, and decide cheque by cheque.
Companion workbooks: /abf
Base loss 2.4 per cent, downside 6.0 and transition 1.5: the advance rate lands at 88 per cent and 12 per cent enhancement.
Companion workbooks: /aifmd
A semi-liquid credit fund's reverse stress level, computed: 17.2 per cent of net asset value against a 4 per cent gate.
Fifteen points of headroom sound comfortable. A markdown shrinks NAV faster than exposure, so the cap arrives sooner than the ratio suggests.
The 50 per cent limb of the AIFMD II definition, computed on a levered credit fund, and the three ordinary events that carry it across the line.
Same fund, same day, three leverage figures. The forwards, the cash and the subscription line explain every point between them.
The concentration limit for loans to financial undertakings, AIFs and UCITS uses its own base, and it is neither NAV nor gross assets.
Loan by loan the retention is small. Across a fund that keeps transferring loans it originated, it builds into a sixth of the fund, held for as long as the loans run.
The AIFMD sub-threshold test adds up the assets of every AIF a manager runs, and one open-ended or leveraged fund changes the limit for all of them.
The anti-dilution levy charges the cost of liquidity to the investor whose transaction causes it, and it has to be calibrated, not picked.
The buckets are shares of gross assets, investors' claims are on NAV, and the credit facility sits between the two.
Three tests and an add-on: for most mid-sized managers the fixed overheads test binds, and assets under management cost nothing extra until several billion.
The redemption coverage ratio sets the liquidity a fund can raise by each payment date against what investors can ask for by then, and it shows which liquidity tool actually closes a gap.
One impaired loan, one redemption day, the fund run twice: with and without a side pocket, and what AIFMD II says about the tool.
A redemption gate is only a liquidity management tool if the fund can actually pay the gated amount every dealing date of a run, so the calibration is a multi-quarter cash projection, not a one-quarter liquidity profile.
Redemption in kind is the one liquidity management tool that removes the redemption from the fund's liquidity problem altogether, provided the slice is genuinely pro rata and the rounding does not quietly turn it back into cash.
A notice period sized on whether the fund can pay is too short. Sized on what the remaining investors are left holding, it is more than three times longer.
Dual pricing charges every dealing investor the full cost of trading, whether or not the fund trades. That makes it the most protective tool for the investors who stay, and the dearest for those who deal.
AIFMD II lists the redemption fee among the liquidity tools but does not say how to set the range. The fund's own liquidity slices do.
Two AIFMD II anti-dilution tools calibrated to the same cost of liquidity, compared on one-way and two-way dealing days.
The carve-out for borrowing covered by uncalled commitments is generous at launch and can quietly stop applying as capital is called.
The leverage cap is the obvious cost of running a loan-originating AIF open-ended, and the smallest part of it.
Companion workbooks: /alts
A net IRR of 13.2935 per cent, a sleeve return of 6.2571, and a 2.9307-point treasury decision nobody minuted.
A beta-adjusted public market equivalent worked year by year, with the beta at which the fund stops beating the market.
The three fund multiples computed from one call and distribution schedule, with the DPI path year by year and what a write-down of the residual does.
The Yale model in four formulas, run year by year on a 100 commitment, and the one input that quietly sets the IRR.
Two and twenty in money, on one commitment, and why the answer depends entirely on the denominator.
The seller's side of a secondary sale, measured on the allocation that has been working for a decade.
Turn the benchmark into a multiple over the fund's own effective holding period, and the question of a good TVPI gets a number instead of a rule of thumb.
One fund's distributions shifted in time with the calls held fixed: the IRR, the peak capital out and the PME move, the multiple does not.
Reported private fund returns are valuations that lag prices; measure the lag, reverse it, and the beta that enters the allocation model changes far more than the diversification.
One chain-links the years and ignores the money; the other weights every year by the capital exposed, and in a private fund the manager decides that.
A private fund's money goes in and comes out over a decade, so the inflation that matters is the inflation suffered while each dollar was invested.
The modified IRR on a fund's own call and distribution schedule, and why it can reverse a ranking that the IRR gets wrong.
How to measure how long a fund actually holds the investor's money, and the shortcut that turns any multiple into an IRR.
Three spending rules run through the same crash on an illustrative endowment with 30 per cent in private equity, and what smoothing the payout does to the liquid assets that have to fund it.
Two and twenty sounds like a quarter of the return at most. Worked backwards from the net, it is a third in one year and nearly half over ten.
The same high-water mark and the same 20 per cent fee, crystallised four times a year instead of once, on one illustrative path.
No management fee sounds cheaper. But the platform and the winning managers are paid before the investor, whatever the fund returns.
Smoothed monthly returns make volatility look lower than it is, and the square-root-of-12 rule turns that into a Sharpe ratio the fund never earned. Lo's correction puts it back.
The management fee keeps running on the way back, so the recovery takes longer than the loss suggests, and the fee-free years are worth real money to the investors who stayed.
Companion workbooks: /ardennes
The commission on a EUR 385,225,000 placement was 13.50 per cent of what it cost. The other 86.50 per cent was uninvoiced.
No existing bond ever sits at the new maturity, so the concession is a measurement made with a chosen ruler, and four common rulers disagree by five basis points.
The reoffer spread is what investors earn. The issuer pays that plus its fees and expenses, spread over the life of the bond at the annuity factor, not by the number of years.
The yield is priced, the coupon is rounded, and the reoffer price is whatever reconciles the two, which is why the coupon tells you nothing about the cost.
A dollar coupon 86 basis points above the euro yield turns out to be 32 basis points cheaper: the cross-currency comparison, step by step.
One accelerated placement, four reference prices, four discounts: what the choice of denominator is worth in euros.
One basis point turned into euros on a seven-year new issue, three ways, and why the years-times-notional shortcut overstates it by a sixth.
Ownership dilution and value dilution worked on one accelerated placing, with the holder who could not participate and the one who could.
The theoretical ex-rights price, the value of a nil-paid right and the holder who does nothing, worked on one illustrative rights issue.
The make-whole redemption price worked on one euro bond, with the premium over the market price and the refinancing test it almost always fails.
A worked tap of a seven-year euro bond: ACT/ACT ICMA step by step, the clean and dirty price, the cash the issuer receives, and what the other day counts would have charged.
One new seven-year euro bond measured against swaps and against government bonds, with the interpolation, the swap spread that links them and why the choice of reference moves the number.
Bootstrap the zero curve from par swap rates, discount each cash flow at its own zero rate plus a single spread, and solve: why it differs from the I-spread, and when the gap matters.
The over-allotment, the short it creates and the two ways to close it, worked through three aftermarket outcomes, with what the banks earn and what the issuer gives up.
Fair value from the issuer's own curve, the concession a conventional deal would have paid, and the framework costs that come off the saving.
Gross spread, expenses and money left on the table, split between the company and the selling shareholders, and restated in shares given away.
Conversion price, parity, bond floor and the volatility the issuer is really selling, worked on one illustrative five-year deal.
A buyback below par always shows a gain on extinguishment; whether it creates value depends on the tender yield and what the cash costs.
The coupon is already fixed, so the price does the adjusting, and the accrued interest investors pay in is not money the issuer keeps.
The spread divides into three parts, and each part is shared among the banks on a different key.
Companion workbooks: /bizval
Three methods, 18,480,000 apart on one company. Back each into the model and the entire gap is 1.96 points of growth.
A terminal value worth three-quarters of the answer is usually arithmetic, not a defect, and the share can be predicted before a single cash flow is typed.
Half a year of discounting looks like a detail, but applied to the terminal value it is worth more than most arguments about the cost of capital.
Four inputs, one relevering step and target weights produce the discount rate, and each of the usual shortcuts moves the value by five to twenty per cent.
One forecast year built from EBIT and from EBITDA, then the five usual errors, each priced in enterprise value.
The premium measured against the right reference price, then turned into the permanent cash flow the buyer must add to justify it.
A single-period valuation of an illustrative debt-free company, built from EBITDA to cash flow and from the build-up rate to the cap rate.
From a 600,000,000 DCF equity value to a diluted value per share, with three option tranches and restricted stock units.
The minority discount is the control premium read backwards, and it compounds with the marketability discount rather than adding to it.
The last twelve months is the basis most EBITDA multiples are quoted on. The formula is simple; the adjustments and the shortcuts around it are where value moves.
Tangible assets at fair value, a fair return on each, and the excess capitalised as goodwill, then the cross-check that tells you whether the rate on the excess holds.
Growth has to be paid for with reinvestment. The value driver formula makes the return on that reinvestment explicit, and shows what the plain Gordon growth model assumes about it.
Five illustrative peers, one outlier, and the drop-one test that shows how fragile a small comparable set really is.
A two-way data table on an illustrative five-year DCF, built step by step in Excel, and the diagonal that shows which cells are really different views.
A levered DCF and an unlevered DCF must land on the same equity value. Here is the FCFE build, the reconciliation to the cent, and the three ways it goes wrong.
A sum-of-the-parts adds segment values, but most of the work is in what comes after the addition. A three-segment worked example, and the two omissions that double the apparent discount.
A DCF dated inside the financial year, worked line by line, and what the two common shortcuts cost.
Tax losses save tax only as the business earns enough to use them, so their value is a discounted schedule, and an acquisition can stretch that schedule by years.
A weighted conclusion of value is only as good as the basis of the numbers going into it. Strip the control premium out first, then choose the weights on purpose.
Off-calendar peers report years that straddle two calendar years; weight them by months before a single multiple is computed.
Companion workbooks: /buffer
A 40.8 million additional tier 1 shortfall takes 13.6 basis points out of the buffer: headroom is 2.8432 per cent, not 2.9796.
The CRR3 loan-splitting rule on one loan and on a 21.0 billion book, band by band and on the average loan, and why the two disagree by 248.5 basis points.
A worked European bank: the buffer level by level, the outflows line by line, and the 51 points that separate the ratio from the figure that circulates.
Two weighted sums and a division. The work is in the factors, and in the two drifts that are each harmless alone.
The floor is one comparison per year, made on the whole bank. The year it binds is a result of two ladders, and after it binds lower internal weights buy nothing.
The ratio is one division. The useful number is the density of risk-weighted assets below which the backstop, not the risk-based trigger, becomes the constraint.
The formula is a lookup. The work is in measuring how much CET1 actually sits in the buffer once every other requirement has taken its share.
The institution-specific rate is a weighted average. The weights follow risk-weighted assets, not lending, and the result applies to the whole risk exposure amount.
Equity of 5,180 becomes 3,511.9 of common equity tier 1. The ratio is the easy part; the deductions are where the 1,668.1 goes.
Two bases, two readings of one charge, and a buffer that sits on top of the requirement but must never be counted twice.
The standardised approach for operational risk worked line by line, from the profit and loss account to RWA, with the loss multiplier and the four errors that move the answer most.
The large exposures test worked on one group of connected clients, with the conversion factors, the collateral, and the capital base that turns a breach into false headroom.
Under the standardised approach, risk-weighted assets are a sumproduct of exposures and regulatory weights, but the answer turns on three details that are easy to skip: the credit conversion factor, the mortgage split and the defaulted book.
A bank's lending capacity is not its capital ratio but its surplus over the ratio it intends to hold, divided by what each loan consumes, and below a certain risk weight the leverage ratio takes over.
The standardised approach for counterparty credit risk in one netting set, from supervisory duration to the multiplier, and why netting cuts the exposure by more than half.
A tier 2 bond loses eligibility a little every day for five years before it matures, and once the tier 2 slot runs short the gap is filled with common equity that would otherwise sit in the buffer.
Credit conversion factors applied to a revolving facility, Basel II against the Basel III standardised approach, and the commitment fee the capital implies.
The caps are shares of the capped total, so they bind on Level 1, and a euro of Level 2 above the line counts for nothing.
The LCR denominator built line by line from Basel run-off and inflow rates, and why 30-day wholesale funding lowers the ratio even when held as reserves.
The IRB expected loss versus provisions comparison, worked on performing and defaulted books, with the 0.6 per cent Tier 2 cap on any surplus.
Companion workbooks: /cfh
Blind-pool terms cost a rolling investor about €400,000 on a €5 million position — eight points of net multiple.
Companion workbooks: /closing
€1.30 million a year of ordinary accounting entries removes €6.60 million of a €12.0 million earn-out.
The ticker is the seller's only payment for the cash the business generates after the box date, and the usual rate pays for two thirds of it.
The peg is one number in the purchase agreement, and on a seasonal business the choice of that number decides more of the price than the business does.
The two-step price of a completion accounts deal worked line by line: the estimate paid at closing, the final accounts, the true-up, and where the money moves.
The same deal priced both ways, reduced to one line: what the business earns between box and completion against the ticker and the definitions the buyer wins.
Classify, gross up, measure related-party payments at arm's length, deduct: and why the definition decides more than the arithmetic.
At the seller's projection every earn-out shape pays in full, so the shape can only be priced on the range of outcomes around it.
The multiple gets the attention, but the definition of debt in the share purchase agreement moves the price for the shares one euro at a time.
An escrow and a buy-side warranty and indemnity policy priced side by side on one illustrative sale, with the seller's return that makes them equal.
One illustrative sale taken from the announced price to the cash in the seller's account, and then to what the later consideration is worth today.
The same completion balance sheet run through four price adjustment mechanisms: pound for pound, a de minimis, a collar and a capped collar, with the asymmetric version buyers ask for.
From the cash on the completion balance sheet to the free cash the buyer pays for, with minimum operating cash measured from the intra-month trough rather than asserted.
The percentage of proceeds a seller rolls is not the percentage of the new company it owns, and the difference is the leverage.
Between signing and completion the seller's price is fixed and the buyer's is not; here is what it costs to fix it without betting on the deal closing.
A catch-up turns a missed year into a timing difference. Whether the seller gets it, and how it is drafted, can be worth more than the headline rate of the earn-out.
An earn-out closes a price gap only because buyer and seller value it differently. The sizing is the search for a clause where that difference exceeds the gap between the two sides' limits, with room to spare.
Customers paid in advance, the cash went into the cash-free debt-free count, and the buyer has to deliver the service. Who pays for it depends on one question: will those prepayments keep coming?
A defined benefit deficit is a debt-like item, but which deficit, and whether tax relief comes off, can move the equity price by more than a turn of EBITDA.
Taking away the upside of a working capital adjustment is not protection for the buyer; it is an option the seller writes for free.
Banker fees, deal bonuses and financing write-offs are deductible, and the drafting of the tax liability decides whether the seller or the buyer keeps the saving.
Companion workbooks: /cmbs
Marlowe Tower sold at a 25.90 per cent shortfall; the trust wrote off 37.24 per cent. Where the 11.34 points go.
The cushion is collateral value, not points, and a defaulted loan uses it up at the haircut rather than at par.
Subordination class by class, how sequential paydown builds it and realised losses erode it, and what it means in pool defaults.
The first-loss classes are bought on a loss scenario, not a spread, and moving the losses three years earlier costs almost as much as an extra point of loss.
Retained CRE CLO equity is five times the excess spread against five times the losses, and the best advance rate depends on which of the two you expect.
One remittance month on an illustrative $1,000M conduit, followed dollar by dollar from the loans to the bonds.
Vertical, horizontal and L-shaped retention on an illustrative $1,000M conduit, and why the horizontal piece is far thicker than 5 per cent of the deal.
The fee schedule decides what the special servicer earns on each resolution. Discounted, the two paths pay almost the same, and the break-even sits at a recovery of 73 per cent.
The IC test is the overcollateralisation test's quieter twin. It rarely trips first, and rising rates push it down even when no loan has defaulted.
A conduit pool barely amortises, so the senior classes are told apart by when they are paid, and WAL measures it.
An IO class has no principal: it owns the excess interest the loans pay over the bonds, and it shrinks as the deal pays down.
Balance-weighted DSCR, LTV and debt yield from a loan tape, why they differ from the pool's aggregate ratios, and the tail the average hides.
The forward recoverability test worked month by month on a defaulted loan, with and without an appraisal reduction, and what it means for the bonds.
The loan Herfindahl turns a pool's size distribution into an effective number of equal loans, and it falls further than the loan count as a deal pays down.
The blended note spread is a balance-weighted average, and it rises as the cheap senior class pays down, while the equity loses more to the fall in leverage than to the rise in spread.
One loan, one property, and a capital structure cut at the debt yields the rating agencies require on their own cash flow.
The CLO costs more per dollar of loans and still wins, through leverage and the margin call it never makes.
A prepayment ends two claims on the loan's coupon, the principal classes' and the IO strip's, and the base interest fraction splits the penalty between them.
The cap turns a fixed-rate bond into a bet on which loans stay in the pool, and the bondholder only ever loses that bet.
Equal-priority notes share interest, principal and losses by balance, but only one trust controls the workout.
Companion workbooks: /compliance
59 clean allocations prove an error rate below five per cent; twenty prove only fourteen.
A year of shared deals between a flagship and a newer fund: the aggregate test that passes, the deal-by-deal test that does not, and the gain that moved.
Attribute sampling when the sample is not clean: the upper error bound, the ladder of sample sizes, and why two out of 59 is not 3.4 per cent.
Gross to net for a private fund performance page, with a high-water mark, two share classes and the shortcuts that overstate the result.
The remedy for a fee error is the money back with interest, allocated to the investors who paid; each of the four choices behind the figure can be challenged.
Each grey-zone cost is too small to argue about on its own. Added up over the fund's life and set against the management fee, they become an undisclosed fee rate.
For a private fund adviser, regulatory assets under management are gross, not net, and include capital investors have committed but not yet paid in.
The SEC pay-to-play rule is a two-year fee holiday, so the price of one political cheque is every fee the government investor pays, multiplied by the months left.
The Rule 501(a)(5) net worth test worked line by line for one investor, with the primary residence, the mortgage and the 60-day look-back that onboarding files most often get wrong.
Lowest-in, highest-out matching worked trade by trade for a director of a listed portfolio company, and what it means for pre-clearance.
The benefit plan investor test worked on one fund's investor list, with the partial count for feeders, the exclusion that raises the percentage, and the size of the cure.
The Rule 13d-3 percentage worked across two funds and a separate account, with the 60-day rule, the share count that moves on its own, and the errors that hide a filing.
The qualified purchaser test looks like a wealth test and is not one: it counts only assets held for investment, at market value or cost, less the debt incurred to acquire them, against 5,000,000.
The 3(c)(1) limit counts beneficial owners, not names on the register, and two look-through rules can put a fund well over 100 while its investor list shows 80.
The test runs on twelve month-ends, not four quarter-ends, and a private equity adviser can cross it the year a portfolio company lists without ever trading a share.
A private fund can buy IPO shares for its whole capital only if restricted persons own no more than 10 per cent of it. Above that, the new issue profit has to be carved out, and the count of who is restricted decides everything.
The arithmetic of a trade error is simple. The netting policy decides how much the adviser pays, and it is what a reviewer tests.
The arithmetic is one line. The contested input is the post-disclosure price, and it moves the exposure by over a million.
Pro rata to the pre-trade order, rounded to the increment, one average price: and the minimum-piece rule and fill sequence that quietly move money.
The measure runs from the short sale prices, not from the allocation discount, so it is usually far larger than the trade looked on the desk.
Companion workbooks: /covenant
The add-back bridge is worth 1.6866 turns of leverage; the 4.25x covenant leaves 0.0336 of a turn. A ratio of 50.3.
One borrower, one soft year, and the two multipliers between the top line and the cash that services the debt.
A worked loan: recovery on the downside EBITDA, expected loss against the margin, and the exit multiple that decides the price.
Debt capacity is two calculations, a multiple of EBITDA and a multiple of cash, and the answer is whichever is lower on the number the lender believes.
One balance sheet, four leverage ratios, and the IFRS 16 mismatch that makes a 3.86x credit look like 3.21x.
A term loan and a part-drawn revolver: exposure with a conversion factor, a recovery built from the default case, and the shortcut that compounds two errors.
Five readings of interest cover for one borrower and one year, the rate and the EBITDA fall that break the covenant, and what a good ratio actually means.
Funds from operations built top down and bottom up, adjusted debt with leases, pension and trapped cash, and what a borrower must do to reach a target ratio.
The three versions of the Altman Z-score worked on one private borrower, with the cut-offs that go with each and the ratio that quietly carries the score.
Leverage in turns of EBITDA is not a repayment period. The years come from cash after interest, compounded as the debt falls, and they are more than twice the multiple.
Sources and uses, the target's full twelve months, the synergy line kept separate, and why a debt-funded bolt-on at 8.0x levers up a borrower at 3.33x.
Depreciation, the sales-growth method and replacement cost on one borrower, and what each does to cover and cash leverage.
The room a covenant reset buys, the fee and margin ratchet as actually collected, what the step-up does to the covenant nobody reset, and the recovery the lender gives up by waiting.
Net debt to equity, debt to capital and tangible gearing, worked on two borrowers, and why the balance sheet ratio and the leverage multiple can rank the same credits in opposite order.
Margin, fees, funding, costs, expected loss and the capital benefit in one ratio, then solved backwards for the minimum margin.
The formula worked step by step for a private borrower, the listed-company version, and why the EBITDA definition moves the answer most.
A weighted scorecard in the shape agencies use, run on a fictional borrower, and why one soft year moves it a full category.
Twelve months of cash flow, working capital from its drivers, two stresses that hit the trough in different ways, and what the headroom costs.
Capitalising rent with a multiple or with the IFRS 16 lease liability, why the two differ by the remaining lease term, and the double count that mixes them.
The M-score does not prove manipulation, but it tells a lender which lines of a borrower's earnings to test first.
Companion workbooks: /credit
A 50 basis point MFN steps the margin from E + 550 to E + 700 and pays existing lenders €2.06 million a year.
The same breach costs the sponsor 5.50 times more when the agreement says the cure must repay debt.
The definition deducts the cash actually spent; the leverage grid then decides how much of what is left goes to the lenders.
Headroom in EBITDA, in debt and in turns, why they are three different numbers, and what add-backs, cash and a step-down do to each.
A five-step leverage grid run quarter by quarter, with the opening margin, the 45-day certificate lag and the boundary that decides a full step.
Free-and-clear, the ratio basket and the one sentence on concurrent incurrence, run on a borrower at 4.00x, then run again with add-backs.
Counted usage, the threshold, the letter of credit carve-out and the quarter-end repayment, worked over four quarters of a covenant-lite facility.
Sizing debt, investment and payment baskets at the greater of a fixed amount and a percentage of EBITDA, what add-backs do to them, and what happens when EBITDA falls.
The commitment fee, the utilisation fee and the day count worked on one quarter of a revolver, with the readings of the clause that get the invoice wrong.
The builder basket, or Available Amount, worked over three years of net income, with the three readings of the 50 per cent clause and the leverage condition that usually binds first.
The add-back cap worked on both drafting bases, and why a percentage cap makes covenant headroom smaller than the compliance certificate shows.
An amend and extend split into the extended tranche and the stub, with the fee and margin uplift taken out of the same cash, and the refusal rate at which it fails.
The standard break costs clause, worked on a mid-period prepayment of a EURIBOR loan: the formula, the zero floor, the margin trap, and why waiting for the period end usually costs more.
The proviso in the definition of net debt that decides whether a cash pile counts as covenant headroom, worked on one borrower: the ratio, the headroom, and what the borrower should do with the excess.
Defaulting lenders, sponsor affiliates and snooze and lose all shrink the voting base, and with it the stake that blocks an amendment.
Lookback, observation shift, weekend and holiday weights, and why the margin is added after compounding rather than inside it.
The asset sale sweep turns on four defined terms: Net Proceeds, the reinvestment right, the step-down and the sharing with other first lien debt.
The dedicated basket is a floor: general investments, the builder basket and the J.Crew trapdoor decide how much can leave the credit group.
Discount the margin saved over the loan's expected life, not its maturity, then price the option of waiting for the soft call to fall away.
Direct order, inverse order and pro rata application of the same prepayment, with the effect on near-term debt service, cover ratios, average life and interest.
Companion workbooks: /datacenter
Turnkey yields 10.86 per cent on cost, a powered shell 10.22 per cent, on one 180 MW site, for $1,980 million against $900 million
A twelve-month energisation slip costs 399 basis points of levered return; an eight per cent rent miss costs 257.
A data centre sells IT kilowatts but buys facility kilowatts, and the hottest hour of the year decides how many it can sell.
One point of escalator priced as starting rent, for the owner who holds to expiry and for the developer who sells at year seven.
The same tariff and the same peak cost a flat data centre load a third of what they cost a peaky one, until a ratchet sets the bill.
A near-fourfold multiple on the winners says nothing until it is set against the share of sites that ever get their power.
A line-by-line build-up of cost per MW, and why the same building can be quoted at three different prices.
Data centres lease power, not floor area, so a per-square-foot rent only means something once you know the density behind it.
Annual consumption is capacity times three factors: how much of it runs, how much the building adds on top, and how many hours there are in a year.
The division is trivial; the money is in what happens when the racks a tenant installs are not the density the hall was designed for.
Data centre water use is one multiplication, but the answer moves by a factor of thirty with the cooling design, and the water saved on site is partly spent again at the power station.
A financial PPA settles on the generator's output and price, while the data centre pays for its own load; the gap between the two is the real price.
Behind-the-meter generation is priced on the energy the campus uses, and the redundant engines are paid for whether they run or not.
Rent, power and NOI per megawatt, and why the same building can show a 94.8 or a 65.7 per cent margin.
A year-by-year equity cash flow for a pre-let turnkey campus, and the inputs that move the answer most.
Rules of thumb for acres per MW hide four inputs. Change two of them and the answer halves.
Size the tanks on the load the generators actually carry, cooling included, and the 48 hours turn into a logistics question as much as a storage one.
Phasing costs more per megawatt and pays it back in deferred capex, avoided idle carry and an option not to build. Absorption speed decides which wins.
The conversion from megawatts to tons is a constant. The installed plant is not: it depends on which heat counts, the design-day derate and the redundancy the tenant buys.
Tenants lease megawatts, utilities and transformers are rated in MVA, and the gap between them is where site models go wrong.
Companion workbooks: /deal
Treating 4,150,000 of operating leases as debt moves year-one accretion 4.1351 points. Both legs of that treatment are wrong.
The shortcut capitalises the run rate from day one and charges nothing for getting there. Timed and paid for, the same synergies are worth a fifth less.
The sign of the answer is decided by one comparison per funding source: the target's earnings yield after amortisation against the cost of the money.
Goodwill is the residual of the purchase price allocation, and the deferred tax on the fair value step-ups is the line most often left out.
The earn-out formula applied to each outcome, weighted and discounted, with the shortcut that misprices it by 8.3 per cent and the remeasurement that follows.
The ratio, the shares issued and the ownership split, then what a fixed ratio, a fixed value and a collar do when the acquirer's stock falls before closing.
One illustrative 180,000,000 acquisition, measured on what the acquirer actually paid rather than on the target's own balance sheet.
Break-even synergies for an illustrative 660,000,000 acquisition, under stock, debt and mixed funding.
Contribution analysis says what each side brings to a stock merger. On EBITDA it only means something once each company's net debt has been taken out.
An asset deal gives the buyer a stepped-up tax basis. What it is worth depends on how fast the deductions arrive and what the structure costs the seller.
The spread, its annualised return, and the completion probability the market price implies, for a cash deal and a hedged stock deal.
From the offer price to the enterprise value paid, through diluted shares at the offer and every claim the buyer takes on, then the five multiples one deal can report.
A tiered success fee, worked tier by tier, and the one sentence in the engagement letter that moves it by a quarter.
One fee, four bases, and the band of rival bids it quietly removes from the auction.
A mixed offer is a fixed amount of cash plus a floating amount of stock. The value per share, the premium, the dilution, and what proration does to holders who elect cash.
The break-even is the same either way: synergies equal to the premium. What the method of payment changes is who wins above it and who loses below it.
IFRS 3 offers two measurements of the minority's stake, partial and full goodwill. The acquirer's own goodwill is the same either way; what changes is the balance sheet, the impairment and the enterprise value.
The buyer takes the EBITDA. The seller keeps the people, systems and floor space the overhead charge paid for, and the multiple it really sold at falls.
Deferred consideration is a zero-coupon loan from seller to buyer: price it at the buyer's credit, then carry the unwinding into the buyer's earnings.
The multi-period excess earnings method for a purchase price allocation, with the contributory asset charges and the tax amortisation benefit worked line by line.
Companion workbooks: /development
16,000 a year of rent conceded shows as 145,727 in the appraisal and costs 278,261 in the price — 1.91 times.
The residual is not the land price: the land has to carry its own purchase costs and its own interest, and the appraisal is far more sensitive than it looks.
The half-the-cost-for-half-the-time rule is roughly right for the build and wrong for the scheme, because the loan is at its largest after construction ends.
Profit on cost measures margin with no clock attached. Lay the appraisal out as a quarterly cash flow and the same hurdle gives very different returns.
Two ratios for the same developer's profit, the exact conversion, and what the denominator does to a residual land bid.
Single-variable tests, the break-even of each, and a two-way table, on an illustrative £52,000,000 residential scheme.
Gross development value built from an accommodation schedule and an investment valuation, with the checks a lender's valuer runs first.
Loan to cost and loan to gross development value tested on one illustrative scheme, with the equity solved through the rolled-up interest.
Each affordable home loses sales revenue but also needs less profit and no marketing: net, the land value falls by a fixed amount per unit that the appraisal can measure.
The net-to-gross ratio is a design number that behaves like a financial one: a few points of core and circulation can move the land bid by a third.
Peak funding is the highest point of cumulative cost plus rolled-up interest less sales receipts, and on a phased scheme it is set by when sales start, not by how much the scheme costs.
An unconditional price has to carry the planning risk; a conditional contract moves it to the landowner, and the gap between the two headline prices is far wider than the gap in what the landowner can expect.
The bigger profit comes with the developer's own equity and finance; the right comparison is the return on that equity, not the two margins.
Overage shares the value a better planning consent adds to land; how the clause measures that value decides whether the payment is fair or ruinous.
The Community Infrastructure Levy charges gross internal area, credits floorspace in lawful use, and indexes the rate: each step moves the bill by six figures.
One takes a discount off a valuation, the other a share of an open-market price after costs: compare them on the same base before you sign either.
Slower sales after completion barely dent the profit margin. They do real damage to the IRR, and that changes whether a price cut is worth making.
Take a share of the value the strip unlocks, then cap it with the cost of getting round it.
Price a main contractor failure at each stage of the build, and the 10 per cent bond turns out to be short exactly when failure is most likely.
The review shares the upside of a scheme consented below the affordable housing target, and it never shares the downside.
Companion workbooks: /esg
€1.1 million of delivered EBITDA at 8.5× is €9.4 million of enterprise value, against €830,000 of cost.
The PCAF attribution factor worked on a four-company buyout portfolio, and why the ownership share overstates a leveraged fund's footprint.
Building a marginal abatement cost curve for a portfolio company, and the two shortcuts that rank the actions wrongly.
The metric investors ask for is easy to compute and easy to move without cutting a tonne: here is the calculation, and what it does and does not measure.
The 1.5 degree pathway is linear, not compound, and once the company grows, the intensity it implies has to fall far faster than the absolute number.
Same electricity, two correct answers 38.6 per cent apart. The difference is contracts, not physics, and the residual mix is where most market-based figures go wrong.
Injury rates for each company and for the portfolio, and why averaging the rates understates the result.
Stationary combustion, fleet fuel and refrigerant leaks for one portfolio company, with the factor errors that move the total most.
A worked Scope 3 estimate for one portfolio company: which spend goes in, how the factors are applied, and the two adjustments most first attempts miss.
The unadjusted gap for one portfolio company, worked from hourly pay by band, then rolled up to the fund's SFDR principal adverse impact figure.
The division is trivial; the denominator, acquisitions and how a fund adds companies together decide whether two turnover figures can be compared.
Alignment needs eligibility, substantial contribution, no significant harm and minimum safeguards at each company, then a value-weighted sum at the fund, and a single finding can move it by most of its value.
A shadow carbon price is not a cash cost. Run through the hold and the exit multiple, it is a valuation adjustment, and the test of whether a decarbonisation plan is worth its capex.
The distance-based method for Scope 3 category 6, flight by cabin class, rail, car and hotel nights, and the method choices that can move the total by as much as half.
Pricing the ESG margin ratchet on a portfolio company's term loan: the saving, the tax, the cost of proving the KPIs and the size at which it pays.
The distance-based method for Scope 3 transport, worked lane by lane for an illustrative portfolio company, with the two levers that cut a quarter of it.
The fund's PCAF score is one weighted average. Which holdings you upgrade to improve it decides whether the carbon figure gets any more reliable.
In a buy-and-build, every add-on moves the baseline. Skip the recalculation and a group close to its trajectory shows a 15.8 per cent rise, or a disposal makes it look 20.0 per cent better.
Avoided emissions are a counterfactual, and every input is a choice. The worked case shows each choice and why the result sits next to Scope 1 to 3, never inside them.
The cost, the payout per employee and the improvement needed to pay for it, worked on one illustrative buyout.
Companion workbooks: /estate
The promote peaks at 2,993,873 at 65 per cent gearing and falls to 2,876,129 at 70, while the equity return still rises.
A reversionary building has two easy yields and neither describes it; the equivalent yield weights each rent by when it arrives, and averaging gets it wrong by over a million.
A step-by-step return bridge gives a different answer for every order the drivers are switched on in, and the person drawing it chooses the order.
The IRR function is one cell; what decides the answer is the column before it: purchase costs, the void, the sale on the forward year's NOI and the timing convention.
Cap rate plus growth is an exact identity for a frictionless asset sold on its entry yield, and a ceiling for every real one.
A lease expiry is a dated, lumpy cost: price the void, the empty-property costs and the fees, weight them by the chance the tenant stays, and put the result in the year it lands.
A two-number screen that ignores the two numbers that decide value, and the one-line formula that converts it into a cap rate.
Goal Seek the growth rate, then bridge the gap to the rule of thumb: costs, capex and a wider exit each have to be earned back.
NPV answers the question IRR dodges: how much value, in money, the deal creates at the return you require. The arithmetic is short; the Excel trap is in the first cell.
Two ways of slicing the same income, horizontally or vertically: the gap between them is never the method, only the yields typed into each slice.
Why the expansion in an exit assumption must be measured from the stabilised entry yield, not the headline one, and what 25 basis points does to the IRR.
The four YP factors valuers use, perpetuity, fixed term, deferred and quarterly in advance, worked on one rent, with the error each one prevents.
Rent paid on the quarter days, in advance, earns more than the yield a valuer quotes. Here is the conversion, and what it is worth in a bid.
The sale price catches up with the money paid in after a few years. The return never quite does, and the gap is larger than spreading the costs over the hold suggests.
Vendors offer to top up missing rent so empty space can be priced as if let. The guarantee rarely covers the rent-free, the holding costs and the fees.
A flat ground rent is a bond and a geared one is a share of the building's rent for a century: the review clause, not the yield, sets the price.
A leasehold interest is income plus the return of its own capital. The dual rate method prices both, and the single rate needs a much higher yield to agree.
When a freeholder buys out a long head lease, the merged interest is worth more than the two parts. Here is how to measure the gain and price the deal around it.
The exchange postpones the tax rather than cancelling it, and the replacement property inherits the low basis. Both belong in the sum.
Prime rental growth describes a new building. The one you buy ages, its rent lags the market and its exit yield widens, and almost all of the cost lands at the sale.
Companion workbooks: /finance
Twelve years of 520,000 over-rent comes to 6,240,000 against an over-price of 7,619,048. The buyer is never repaid.
Three covenants, three headrooms, and only one of them matters on the day income turns. The ranking is arithmetic, and it changes with the asset and the debt.
An appraisal reduction realises no loss. It cuts the servicer's interest advances and can move control of the trust, which is why junior bondholders watch it more closely than the loss itself.
Break-even occupancy is the lender's simplest downside test, and the textbook version of it is off by a point and a half before the rate even moves.
The margin is one line of the cost of a loan; the fees paid at the start and the end make the rate on the money actually used higher, and more so the sooner the loan is repaid.
The yield move is quoted in basis points, the damage is a percentage that depends on the starting yield, and the loan-to-value covenant feels it first.
One property at five coverage levels: the income cushion, the rate headroom and the loan each DSCR buys.
The rate only enters the cover test, so proceeds hold flat under the LTV cap and then fall almost in line with the mortgage constant.
Loan-to-value is set on day one and tested on the last day. A good LTV is the highest one that still refinances when the loan matures at a higher rate.
Interest-only buys cash yield and cover today with a bigger balloon tomorrow. The arithmetic shows exactly how much of each, and which party the trade really helps.
Interest cover worked on one property loan, at the actual rate and at the stressed rate a lender sizes on, with the headroom it leaves and the loan it supports.
The structural (Merton) model applied to a commercial mortgage, step by step, with the refinancing test that matters more and a grid by LTV and volatility.
Mortgage lending value worked from rent to capital value, bridged step by step to market value, and what lending 60 per cent of it means when the market falls.
The cheap loan is smaller and shorter than the buyer wants. Value it against the financing the buyer would otherwise use, not against the same balance at today's rate.
A view on rates is only half of it. The break-even tells you which view you are taking, and the sizing test tells you how much each structure will lend.
The headline loan-to-value measures the distance to the owner's valuation. The lender is repaid from a forced sale, and the cushion has to be measured against that.
The valuer adds the over-rent strip to the value. The lender sizes on market rent and on the day the lease ends, and the strip ends up paid for in equity.
The supervisory slotting approach fixes the risk weight by grade. Here is the capital it implies, the margin that capital costs, and what a downgrade does to both.
Why acquisition lenders size on the lesser of price and valuation, and what a down-valuation does to the loan and the equity cheque.
Cure rights in an intercreditor agreement are an option with a premium paid monthly. Price the premium against the equity it lets the mezzanine lender keep.
Companion workbooks: /franchise
A bank showing 639,600 of CET1 capital is worth 278,809 to a buyer, once the loan book is marked.
One bank, one rate shock, one repricing decision: two betas a factor of 1.54 apart, and a break-even that is 17.32 points away or 5.00 depending on the denominator.
A worked bank: the liquidity sources marked and haircut, the two coverage figures, and how many days each one lasts in a run.
Economic value of equity sensitivity is arithmetic on durations. The hard part is the one duration nobody can observe: the deposits'.
Interest income less interest expense, over the assets that earn interest. The formula is one line; what moves it is which side of the balance sheet reprices first.
Two subtractions and a division. The ratio is lower than CET1 for two reasons, the denominator and the unrealised losses, and it falls further still if the held-to-maturity book is marked.
The transfer curve, the asset and funding margins and the treasury residual, worked line by line on one illustrative bank, with the deposit-life assumption that decides the split.
The loaded cost of each deposit product per dollar the bank can lend, and the posted rate at which wholesale money becomes cheaper.
The justified multiple from return on tangible equity, cost of equity and growth, and why the same price can read 1.14 or 1.50 times.
The cost-savings method values the deposit franchise year by year: the spread over alternative funding, on a balance that decays, after tax, discounted.
Selling underwater bonds and reinvesting at today's yield lifts margin at once, but the earn-back arithmetic shows what is gained, what is merely moved, and what it costs in capital.
The ratio worked on one bank, the distance to 100 per cent with losses charged as problem loans grow, and the bond mark the published figure leaves out.
Reported and adjusted efficiency ratios worked on one bank, the four adjustments, and what a fall in net interest income does to the number.
The loan-to-deposit ratio says how much of the deposit base is lent out; read with its denominator it also says what is funding the rest, and what it cannot say about liquidity.
Return on assets measures how well a bank earns on its balance sheet; return on equity multiplies it by leverage, which is why the two have to be read together.
The subtraction is trivial. Where the current accounts and savings go decides the sign of the answer.
The rate tells a board how fast it can grow and how much it can pay out without raising capital, provided it is measured on the right base.
The LCR asks whether the buffer covers 30 days. The survival horizon asks how many days it covers, and the answer moves fastest with the largest uninsured deposits.
Pre-provision earnings are a bank's first line of defence: strip out one-offs, then run them against the capital above the floor.
Net the recoveries, use average loans, annualise, then split by segment and set it against the allowance.
Turn each pool's annual loss rate into a lifetime one, adjust the forecast years, and see which inputs move the reserve.
Companion workbooks: /fundmanagement
Yield on cost is NOI over total cost: $5.6M on $80M is 7.0 per cent, worth about $97.4M at a 5.75 per cent cap.
A 20 per cent promote paid $17,200,000 on $70,000,000 of profit — 24.6 per cent. The definition, not the rate, decides.
A cap fixes the worst rate the loan can pay. Whether that rate passes the covenant is a separate calculation, and the premium belongs in it.
Name the test that created the gap, then price each dollar of it as fund cash against a coupon.
A trailing-twelve statement is a record of the seller's year. Underwritten NOI is a defended forecast of yours, and the gap between them has a price.
Three occupancy figures sit in every rent roll, and the one in the marketing deck is usually the one that pays the least.
A cap rate is only high or low against the return you need and the growth and capex the building comes with, and the arithmetic takes three lines.
Exit cap expansion is a one-off loss of value, so its cost in IRR depends on how many years you have to spread it over, and on the leverage that concentrates it.
A rent line that lands on budget can be two large variances cancelling out, and the split takes two multiplications.
Net operating income is gross potential rent taken down through five deductions and seven expense lines, and the lines it leaves out matter as much as the ones it keeps.
Both halves of a property's return share one denominator, and the capital half is the value change after the capex that bought it.
A replacement reserve built from the building's components, and why the capex it hides usually lands on the next owner.
A ten-year office lease priced year by year, with free rent, renewals and the term sensitivity an asset manager budgets from.
Unit-type rent roll, the formula, and how much of the gap a year of lease expiries actually recovers.
Debt yield translated into the LTV and DSCR it implies, so that a lender's three tests sit on one scale.
Build the cost of a real estate fund's loan book in dollars, loan by loan, then divide by the debt that is actually drawn.
The rate is negotiated; the definition of gross receipts and the share tenants reimburse decide what the fee costs.
One line in the fund documents, three readings of it, and a cure that fails if the manager sells assets and keeps the equity.
The operating expense ratio is operating expenses over effective gross income. Three-quarters of the costs are fixed, so the ratio says as much about occupancy as about management.
On a multi-tenant building most of the saving flows back to the tenants. Run the appeal on the landlord's share and on who pays the consultant.
Companion workbooks: /hedge
A locked five-year hedge calls 4.48 times the margin of a rolling one and exhausts 36,000,000 of liquidity at 7.09 per cent.
A collar is two options netted into one quote. Value each leg with Black-76 and the premium that was never invoiced turns up on one side or the other.
Credit valuation adjustment is three columns multiplied and added. Done by hand on a corporate swap, it tells you how much of the credit charge in the rate is credit.
Covered interest parity worked on one-year GBP/USD, proved by replication, and why the forward points a treasury report calls a cost are not one.
Discount factors bootstrapped from four par rates, both legs valued, the annuity shortcut, and why projecting today's fixing gets 43 per cent of the value wrong.
A forward sale of USD 20,000,000 against a hypothetical derivative, three quarters of period and cumulative ratios, and the lower-of test that sets the P&L charge.
Forward rates, Black's formula caplet by caplet, the split between intrinsic and time value, and the expiry mistake that overstates the premium by a fifth.
The minimum variance hedge ratio from twelve months of price changes, the number of futures contracts, and why a one-for-one cross hedge leaves almost twice the residual risk.
Pricing a forward rate agreement from two deposit rates, settling it against the fixing, and showing why the discounted payment locks the borrower's rate exactly.
The DV01 of a swap two ways, by the annuity shortcut and by bumping and repricing a bootstrapped curve, with the tenor table and the hedge sizing that follows from it.
The Garman-Kohlhagen formula worked on one exporter's dollar receipt, the option set against the forward at five settlement rates, and what volatility and strike do to the premium.
The par swap rate built from five forward rates, why it is a discount-weighted average and not a simple one, the net cash flows it implies, and what the dealer's spread is worth.
One option on the whole swap rate, discounted with the annuity: the forward swap rate, Black-76, and why it costs less than a cap at the same strike.
The futures price is the cost of buying today and holding until delivery. The contango that follows is not a cost of hedging, and a quote below it tells you something.
The mark-to-market of an outstanding currency forward, step by step: the new forward, the sterling difference, the discounting, and the spot shortcut that overstates it.
Two legs, two curves, one spot rate: the mark-to-market of a fixed-for-fixed GBP/USD swap with notional exchange, and why the final exchange carries most of the value.
A zero-premium participating forward on a USD 10 million receivable, priced with Garman-Kohlhagen and compared with the plain forward at every settlement rate.
Fixing a rate today for a loan that starts in two years: the formula, the check against the spot curve, and why the gap over today's rate is not a fee.
The difference is measured in rupees and paid in dollars, which is why the formula divides by the fixing and not by the contract rate.
The fixed price is a weighted average of the forward curve, and the weights are your own consumption profile and the discount factors.
Companion workbooks: /infrastructure
A constant WACC against amortising debt values this concession at 263.05, not 242.18 — an overstatement of 8.6 per cent.
An annuity fixes debt service and lets coverage drift upwards; sculpting fixes coverage and borrows against the drift.
The loan life coverage ratio averages the whole tenor; the DSCR finds the one year that cannot pay.
Energy at P90 is a little lower than at P50; cash flow after fixed costs is a lot lower, and that sets the debt.
Cash flow available for debt service starts at EBITDA and ends after every cash call that ranks ahead of the lenders.
The building blocks of a regulated utility's revenue, one year, with the indexation that most first models get wrong.
Same asset, same cash flow, two returns: the gap is the debt, and it is not the textbook leverage formula.
A concession ends, so its exit value is the present value of the years that remain, and the multiple falls every year the fund holds it.
Indexed infrastructure cash flows invite real models, and the discount rate on the committee paper is almost always nominal.
On a concession that ends at zero, part of every distribution is your own capital coming back.
Borrowing a listed company's beta for a privately held, more highly geared asset, step by step.
The payment mechanism of an availability-based PPP, worked for one month and tested against the lenders' cover ratio.
Traffic by class, toll by class, 365 days and a leakage haircut: four lines that every toll road model rests on, and one input that is often the wrong count.
A forward-looking reserve turns two resurfacing years that would break the covenant into twelve years that clear it, at a price equity rarely sees itemised.
A buyer paying exactly the RAB earns exactly the allowed return. Every point of premium has to be traced to a line, and this is how to build those lines.
Is infrastructure an inflation hedge? Run the same concession at five inflation rates with full and partial indexation, then with index-linked debt, and read the real equity IRR.
A lock-up does not take cash away from equity, it parks it. What it costs is time, and the rate the parked cash earns while it waits for the coverage ratio to recover.
When depreciation runs ahead of debt repayment, profit lags cash and company law blocks the dividend. Here is how to measure the trap and what a shareholder loan is worth.
A new road does not open at its mature traffic. Pricing the ramp-up is a small adjustment to value and a large one to the first years of debt cover, unless the ramp never closes.
Voluntary termination of a concession, worked three ways: base-case IRR make-whole, market value, and the current forecast at the base-case rate.
Companion workbooks: /insurers
No look-through pack means 49.00 per cent, not 18.90 — €45.2 million of capital on a €150.0 million allocation.
The standard formula spread charge from rating and modified duration, worked on a private credit fund, with the grid and what rating drift and longer loans do to it.
The formula, the index levels at which it hits its bounds, and what it does to the capital and the return on capital of a private equity fund held by an insurer.
The standard formula correlation matrix, the interest rate switch that changes three of its entries, and what a new fund really costs once diversification is shared out.
Divide what the fund earns by the capital the insurer must hold against it. The ranking it produces is often the reverse of the ranking by return, which is the whole reason insurers compute it.
The standalone charge is not what an asset costs an insurer. The increase in the aggregated total is, and it depends on what the insurer already holds.
The 25 per cent currency shock, the aggregation with the insurer's other market risks and the hedge cost that breaks even, worked on one illustrative dollar share class.
The look-through gross-up, the return on capital and the marginal cost to an insurer, worked on one illustrative levered property fund at loan to values from 0 to 60 per cent.
The charge sits on the gap between asset and liability duration, so the same credit fund can raise one insurer's capital and lower another's.
Discount the matched liabilities at the risk-free rate plus the adjustment, and the cap and the compounding take almost a third off the pitch-deck figure.
A flat 22 per cent, untouched by the symmetric adjustment, turns the private equity fund from third in the mandate into first.
The lower charges attach to qualifying assets the insurer can see, not to the fund's label, and they take only part of the symmetric adjustment.
The sub-module that charges a single name for being large, why it is computed on the look-through, and why the same fund triggers it at one insurer and not another.
Aggregate the modules into the basic SCR, add operational risk, deduct the tax adjustment, divide own funds by it, then run it again with the fund in.
The securitisation spread charge in the standard formula, worked on a CLO tranche, set against a corporate bond of the same rating and against the loans inside the CLO.
The volatility adjustment worked on an annuity book: the discounting, the release at four levels, the duration shortcut that overstates it, and why it matters to the manager of the assets.
The two equity classes of the standard formula, how they combine inside the equity sub-module, and why the 10-point gap mostly disappears at an insurer that already holds listed equity.
The loss-absorbing capacity of deferred taxes, worked from the shock loss to the recognition cap, and why the cap decides what a new fund costs an insurer.
The spread grid is concave in duration and convex in rating, so a factsheet's two averages misstate the capital in opposite directions.
Headroom divided by the standalone charge is the wrong answer, and the right one gets more expensive with every euro.
Companion workbooks: /jv
The same 1.5 times dilution leaves a defaulting sponsor on 7.04 per cent or 2.99 per cent, depending on the formula.
A shotgun notice names a value for the building; the price of each interest comes out of the waterfall, and the promote makes it convex.
One hurdle rises every year the asset is held and the other stands still, so the choice between them is really a bet on the holding period.
A three-tier JV waterfall solved year by year, with the gross-up most hand-built models miss and the hurdle definition that moves the promote.
Co-invest, promote and fees added up across three outcomes on an illustrative joint venture, and what the mix says about alignment.
Promote drag across deal outcomes and hold periods on an illustrative two-tier joint venture waterfall, and why the rule of thumb understates it.
A year 3 cash-out refinancing run through an illustrative 90/10 joint venture waterfall, capital account by capital account.
A promote paid early out of a refinancing, a capital call, a weak sale, and the giveback that the lookback clause calculates.
The agreed value of land put in as equity sets the landowner's capital account, its share of the preferred return and its share of the profit: one negotiated number, three transfers.
In a programme of JV deals the promote can be earned deal by deal or on the pool. The difference is largest exactly when one deal fails.
The promote starts where the investor's hurdle account is cleared, so the threshold is a price you can solve for in advance and compare with the purchase price and the entry yield.
Removal clauses differ in three things: whether the promote survives, how the sponsor's capital interest is valued, and whether that value is discounted, and each is worth a different amount.
A co-GP partner pays for its seat with promote: the split inside the general partner decides who is actually paid for the work.
A sponsor that subordinates its co-invest writes the investor a put on the downside and gives up nothing on the upside.
Rescue capital's priority return moves the point at which the promote pays. A preferred return reset moves it back, at a price.
The rate gets negotiated; the word after it moves more money. Convert every asset management fee into a load on contributed equity.
Pro rata, a sponsor loan or a completion guarantee: the same overrun run through the same waterfall gives three very different answers.
A promote is a convex claim on the venture's upside, so the base case and a liquidation at today's value both understate what it is worth.
When a new investor buys out the original capital partner, the sponsor's promote is settled at an agreed value and the hurdle resets. Whether the sponsor takes cash or rolls it changes who carries the risk.
Whether the promote runs on operating cash flow barely matters when the deal works. It decides what the sponsor keeps when the deal fails.
Companion workbooks: /logistics
A five per cent labour saving is worth 32 per square metre of rent, a 36 per cent premium. Property is 10.2 per cent of cost.
Occupiers store goods in volume and pay rent on a floor plan. Cube parity turns that mismatch into a rent, and the wrong one.
A headline yield divides gross rent by price. Multi-let and single-let industrial convert gross rent into net income at very different rates, before any risk premium.
A capped CPI review is a fixed uplift with an option sold to the tenant. Price it under a few inflation paths and the fixed equivalent is lower than it looks.
The floor-divided-by-pallet shortcut overstates capacity almost fourfold; aisles, beam pitch and the unracked floor decide the count.
Speculative logistics has two dates, the one developers quote and the one the equity needs, and the letting risk lives between them.
One warehouse letting with 1,850,000 of landlord works, run three ways, and the split between permanent improvement and true incentive that decides which figure is evidence.
An elemental cost plan for a 12 m clear distribution unit, how the rate moves with size and height, and the gap between construction cost and total development cost.
The demand figure behind every logistics forecast, built from inventory days, the value of a pallet and how much of an e-commerce shed is racking at all.
Door counts are set by trucks, time at the door and the loading window, not by floor area, and the loading window moves the answer as much as the volume does.
Rent, rates, racking and overhead turned into the storage rate a pallet has to bear, with utilisation and density as the levers that move it most.
Turn the stem time a far depot adds to every route into vans, drivers and kilometres, then into the rent per square metre an occupier can afford to pay for being close.
Half of a logistics site is not building, and the yard decides how much: a single-sided warehouse and a cross-dock on the same footprint need sites 21 per cent apart.
Whether the landlord should own the panels or rent out the roof turns on one number: the share of the power the tenant will buy, for longer than its lease.
Rent more than doubles from ambient to frozen. Cost more than doubles too, and the yield rises, so the premium has to clear both.
A mezzanine is cheap per square metre and expensive per year when the lease is short. The remaining term decides it.
A yard costs a fraction of a building to deliver, but almost all of that cost is land. Which scheme earns more on the money spent comes down to one input: what the land cost.
Owning a warehouse is occupying it plus investing in it. Price the investment, and leasing usually wins for an occupier with an equity-like cost of capital.
Value an ageing warehouse twice at lease expiry, refurbished and as a residual site, and the higher figure is the floor of its price.
Building up adds 80 per cent more floor but almost doubles the cost per m², so the rent has to pay for the ramp before the land does.
Companion workbooks: /mandate
Time-weighted 4.8012, money-weighted 4.1272: flow timing cost the scheme 6,357,745.18 and appears in no report.
A five-segment Brinson attribution worked line by line, reconciled to the active return, with the allocation formula that misleads at segment level.
Five years of active returns taken to a tracking error and an information ratio, gross and net, with the mistakes that move the answer more than the manager does.
Two lines of arithmetic, five choices hidden inside them, and a worked mandate that wins on return and loses on risk-adjusted return.
The formula is one line and the Excel is two functions. The trap is what the number measures when a large flow lands mid-period.
Beta is a slope and alpha is what is left after it. A fund can beat its index every year and still show no alpha at all.
Two funds with the same average return, worked month by month, and the denominator error that halves the ratio.
A sliding-scale fee schedule worked band by band, with the effective and marginal rates, the aggregation clause and the cliff that is not a tier.
Active share worked stock by stock on one fund, checked by the overlap method, and turned into the fee the client pays for the part that is actually active.
Upside capture, downside capture and the ratio between them worked on twelve months of one fund, with the Excel formula and the sorting error that flatters a manager.
Excess return per unit of beta: a useful ranking for a fund inside a diversified portfolio, and a misleading one for a fund that is the whole portfolio.
Value the portfolio before every external flow, compound the sub-period returns, and the client's timing drops out of the manager's number.
Commissions, spread, market impact and a week in cash, priced on one mandate, then set against what the new manager has to add to repay them.
The formula, the Excel GEOMEAN shortcut, the full table of windows, and why a fund that wins half its calendar years can lose most of its three-year periods.
Both formulas, why only the geometric one compounds across periods and survives currency translation, and how far apart they drift.
A blended benchmark is rebalanced at a stated frequency, and computing it at the wrong frequency can turn a manager's outperformance into underperformance.
Turnover is defined so that client flows do not count, which makes it a measure of the manager's own trading and a quick estimate of what that trading costs.
The fee is only part of the bill. Trading and cash drag add more than a third on top, and tracking error decides how long the client waits to see any edge.
M-squared keeps the Sharpe ranking and turns it into percentage points of return at the benchmark's risk, which is the unit a client reads.
Count the periods the manager beat the index, then put the size of the wins beside the frequency, or the number misleads.
A symmetrical performance fee, the kind US mutual funds must use, and why its expected cost equals the base.
Companion workbooks: /model
The optimum cut-off moved from 550 points to 580; the policy did not. One year of that inertia cost 2,713,298.
A credit scorecard is a logistic regression rewritten in points. Three choices fix the scale; the arithmetic that follows turns every coefficient and weight of evidence into a number an underwriter can add up.
The PSI is ten subtractions, ten logarithms and a sum. The bands it is computed on, and what it cannot see, matter more than the threshold it is compared with.
Both discrimination statistics fall straight out of a score band table, provided you count the ties. Here is the full calculation, and what the bands cost you.
Two columns of counts, one logarithm per bin and a column total. The binning decides more of the answer than the formula does.
One number added to the intercept repairs the level. Solving it from the averages misses, and solving it from the change in bad rates double counts.
The confusion matrix of a credit scorecard, cut-off by cut-off, and why the threshold that maximises F1 is not the one that maximises profit.
The calculation takes ten rows. Reading it takes one more test, because the statistic can pass a model whose overall default rate is plainly wrong.
The confidence interval around an AUC is set by the number of defaults, not the number of applications, and on a small out-of-time sample it is wide.
Parcelling turns a bad rate you can see into one you cannot, through a factor nobody can measure. The decision often turns on that factor alone.
A logistic regression credit model gives a probability of default in three exact steps, and each answer on the application can be read as an odds ratio rather than a change in percentage points.
The Brier score measures probability accuracy, level as well as ranking, but its size depends on the default rate, so it has to be decomposed before anyone concludes the model got worse.
Binary cross-entropy computed from band counts, read against the base-rate model, and the reason an overconfident PD model can score worse than no model at all.
The exact one-sided binomial test, the Jeffreys variant supervisors use, the normal shortcut that misleads on low-default grades, and what default correlation does to all three.
Rank the book by score, cut it into deciles, and read lift against the break-even bad rate rather than against 1.
A development AUC gap is not a profit figure. Fix the approval rate, count the bads each model lets through, and price them.
For a logistic regression the SHAP value has a closed form, adds exactly to the logit, and gives reason codes a decline letter can defend.
A pairwise correlation screen catches duplicates. The variance inflation factor catches the combinations that make scorecard coefficients unstable.
Constant hazard, a transition matrix, and what the choice does to an IFRS 9 lifetime provision.
Two tests, not one: bads per parameter for the regression, and bads per bin for the weights of evidence the points are built on.
Companion workbooks: /office
Quoted at 6.00 per cent, this office returns 3.20 per cent once the re-letting cycle is deducted: €160.04/m² a year.
The business plan underwrites a net effective rent; the negotiation is about a headline and a package. Work backwards from one to the other.
A break clause is negotiated as a concession on a list and priced as though it were free. It is the most expensive incentive in the package.
Residential prices per square metre look far higher than office values. Run the same residual for both uses and the margin is a few per cent.
One line of arithmetic, five defensible-looking answers between 5.20 and 6.50 per cent, and only one of them is rent the owner will bank.
The tenant pays the energy bill, so the saving is the wrong test; the value sits in the void, the re-letting rent and the yield a buyer applies.
Rent, service charge, rates, annualised fit-out and running costs turned into a cost per desk, per employee and per desk-day used, with density as the lever that moves it most.
Rental depreciation and yield drift separated on one 10,000 m² office over ten years, and why a building that holds its nominal value can still lose 22.6 million against prime.
An empty office is worth the let building it will become, less the wait for the first rent and the cash spent before it arrives. Both halves can be computed.
Vacancy can rise while demand grows and fall while it shrinks. Net absorption separates the two, and split by grade it shows where an ageing office really stands.
Fit-out, dilapidations, moving and dual running come first and the rent saving comes slowly, which is why the tenant's cost of leaving is the landlord's negotiating room.
A plug-and-play floor lets faster and at a higher rent, then lets again sooner: price it as a strategy over several letting cycles, not as a capex with an uplift.
Start from the busiest day, not the headcount or the average, and the rule of thumb turns out to overstate the space by more than a quarter.
The service charge is recovered from tenants, which is exactly why it is paid for by the landlord: out of the rent the next tenant will offer.
A 60-desk occupier compares an all-inclusive flexible office with a conventional lease, with every upfront cost converted into a monthly figure per desk.
A single-let office valued at each unexpired term, with the void, rent-free, fit-out and fees of the coming re-letting weighted by the chance the tenant stays.
A gas-heated office run against an illustrative decarbonisation pathway, and why its gas use decides the date.
An amenity floor trades certain rent for a hoped-for premium and occupancy gain. The largest cost is the rent the floor would have earned.
Suites let faster and at a higher rate per square metre, but they lose area to corridors, cost money to create and re-let twice as often. Price the whole cycle before deciding.
Daily attendance is a distribution, not an average: the desk count comes from the busiest weekday and the service level you choose.
Companion workbooks: /operatingpartner
Organic operating improvement contributes 59.85 million whether the deal is levered 3.5 times or 6.5 times.
Enterprise value is EBITDA times a multiple, so when both move the change splits into three parts, not two, and the third is where bridges get argued.
The formula is one line. The input most teams get wrong is the margin, and the error always runs in the dangerous direction.
A receivables project is worth one day of revenue per day of DSO, plus what shorter terms save on growth and interest, and it is valued once, never at the exit multiple.
Buying small and selling large is the most repeatable part of buy-and-build, and the most overstated, because the usual arithmetic forgets the price.
Two companies with identical EBITDA can return very different equity: the difference is how much of it turns into cash that repays debt.
Run-rate EBITDA adds the part of each initiative the trailing twelve months do not yet show; the buyer then decides how much of it to believe.
Operating partners talk in margin points and investment committees think in multiples of money, and the conversion runs through exit revenue, not entry revenue.
A procurement programme reports savings against budget, a buyer values EBITDA against last year, and the difference is usually half the headline.
The cycle in days, the cash in each day, and why a day of inventory or payables is worth less than a day of receivables.
The anniversary rule, the pro forma alternative, and the half-year comparison that turns an acquisition into organic growth.
The simple ratio divides an up-front cost by a saving that arrives over a year; the phased cash payback is the one lenders and buyers check.
Split costs by behaviour once, at entry, and you know how much margin expansion volume will deliver on its own and how hard a miss will hurt.
The three OEE factors from a line's own data, then the value of a point, which depends on whether the plant is short of capacity or short of orders, and on which factor moves.
The manager count implied by a span of control, the saving function by function, and the redeployment and severance that turn the gross figure into the one a buyer will credit.
An across-the-board increase always looks bigger on paper. The test is how much churn it can absorb before a rise aimed at the underpriced customers overtakes it.
Stretching supplier terms releases cash once. A supplier who prices the extra days back in costs EBITDA every year, and the buyer capitalises it.
Cutting the long tail of a product range is a staple of value creation plans. Counting allocated cost as saved cost can more than double it.
A point of churn looks like a point of revenue. Because every retained customer stays in the base and keeps paying, it compounds into more than four times that by exit.
The overtime premium looks like 50 per cent. Against the full cost of a hire and a seasonal workload, the real break-even is a utilisation rate.
Companion workbooks: /pbsa
A nomination quoted at 8.8 per cent off the rate is really 21.2 per cent: 6 unpaid weeks, £153,568 a year.
Revenue per available bed on both bases, the identity with occupancy and achieved rate, and the mixed-basis error that flatters a 51-week scheme.
Three break-even points, operating, cash and covenant, computed from the contribution of one let bed, and why the opex ratio shortcut flatters them.
Rent collected on the weeks actually sold, the summer as a separate business, and the cost base per bed, on an illustrative 600-bed scheme.
Price per bed is the output of a valuation, not the method: two 400-bed schemes show why.
The rate-or-occupancy trade solved for the beds a rent cut has to win, and why the answer depends on how many beds are already sold.
The eight weeks between tenancies worked from bookings to net contribution, with the occupancy at which summer letting stops paying.
One city, three numerators, and the pipeline that turns a shortage into a city that is filling up.
Bills-included rents make the owner short energy. What matters is the months before the rate card can move.
A quoted yield sits above capital expenditure, and student rooms wear out faster than almost any other real estate.
Student rents can outgrow the funding students live on for a few years, and then the catchment narrows.
Put both tenancies on a 52-week year, net of the summer's VAT, commission, cleaning and utilities, and the break-even premium is about half what scaling the rate suggests.
Build the cost per bed up from area per bed and the build rate through every layer to total development cost, then test it against net income per bed.
Sizing a loan on purpose-built student accommodation the way a lender does: re-underwrite the NOI, run three tests, and find out which one binds.
Turning a reservations count in spring into a September occupancy forecast, the two methods that bracket it, and what the gap to budget is worth.
A studio lets for a third more and takes a third more space. The mix is decided by yield on cost, and the margin is a couple of pounds a week.
The headline rate is the least useful number in an operator agreement. Price the fee in pounds a bed, as a share of NOI, capitalised, and across occupancy.
A student housing rent roll is sold once a year, so a late practical completion is priced in lost academic years, not lost weeks.
A returners' discount is paid to everyone who rebooks, and most of them would have rebooked at full rent.
Paying the year at check-in brings cash forward and avoids some bad debt, but the residents who take the offer are the ones least likely to default.
Companion workbooks: /pmp
Three funds at 11.52, 10.12 and 19.51 per cent average to 13.72 per cent. Pooled, they earned 11.78 per cent.
The Kaplan-Schoar public market equivalent worked on an eight-year fund, with the Excel formula, the sensitivity to the index, and the price index trap.
Direct Alpha worked on a nine-year fund: the compounded flows, the Excel steps, and why IRR minus the index CAGR is a different number.
The index comparison method worked year by year, with the Excel formula, and the case where it breaks: a fund good enough to drive the index account below zero.
The fix for Long-Nickels when a fund distributes faster than the index could have paid, worked to the last decimal.
The one, three and five-year returns an investment committee asks for, and why the opening mark decides them.
A policy benchmark of public equities plus a premium, applied to one fund's cash flows two ways: the shortcut most reports use and the cash-flow-matched test.
One fund's since-inception IRR recomputed every year with the NAV 20 per cent lower and higher, to see when the number starts to mean something.
The multiple falls by the markdown times RVPI at any age; the IRR falls by far more when the fund is young, because the NAV is most of the value and there is little time to spread the loss.
Time-zero strips out the calendar order of the deals; the pooled IRR on actual dates rewards an early winner. Neither is an investor's return, and the average of deal IRRs is neither.
Net TVPI and IRR computed with and without the fee calls, why the IRR error is so much larger than the multiple's, and when excluding fees is legitimate.
A euro fund measured in US dollars, flow by flow, and why the currency cost more than its own annual fall.
Why deal IRRs cannot be added, the three attribution lenses that work, and how a profitable deal can pull a fund's return down.
A quartile boundary is an estimate from a sample: the formula for its precision, the cohort size it needs, and how often a second-quartile fund ranks top quartile.
One set of fund cash flows run against four plausible benchmarks, to show how much of a PME is the fund and how much is the choice of index.
Most PMEs are run with a NAV one quarter older than the index date. What that mismatch does, when it matters, and the two ways to remove it.
A late call after a large distribution turns the IRR equation into a quadratic, and Excel picks a root by its starting guess.
Appraisal-based NAVs book market moves a quarter or two late. Summing the coefficients on lagged index returns recovers the exposure the ordinary regression misses.
Cambridge Associates' modified public market equivalent, worked year by year, and why its index replica can never go negative.
Why the same-day netting of a call and a distribution moves every multiple and no rate, which way it pushes DPI and TVPI, and how to rebuild the series gross.
Companion workbooks: /quant
Monthly rebalancing leaves a standard deviation of 2.3031, 20.1 per cent of premium; daily leaves 0.5265.
Implied volatility has no closed form, but on an ordinary option Newton's method gets there in two steps. The work is in the seed, the units of vega and the cases where it fails.
A delta-hedged option pays for its time decay with the squared daily move. The break-even is one formula, and which theta goes into it decides whether it agrees with the implied volatility.
Four lines of arithmetic, one lookup table and a parity check: a full Black-Scholes worked example you can rebuild in a spreadsheet.
A three-step Cox-Ross-Rubinstein tree worked by hand, its convergence to Black-Scholes, and the American put it can price and the formula cannot.
The standard error of a simulated option price, computed exactly, and what it says about the paths you need and the runs you already have.
Realised volatility worked from twenty daily closes, in Excel and by hand, with the conventions that change the answer and how uncertain a one-month estimate is.
Black-Scholes delta for a call and a put, the hedge ratio in shares, how gamma moves it, and delta across spot and time to expiry.
Parity follows from payoffs alone, so it holds whatever the volatility: the first identity to check on quotes, and the first test to run on a pricing library.
Vega is quoted per volatility point, peaks slightly above the spot and grows with the square root of time; a finite difference checks it in one line.
One standard deviation from the implied volatility, the probability it actually carries, the 252 against 365 trap, and why the straddle price is a smaller number.
N(d2) worked by hand, why delta overstates the probability, how much an assumed real-world drift changes it, and the digital option that prices it.
The closed form in two terms, the calendar-day and trading-day conventions, and why an at-the-money option's decay is anything but linear.
A Taylor expansion turned into a P&L report: each Greek's share of one day on an option book, what is left unexplained, and when the approximation breaks.
The formula, a finite-difference check, the conversion into shares and currency, and why gamma explodes as expiry approaches.
From three quoted numbers to the two wing volatilities, the strikes they sit at, and what the skew does to the premium.
A digital pays all or nothing across one price, so it cannot be delta hedged near expiry. Dealers replicate it with a call spread and charge for the gap.
In-out parity, the reflection formula for the knock-in, and the barrier shift that daily monitoring requires, worked on one at-the-money option.
From vega notional to variance notional, realised variance from daily returns, the payoff, the cap and a mid-life mark.
The escrowed dividend model step by step, the parity check that proves it, and when an American call is worth exercising before the ex-date.
Companion workbooks: /raising
A 100,000,000 first close at 1.5 per cent pays 125,000 a month against a 200,000 burn: the house loses 75,000 a month.
Price the fee discount and the carry share on the same basis, then turn the total into the extra capital the anchor has to unlock to pay for itself.
Payback in months of management fee, value per dollar of incremental capital, and the overlap at which the agent stops paying for itself.
Investors size a fund from the team's record, not from the manager's ambition. Three tests give the range the arithmetic allows.
A commitment is the last stage of a funnel whose losses multiply, so size the list from the money and then check the diary can carry it.
Investors will ask what your pre-fund deals would have returned on the terms you now offer; the answer is a waterfall run on pooled cash flows, not a deduction from the gross.
A formation budget line by line, the organisational expense cap, and why the size the fund closes at decides who pays.
The same headline rate on two bases, year by year, and what each does to the management company during the investment period.
Fees pay for the house; carry is the profit. Running one fund through its eight years shows how much of each a manager really keeps, and how sharply the carry depends on the last tenth of a multiple.
Deal fees look like a trade for a lower management fee. Charged on gross asset value, they are also a fee on the fund's borrowing, and the trade only breaks even on an unlevered fund.
A seeder's revenue share turned into the manager's lost profit, with the break-even fund size and what extending the share to Fund II does to it.
The same pipeline under a blind pool and deal-by-deal syndication: fees, carry with and without netting, and the deals that never close without committed capital.
Present value of fees and carry under each structure, after the time and cost of raising the fund and the probability that it never closes.
The preferred return is the term a first-time manager is most tempted to sweeten. Here is what two extra points of hurdle cost in carry, outcome by outcome.
How to price a seed asset bought before first close into a real estate fund, who carries the risk under each rule, and what each does to the first-close investors.
Trading management fee for carry looks like alignment. In present value it is close to neutral, and the manager bears all the downside.
The net target in the deck is only as credible as the gross IRR the deals can deliver after fees, expenses and the waterfall.
A compounding preferred return makes carry a function of time: the same exits, shifted by one and two years, through a whole-fund waterfall.
The fee waiver against a cash GP commitment, on the same pre-tax money, with the fund multiple at which it stops paying.
Pipeline coverage computed the way investors test it: stage conversion, leverage and the year-one equity plan, with the probability the named deals deliver.
Companion workbooks: /ream
The plant package saves 1,400,000 on the contract and loses 501,000 at the exit, where the buyer prices its remaining life.
The weighted average unexpired lease term is easy to compute and easy to flatter: run it to the break as well as to expiry, and look at what the average hides.
Leasing arguments are conducted in rent per square metre; the decision turns on months of vacancy, and on the costs an empty unit keeps running.
The price you paid is not in the decision. Today's net realisable value is the investment, and the forward IRR on it is the only return that counts.
A tenant two years from expiry asks for rent-free in exchange for a new ten-year lease. The answer depends less on the rent than on what happens if the tenant leaves.
Reversion is quoted as one percentage for the whole building. The business plan can only bank the part that reaches a rent review or an expiry before the exit.
Four office lettings with different incentives turned into one estimated rental value for a vacant floor, step by step, with the rent-free assumption that moves it most.
A vacant office sold as it stands or refurbished, let and sold three years later, with the as-is price treated as what it is: the first cost of the project.
The premium is not the rent left on the lease. It is the difference between two futures for the same building, and the landlord's void arrives in both of them.
The schedule prices the works; the diminution valuation decides what is recoverable, and the landlord's own plans for the building can shrink the claim to a fifth.
The EPRA vacancy rate weights empty space by the rent it could earn, not by its size, so a vacant basement and a vacant top floor count very differently.
An upward-only review is a floor under the rent, and a floor is worth the probability-weighted shortfall it prevents, not nothing because the market is expected to rise.
The EPRA cost ratio shows how much of the rent is absorbed by running the portfolio, and the version without vacancy costs shows how much of that is the platform itself.
Collection rates are quoted constantly and defined loosely. Here is one quarter on a multi-let building computed five ways, then the arrears provision that tells you what was really collected.
Top-tenant share, Herfindahl index and the effective number of tenants, worked on two rent rolls with the same rent and the same expected loss, and what the difference does to the bad years.
Total rental income moves every time the fund buys or sells. Like-for-like growth isolates what the asset manager actually achieved.
Two offers for the same floor, priced twice: once as an investor would value them on the day, once as the cash a landlord holding the lease expects to collect.
A deferral collects more if the tenant survives the repayment year; the arithmetic is whether the extra burden makes it fail.
A provision matrix for ordinary arrears, a specific provision for the tenant in administration, and the charge that reaches the year's income.
The average condition cuts every claim, not just a total loss, and the premium saved by a low declaration is not even the landlord's.
Companion workbooks: /refm
Two downside moves together cost 5,906,035, not the 6,220,557 they sum to: the cross term is 314,523.
Annualising the IRR of a quarterly property model, and why the popular rule of thumb has the sign of the error backwards.
Four break-even exit yields sit in every property model, hundreds of basis points apart, and the comfortable one is rarely the one that matters.
One row reference in the exit formula decides it, and it should match the convention the entry price was quoted on.
The blended market leasing assumption gives the correct expected cost and a cash flow that will never actually happen.
A bid is a model run backwards, and the levered and unlevered targets rarely give the same ceiling.
A one-way sensitivity for every input, ranked, and why the ranges you choose decide the ranking.
A value-add hold with a capital call in year two, worked by hand and with Excel's MIRR function, and why two 15 per cent IRRs are not the same.
The Meridian House acquisition taken from purchase price to equity cheque, with the two errors that understate the equity.
The equity cheque is the same size either way; what changes is when it goes in, and so the interest and the return.
The Excel mechanics of a two-way sensitivity on exit cap rate and rental growth, the grid it produces on one levered deal, and how to read the trade-off line off it.
A quarterly lease-up of 40,000 vacant sq ft modelled signing by signing, what it costs in lost rent, carry and leasing capital, and how far the vacancy-percentage shortcut overstates the IRR.
A cap rate and a DCF are the same calculation under strict conditions; every gap between them in a real model can be named and priced.
A lease with open market reviews pays a flat rent between reviews, and a model that grows the rent every year quietly adds income the tenant never pays.
Four columns, six rows and one switch cell: how to set the scenarios up in Excel, and why the base case is not the expected case.
Distributions for three inputs, a correlation between two of them, and what the simulated IRR tells a committee that a single base case cannot.
How long a completed scheme can sit unsold before finance on its costs consumes the developer's profit, with the formula, the Excel and the mistakes.
Operating, exit, lease and void flags, the Excel formulas behind them, and the off-by-one errors that produce a plausible wrong IRR.
Modelling staged land payments in a development cash flow: the IRR, the profit, the implied vendor rate and the effect on peak equity.
After-tax IRR is a set of cash flow rows, not a haircut on the pre-tax answer. Depreciation and recapture explain why the gap is smaller than the tax rate.
Companion workbooks: /reit
REIT acquisitions turn dilutive at a 6.2 per cent discount to NAV, not at zero — 11.6 per cent funded at the target mix.
The implied cap rate turns a share price into the language of the property market, and three small choices in the build move it by more than half a point.
FFO measures earnings before the cost of keeping the buildings let; AFFO deducts it, and the dividend that looked comfortable on one is tight on the other.
Net asset value is the private market price of the portfolio less every claim ahead of the common shares. Most of the judgement sits in three lines.
A P/FFO multiple compresses three assumptions, conversion to AFFO, cost of equity and growth, and borrowing a peer's multiple without adjusting for the first one overstates value.
Total NOI growth mixes what the buildings earned with what the company bought, built and sold; a strictly defined same-store pool separates the two.
The Nareit bridge line by line, the share count to divide by, and what each common error does to the multiple.
The Nareit EBITDAre bridge, the pro forma adjustment, and the joint venture debt and preferred equity that a reported ratio often leaves out.
A rate rise reaches a REIT through two doors: the cap rate on its buildings and the coupon on its debt. Sizing each shows which one the share price is really pricing.
An external manager's fee looks small against assets. Measured against NOI, equity and value per share, it is the largest line after interest, and it rewards growth over accretion.
The two re-leasing spreads a REIT reports, computed lease by lease on one quarter's signings, and why fixed escalators drive them apart.
Four ways to put construction in progress and land into net asset value, worked on one illustrative pipeline, and why the choice moves NAV more than the cap rate on the stabilised portfolio suggests.
The 90 per cent rule is applied to a tax number that sits far below FFO, so it is almost never the constraint that sets a REIT's dividend.
The three EPRA net asset values answer three different questions, and the discount a share trades at depends entirely on which one you pick.
A buyback below NAV always adds to NAV per share; whether it adds to AFFO per share depends on how it is funded, and the leverage-neutral test is the one that counts.
Five adjustments turn the loan to value a company reports into the EPRA measure, and most of them push it up.
A five-year maturity ladder rolled tranche by tranche, and the refinancing rate at which the dividend is no longer covered.
Reverse the dividend discount model, then split the growth the price requires into what retained AFFO can fund and what the rent roll must deliver.
REIT unsecured notes carry four incurrence tests on cost-based assets. Converting each ratio into dollars shows which one binds and how much the REIT can still borrow.
Why capitalised interest and preferred dividends belong in the denominator, three published variants of one ratio, and the shocks that close the gap.
Companion workbooks: /resecondaries
An 18 per cent discount to reported net asset value is worth 9.18 per cent once three computable deductions are made.
One line per quarter recovers the true return from an appraisal series, and shows how far the reported net asset value has drifted from spot.
A queue pays the reported net asset value on the dealing date, not today's, and after a fall in values that number still has to come down.
The bridge from gross asset value to net asset value is five lines, and it decides what a secondary discount to NAV really says about the buildings.
Reported NAV carries the fund's loans at par. A secondary buyer inheriting cheap fixed-rate debt is buying an asset the accounts do not show, but only for as long as the loan survives.
A discount to NAV is a cushion against the appraisals being too high. Leverage makes that cushion thinner than the headline, and it is worth knowing how thin before bidding.
A portfolio sale is priced line by line and quoted as one number. Only the NAV-weighted discount says what fraction of reported value is paid.
In a fund past its term the NAV appraises assets the manager has already decided to sell. The price is the cash the sales will return, and when.
INREV NAV adjusts the accounts towards what the units are worth, but two of its lines are sunk costs, and a secondary buyer has to know which.
Accounts carry latent capital gains tax in full and undiscounted; a buyer should deduct what the fund is likely to pay, when it is likely to pay it.
Rebuilding gross asset value asset by asset, without the reported NAV, is the second road to a secondary price, and the only one that tells you what the appraiser assumed.
A real estate fund interest bought below its hurdle, run through the whole-fund waterfall it inherits: three zones, and a bid model that gets the carry wrong both ways.
Fund leverage does not average by NAV: the most geared interests carry most of the debt, and the portfolio's exposure to property values follows the debt.
When a property fund's loan matures into a smaller one, a buyer of an interest inherits its share of the gap, and a price quoted on NAV hides it.
Lay out the price, the fund's income distributions and the exit NAV with property growth geared through the fund's debt; the discount adds more than its straight-line share, and fund leverage decides how much an exit shock takes back.
Reported NAV ignores the fees and expenses the interest will pay until the fund winds up; a buyer has to price them in before reading the discount.
Split the NAV: price the standing assets on a discount, and price the development as the cash it will return, net of the capital still to be called.
Two discounts to NAV, quoted the same way and not comparable: one is diluted by more leverage, the other has no date on which it must close.
The reported NAV of an LP interest is net of the fund's borrowing against commitments, and the buyer will repay it. Price the property, not the net figure.
The data room compares sale prices with the last appraisal, which the valuer has already moved to the agreed price. The test that matters uses an earlier one.
Companion workbooks: /retail
An anchor paying €561 600 exposes €1 985 894 of rent when it leaves — 3.5 times its own rent.
Retail is the only asset class whose tenants report their sales. The occupancy cost ratio turns that report into a test of the rent, if both halves of the fraction are right.
Indexation assumes a tenant's ability to pay grows with prices. It grows with sales, after the service charge and rates have taken their share.
Halving back puts shops of different depths on one footing. It tells you what the comparable implies, not what the occupier can pay.
The rent is one MAX formula; what the lease is worth depends on treating the top-up as the geared, fragile income it is.
Every lease can be fully recoverable and the centre still is not; the shortfall is a landlord cost that grows faster than the budget.
A hardcore and top-slice valuation of an over-rented centre, with the sustainable rent set by each trade's sales and occupancy cost ceiling rather than by comparables.
Footfall, capture, conversion and basket chained into a shop's sales and the rent it can pay, with the gearing that makes a footfall fall hit rent harder than sales.
The number a retailer uses to decide which stores to keep, rebuilt from the sales line a landlord already receives, with the central costs that four-wall leaves out.
Total centre sales mix the tenants' trading with changes to the line-up. The like-for-like separates them, and stripping out the anchor shows what the line shops are really doing.
Sales density is the one number a shop's rent depends on, and three choices, area, VAT and period, decide whether it is right.
A gravity model turns a catchment into a sales forecast in four steps, and the tenants' reported sales tell you which distance exponent to believe.
Measure the compromise against what the unit would earn if you took it back, then against the rent the tenant's own sales can carry.
The definition of turnover in the lease, not the store's trading, decides whether the landlord shares in sales that are paid for online and handed over in the shop.
The test for a rent concession to an anchor is not its own rent but everything its departure would take with it, weighed against the fall in the probability that it leaves.
Value marginal shop space on what it earns through one complete cycle of letting, void and re-letting, not on its headline rent, and the conversion threshold falls by two thirds.
On a turnover lease every sale the tenant moves down the road is rent the landlord loses. The radius clause is priced by the top-up it protects.
A kick-out clause is an option the tenant holds on its own sales. Priced with a probability, it is neither free nor a certain break.
A fit-out contribution buys a higher headline rent, and the valuation rewards it at once; the cash case depends on the break and the tenant's credit.
An exclusive restricts every future letting in the centre, not just this one. Priced as blocked lettings, it is rarely free and the definition decides the bill.
Companion workbooks: /risk
A four-sleeve credit fund's diversification is worth 0.767 of a point; only 27.6 per cent of it survives a crisis.
The square-root-of-time rule is one line of arithmetic. Whether it holds depends on two things the rule assumes away: independent days and a book you can sell.
The traffic light is a binomial table with two probability cut-offs. Built by hand, it also shows how weak a count test is at catching a model that is merely wrong.
Expected shortfall averages the tail that value at risk only locates. On a normal model the switch changes almost nothing; on a real history it changes the answer.
Component VaR splits a diversified VaR into pieces that add back to the total. Standalone and incremental figures do not, and they point to the wrong sleeve.
Spread duration turns a scenario in basis points into a loss in money. The arithmetic is one line; the calibration and one duration decide the answer.
The variance-covariance method for a two-asset portfolio: volatility from weights and correlation, the confidence multiplier, the diversification benefit and the scaling mistakes.
Days to liquidate position by position, the fund's liquidity profile, and what meeting a redemption from the most liquid assets leaves for the investors who stay.
Historical simulation VaR worked on one fund: the ranking, the three percentile conventions, the window length and why the same volatility gives a larger number than the normal curve.
Maximum drawdown worked month by month on one fund's NAV: the running peak, the trough, the recovery, and how sampling frequency and leverage change the number.
The RiskMetrics recursion worked day by day on an 840M fund, with the weights, the half-life, the choice of lambda and the mistake that turns it into noise.
The Bangia spread adjustment worked sleeve by sleeve, with the multiplier, the stressed case and the two mistakes that make the number useless.
Cholesky, simulate, revalue, sort: the four steps on a four-sleeve credit fund, how many scenarios the answer needs, and why the distribution matters more than the method.
The Cornish-Fisher quantile in three correction terms, worked on a credit fund, with the grid that shows where it helps and the range where it breaks.
The Kupiec test only counts exceptions; the Christoffersen test asks whether they arrive together, and on the same count it can turn a green model into a rejected one.
A repo margin call is not the mark-to-market loss: when the lender raises the haircut on the same morning, the cash demanded is more than twice the loss.
The exposure profile of a fund's currency hedge, month by month, at 95 and 99 per cent, with expected exposure beside it and what daily margining does to both.
Inverse-volatility weights, equal risk contribution and the leverage to a volatility target, worked on one covariance matrix.
Adding the gamma term to parametric VaR, why a delta-hedged book needs the two-tailed quantile, and why gamma losses do not scale with the square root of time.
The square-root impact formula worked on a concentrated position, with the trade-off between impact cost and timing risk and the mistakes that understate it.
Companion workbooks: /senior
At 1.80x cover and a 6.0 per cent yield the buyer pays 9.26x EBITDARM, not 11.00x — £2,661,227 apart.
Self-funders convert to council funding when their capital runs out, so the private share of beds is always lower than the private share of arrivals, and it falls when the fee rises.
A care home has three break-even occupancies, more than twenty-five points apart, and the one in the sale memorandum is the one that ignores the rent.
EBITDARM is built from beds, occupancy, fee and the rota, and the two lines it leaves out, rent and the management charge, are exactly where rent cover goes wrong.
Build the rota from resident dependency, then count people, not equivalents, because that is how employer costs are charged.
Every resident admitted is a resident who will leave, so occupancy curves towards admissions times length of stay and slows as it gets close.
The profits method on one 70-bed home: from the reported year to fair maintainable occupancy and costs, FMOP, the multiple and the value per bed.
Land, construction, equipment, fees, irrecoverable VAT, contingency and the finance carried through the fill, added up per bed and set against what the stabilised home is worth.
A wage-floor rise is costed on paid hours, carried up the pay scale and loaded with employer costs, and then someone has to pay for it, usually the self-funders.
A cost-based weekly fee divides the home's costs, rent included, by the resident-weeks it expects, so the occupancy assumption sets the fee as much as the costs do.
An embargo stops admissions, not departures, so occupancy keeps falling for as long as it lasts and the cost runs on for months after it is lifted.
A care home's debt capacity is set by its trading cash flow, not by bricks, and the same occupancy that sizes the loan decides how close it sits to its covenant.
The agency invoice is not the cost of agency. The cost is the gap between the agency rate and what the same hour costs on the payroll, and that is also the only part a buyer should add back.
Projecting rent cover on a care home lease year by year: why operating leverage makes EBITDARM lag the rent, and which input moves the answer most.
Pricing an en-suite conversion on a care home room by room: the fee premium, the occupancy it buys back, the beds it costs and the months of disruption.
Same building, same residents: the lease sells the upside to the operator in exchange for rent cover, and the cover is only as good as the operator.
Revenue per occupied unit is the pricing half of senior living performance, and three unstated choices change it.
Brochures compare sticker prices. The right comparison discounts the refund to the date the unit is resold, and the operator sees it differently.
Rent cover and the profits method both start from EBITDARM, which is measured before the replacements a care home has to keep buying.
The extra care hours are the obvious cost. The beds given up and the works are the ones that get left out of the fee.
Companion workbooks: /slb
The over-rent implies 269 basis points of credit spread, against 385 on the tenant's own bonds.
Rent cover is a simple ratio, which is why it is so often computed on the wrong earnings, at the wrong company, on the wrong date.
A long leaseback hands the buyer the building and leaves most of the gain in the seller's right-of-use asset, whatever the board paper says.
The rent is not the cost of a leaseback; the cost is the rent plus the building handed over at the end, and the extra 40 per cent of proceeds is the most expensive money in the deal.
The proceeds repay debt, the lease creates a new one, and the leverage you report depends on which definition of debt the reader uses.
The rent grows for twenty years and then resets to market; the tenant may not last that long. The cap rate has to price both.
The headline price is what the buyer pays. The cash the company can spend is what is left after tax, the old mortgage and the buyer's security.
Each extra five years of lease adds less to the price and more to the share of it that depends on one tenant paying.
Rent is deductible, but the tax on the gain is paid at completion out of the proceeds, and that changes the after-tax cost more than the deduction does.
A strike above today's price looks like a premium to the buyer; set against the values the building could have at expiry, it is a cap on its upside.
A fixed-price repurchase option turns the sale into a loan: the gain disappears, the debt is the full price and the rent becomes debt service.
A master lease stops an insolvent tenant from keeping the good sites and returning the bad ones, until aggregate cover falls below the threshold and it returns them all.
Under US GAAP the seller-lessee recognises the whole gain on a qualifying sale, but only after pulling any off-market element of the price out into financing or prepaid rent.
A single-tenant building is worth its lease until the lease ends. The lender's question is what the loan balance is when the building is empty.
The lease is signed by an operating subsidiary and the price is quoted on the group. A survival-weighted cash flow shows what the guarantee bridging the two is worth.
Inverting a leaseback price into the tenant default rate it assumes, with rent, recovery and residual valued separately.
The arithmetic of the opco-propco split at the close of a buyout: how much is multiple arbitrage, how much is leverage, and what has to stay true at exit.
The same transaction raises or lowers return on capital employed depending on how the lease is counted, and the building's book value drives most of the answer.
The bankruptcy cap applies to the claim before the recovery rate, so a leaseback investor gets back far less of the rent it loses than a simple recovery assumption suggests.
Accretion is not a property of the leaseback. It is a comparison between the after-tax cost of the proceeds and what the cash earns, and for a buyback, the share price.
Companion workbooks: /srt
Risk-weighting a retained 1250 per cent position costs 168.75 per cent of face at a 13.50 per cent target; deduction costs 100.
A worked synthetic securitisation: the p-factor term by term, the exponential formula, and the attachment point where the floor takes over.
A worked synthetic securitisation from the bank's side: capital released at its own target, the true cost of protection, and the two ceilings.
The IRB formula looks forbidding and is five cells in Excel; worked once on a single loan, it explains why a bank's capital sits where it does and what a risk transfer can release.
The investor's return is not the coupon. It is the coupon on a balance that losses shrink and amortisation repays, and the losses are levered about fourteen times through a thin first-loss tranche.
Two changes to SEC-IRBA, one input halved and one floor lowered. On a typical structure only the first binds, and it is worth a third more capital relief.
The retained share, the margin over expected loss and the clearance above KIRB, worked on one fictional synthetic securitisation, with what each point of retention costs in capital.
The protected tranche's schedule under both repayment clauses, the investor's IRR by call date and the extra margin the bank pays, on one fictional synthetic securitisation.
Bucket by bucket from PD, LGD and maturity to the one number that anchors every SEC-IRBA tranche weight, worked on a fictional seven-grade corporate portfolio.
The three ways a bank can meet the 5 per cent risk retention rule in a synthetic securitisation, priced in capital released on one fictional corporate portfolio.
Each point of protection makes the senior lighter and the bill larger. The best detachment is where the risk-weight floor binds, and not one point further.
Four lines of arithmetic, two of which are usually left out: the deduction from capital, and the leverage ratio the trade cannot move.
The standardised formula worked step by step on a fictional SME pool, and why a standardised bank has to sell a much thicker tranche than an IRB bank to get the same relief.
Cash-collateralised notes against an insurer's guarantee on the same tranche: the capital each leaves behind, and the premium discount that makes unfunded cover worth taking.
The clearance between KIRB and the attachment point is not a buffer that holds the relief steady until it is crossed. The senior gets heavier with every notch of migration.
A worked example of the capital charge on committed excess spread, and the coupon cut an investor must give for it to pay.
A worked example of an SRT measured on both ladders, year by year to 2030, and the tranche thickness that restores the relief.
From pool expected loss to tranche expected loss with the one-factor model, and why correlation matters for thin layers but hardly at all for a thick first-loss piece.
The test runs on risk-weighted amounts, not notional, so the tranche a bank keeps matters more than how much of the mezzanine it keeps.
A funded SRT investor lends to the bank as well as insuring its loans. In expectation the second exposure is small; in the scenario where both go wrong it is the larger loss.
Companion workbooks: /statements
Gross fee 4,312.50, offsets 2,175, net 2,137.50. Recomputing a private fund's management fee quarter by quarter.
A capital account statement is the one page an investor receives about its own money, and it can be rebuilt line by line from the fund's statements and a side letter.
The financial highlights note prints an expense ratio, and the number depends on three choices the note rarely states: which costs, which offsets and which denominator.
A concentration test any investor can run from the schedule of investments in ten minutes, and what it says about the NAV the fund reports.
The manager's figure and yours can both be right; the gap is two choices, the dates and the carry basis, and you can measure each one.
The statement of operations already holds the year's result; the denominator has to account for the capital that came in and went out, and the realised gain has to be read beside the unrealised line.
The percentage column on a schedule of investments passes 100 by exactly the fund's net liabilities, and the largest of them is usually the carry accrual, not the borrowing.
The top half of a fund's statement of operations is its cost base with a little income netted against it; the return sits in the gains below.
The one page that shows deployment, facility use and where distributions came from, worked line by line on an illustrative buyout fund.
The statement of changes in net assets, with its two partner columns, worked line by line on an illustrative buyout fund.
One fund's Level 3 reconciliation taken apart line by line, from the exits and their opening marks to the transfer that stops it tying to the statement of operations.
Where payment-in-kind interest hides in a private credit fund's statements, and what it does to the distribution coverage the report leads with.
Rebuilding the sensitivity the Level 3 note leaves out, from fair value, ownership, multiple and net debt, and why leverage doubles it.
The fund's balance sheet shows one rung of the debt ladder. Rebuilding the rest from the schedule of investments, and the check that proves it complete.
Deferred tax in a blocker corporation is a proportion of the gain, not a fixed deduction. It cushions a fall until the asset reaches its tax base, and then stops.
The two partner columns of a fund's statement of changes in net assets move by different proportions in a bad quarter. The carry accrual explains the gap.
Reading the age of the portfolio from the schedule of investments, by cost, by fair value and by tranche, and what each one hides.
Where non-accrual loans hide in a private credit fund's statements, and why the rate at fair value flatters the funds that mark hardest.
The fair value note's weighted average weights by equity, so sales and leverage move it as much as marks do.
The distribution notice, the capital account and the statement of operations describe the same cash in three vocabularies.
Companion workbooks: /stor
The £141 discount buys a customer worth £2,188 — and is only 52.7 per cent of what a move-in really costs.
The break-even move-out rate for an ECRI, in closed form, and why the answer depends on whether the size that empties is full or half-let.
The formula, the three inputs it needs from the rent roll, and why a store with lower occupancy can earn more per foot.
From rent roll to value on an illustrative 50,000 sq ft store, and the test every self-storage rent roll needs because it has no leases.
A self-storage store fills one customer at a time and empties the same way. The stabilised level and the time to reach it follow from two numbers.
Operating, debt and covenant break-even for an illustrative store, measured on area, with the rent that moves underneath them.
Three definitions of length of stay run on the same illustrative store, and why the one most rent rolls report is the wrong one.
Supply per head means nothing on its own. Divided into demand, it gives the occupancy a catchment can hold.
The existing customer rate increase that maximises net income, found from one measured cycle and the shape of the response.
Small units cost more per foot than large ones, so the average depends entirely on what it is weighted by.
Tenant protection is the largest ancillary line in self-storage, and the easiest to overstate in a sale pack.
Convert the build rate from gross to net rentable area, then add land, interest to stabilisation and the lease-up deficit before dividing NOI by cost.
Price climate control as a capital project: incremental NOI after the fee and the cost of conditioning every foot, against the cap rate, with occupancy kept in the formula.
A 60,000 sq ft shed with a mezzanine against a purpose-built store on the same road: cost per net rentable foot, yield on cost, and the rent discount that decides it.
Three loan limits on one store with no leases, and why the lender's question is what the rent roll earns at the price on the website.
New supply in the catchment reaches the rent roll through four lines, and most of it arrives after the trailing twelve months have been read.
A worked break-even for handing a store to a third-party manager: the fee, the costs the owner stops paying, and the uplift that has to cover the gap.
An extension shares the store's staff, office and systems, so its margin is far higher than the store's. Costing it at the average ratio understates the value it creates by more than two fifths.
The delinquency rate is a snapshot of who is late today; the cost depends on how many cases end in payment, a quiet move-out or an auction.
The partition is cheap and small units earn more per square foot. What decides the conversion is whether the new doors bring new customers or spread the old ones thinner.
Companion workbooks: /valuation
The protective-put method peaks at 28.6 per cent and cannot reach a conventional 30 per cent discount at any holding period.
Calibration worked on a two-year-old buyout: the discount at entry, the day-one test, the roll-forward, and what happens when the discount is changed.
The yield method on a floating-rate direct loan: the calibrated spread, the market move, the life assumption, and why the base rate hardly matters.
The enterprise value to equity bridge for a fair value mark, line by line, and how much each judgment moves a leveraged company's equity.
A preferred round price values the preferred share, with its liquidation preference, not the company. Backsolving it through a scenario waterfall gives both the equity value and the common.
The multiple is the last step, not the first: the defensible value comes from the normalisation and from adjustments that can each be challenged on their own.
The probability-weighted expected return method is simple arithmetic; what makes it defensible is forcing it to reproduce the price investors just paid.
A DCF run at a textbook WACC rarely reproduces the price a buyer actually paid. The gap is information, and calibration carries it into every later mark.
Once a borrower defaults, the contractual cash flows stop being the asset. The mark has to come from the enterprise value and the queue in front of the loan.
When EBITDA is negative, revenue is the metric left, and most of the spread in revenue multiples is growth, so the median peer is the wrong benchmark.
The model is a standard option formula; the mark is decided by the share value, the term the warrant is expected to live, and the dilution its own exercise causes.
The Finnerty average-strike put formula worked by hand, its grid by volatility and term, and how it sits beside the Chaffe and Longstaff models.
Trailing and forward EBITDA multiples on the same peer set, when they agree, when they should not, and the mismatch that inflates a mark.
One identifiable exit as a PWERM scenario, everything else as an option pricing model, both calibrated to the latest preferred round.
Scenario payoffs from the SAFE's own terms, a discount rate calibrated to the price paid, and the remark when a term sheet arrives.
Breakpoints, Black-Scholes calls and a goal seek: the option pricing model calibrated to the latest round, worked from start to finish.
A worked scenario valuation of a venture convertible note, with interest accruing to each event and conversion at the better of the cap and the discount.
A signed price is the best evidence a valuation team gets, but it is not yet cash: here is the bridge from the term sheet to the mark.
A PIK return, a 1.6x minimum multiple and four exit scenarios: why the floor turns the exit date into the biggest driver of the mark.
The premium is easy to estimate and easy to misapply. Whether it goes in full, through beta or through lambda, and whether the risk-free rate already carries it, moves the value by a fifth either way.
Companion workbooks: /venture
151,970,000 called against a 150,000,000 commitment: the recycling clause, and the 1,970,000 nobody signed for.
From net to gross in two steps: carry on the way down, fees on the way across. And why dividing the target by 0.8 leaves investors at 2.6x.
The median, the mean and the fund multiple of one illustrative portfolio, and how much of the result rests on a single line.
Portfolio size does not change a venture fund's expected multiple. It changes the shape around it, and that shape can be computed exactly.
Gross MOIC and net TVPI on the same twenty-eight companies, and where the 1.60 turns between them go.
The follow-on multiple equals the first-round multiple divided by the step-up, and half the fund sits on it.
One illustrative venture fund, carried interest computed three ways on identical cash flows: no hurdle, an 8 per cent hurdle with full catch-up, and the same hurdle without one.
A venture fund distributes newly listed shares instead of cash. The reported DPI, the cash the investor actually receives, and what happens to the carried interest when the price moves.
Split the manager's take into fee profit and carried interest at four outcomes, and the incentive of a small fund looks very different from that of a large one.
A premium carry ladder costs the investor little at 3x and a lot at 6x, and if the higher rate applies retroactively it creates a band where the investor is worse off when the fund does better.
A venture fund's multiple is earned over the gap between the average call and the average distribution, about 7.7 years here, and that gap sets the IRR.
A probability tree from seed to exit, the expected multiple it implies, and why a 30-company fund with the right average can still return less than half its money.
Carried interest takes the same share of the money whenever it is paid, but the earlier the general partner is paid, the more of the investor's rate of return it takes.
Four lines that tie fund size, number of companies, reserve ratio and ownership target together, and the round price hidden inside them.
From the net target to proceeds, from proceeds to a count of billion-dollar exits, and why fund size multiplies the count while only ownership divides it.
A year-by-year cash profile shows how far the cash return of a venture fund lags its paper multiple, and what moves the date.
A secondary sale of the best position swaps marked value for cash at a discount, and the right test is the break-even exit multiple, not the DPI it adds.
The Section 1202 exclusion is an LP-level number built from fund-level facts: who the LP is, what qualifies, and the per-issuer cap.
A single-deal SPV often has no annual management fee, but its fixed and one-off costs come off the top and its carry has no losers to net against.
Recycling is a loan of the LP's distribution back to the fund, and 1.00x is not its break-even.
Companion workbooks: /wealth
The growth rate peaks at 48.1 per cent in month 29; gross flows are still climbing at month 84. Both numbers are right.
Management, performance, servicing, platform, advice and an upfront load, lined up in one column. The sum of the fixed fees is not the cost.
The wealth channel funnel worked backwards, from the sales target to producing advisors, advisors in scope and the size of the external team.
The feeder layer worked on a 1,000,000 commitment: what the placement and servicing fees take in IRR and in multiple, and why the drag is larger than the fees read.
The trail a manager pays a private bank is a share of the management fee, so it follows the client's NAV, and the manager's real margin is what is left.
The division gives the book size that pays for the team; a flow model gives the month it gets there, and the month the losses are finally repaid.
Two share classes of the same semi-liquid fund, the holding period at which they cross, and what each one pays the distributor.
Cost to serve one investor against the manager's fee after retrocession, the floor below which no holding period helps, and why low minimums need an omnibus platform.
Selling days, meetings and calls on one side, a tiered target list on the other: the coverage arithmetic behind a wholesaling team.
A dedicated, cheaper share class for one private bank, priced on new money, cannibalised money and the side letters that may claim the same discount.
A tiered upfront fee is not a tax bracket: it applies in full at the tier reached, which creates cliffs, dead zones and a 10,000 lesson in household aggregation.
A top-down sizing that starts from the bank's eligible clients and mandate split, and ends at a figure a fundraising plan can carry.
Permanent capital sounds more valuable than a ten-year commitment. Discount the fees, count the retrocession, the redemptions and the cost to raise, and it usually is not.
The three costs of a hedged class in a semi-liquid fund, and the cash a currency move demands at the next roll.
A wealth channel forecast is advisors times conversion times tickets times ticket size. Each driver leaves a different signature when it misses, and a late platform disguises itself as weak conversion.
A monthly model from in-scope advisors, conversion and ticket size shows why the launch ramp, not returns or redemptions, sets the date.
A delay at launch is not lost at the launch run rate. It is lost at the mature one, and it stays in the AUM long after the platform is live.
DRIP shares grow with NAV, not with the sales effort, so counting them as fundraising makes flat sales look like steady growth.
Gross or net of redemptions, flat or tiered: two plans that cost almost the same at target and pay very different wholesalers either side of it.
A 3(c)(7) feeder has no investor cap of its own. The Exchange Act holder of record threshold sets one, and the average ticket of the wealth channel turns it into a dollar capacity.
Companion workbooks: /coo
An administrator 80,000 cheaper on the invoice is only 17,488 cheaper to run, and the 188,000 move takes 10.7 years to pay back.
A capital call worked component by component with one investor excused from the investment, the rounding residual placed once, and the shortcut that overcharges everyone.
Annual utilisation hides the month that breaks the team. The capacity model built by month, the hours over an 85 per cent ceiling, and what moving the audit work buys.
Two bases, two rates and a day count inside one quarter. Get the date or the convention wrong and the invoice is out by six figures.
A recallable distribution pays the investor and restores its obligation to fund by the same amount, so call capacity, DPI and the capital account all move.
The basis-point quote is applied marginally, the minimum turns it into a fixed fee for small or ageing funds, and a third of the bill sits outside it.
Rebuild the fees fund by fund, net the offsets, leave the carry out, and watch what a single step-down does to the management company.
A close is a network of dependencies, not a checklist: compute each path's finish and slack before setting a target or fixing a delay.
One quarter's management fee with a step-down, a side-letter rate, an offset and one investor's waiver, done right and done the way a top-level reconciliation cannot catch.
The cap measured on final commitments, the excess offset against the management fee, and the true-up between the first and the final close.
A fourteen-field administrator scorecard worked month by month, with the critical gate that no average or weighting can replace.
One capital call, a ten-business-day notice period and a facility that has to bridge it, computed as the deal team assumed and as the lender computes.
A NAV error in a fund that deals is not one number but three: what redeeming investors were overpaid, what subscribing investors were short-changed, and the fees charged on value that was never there.
A full annual cost for both models, the break-even NAV, and why adding funds pushes the break-even further away.
An expected-cost comparison of review-only oversight, a targeted shadow of the calculations, and a full duplicate set of books.
The running-cost comparison always favours building; development, upgrades and timing usually reverse it, until the fund count rises.
One invoice covers the funds and the manager's own business; the first split is by coverage, and it moves the answer more than the key.
Every call has a fixed cost and every early dollar has a carrying cost. The cheapest frequency depends on when the fee falls due, and on whose cost you count.
The tax is one investor's, the cash leaves one bank account: why splitting the net amount by share makes the other LPs pay 360,000 they do not owe.
Administration is the visible part. Audit, tax compliance and registered office fees are charged per entity, and the small deal vehicles carry a share of the bill out of all proportion to the money they hold.
Companion workbooks: /costcontrol
A 14,500 weekly damages rate against 34,640 of interest on the client’s facility: it stops covering the interest above a 41.9 per cent draw.
Every priced preliminaries package holds at least three weekly rates, a quarter or more apart, and the one in the contract total is the one that should never be used.
Escalating to the start on site leaves out almost a million, escalating to completion adds one, and on a back-loaded scheme even the midpoint is short.
Retention is a percentage of cumulative value held back on every interim certificate and released in two halves; the arithmetic is simple, its cost to the contractor is not small.
Earned value at month 12 of a building contract, three ways to forecast the outturn, and the input that hides an overrun.
Expected value, exact percentiles and what a flat 5 per cent really buys, on an eight-line register.
Each layer of a contract sum is a percentage of the layer beneath it, so the percentages compound, and a percentage quoted without its base means nothing.
Most change order disputes are about the add-ons, and the same 420 m2 of work can be valued anywhere across a 30.3 per cent range.
The contractor's productivity on the same work, before and during the disruption, is the record that turns lost hours into money.
Omit the sum, add the work valued under the contract: the difference between that and the net expenditure is where final accounts surprise.
Eichleay allocates head office overhead to the contract by its share of billings and spreads it over the days actually worked, which is why it gives less than Emden on the same accounts.
One formula spreads the contract sum over the programme, sets the monthly funding peak, and shows how much a front- or back-loaded programme moves the interest bill.
The anticipated final cost line, built from provisional sums, agreed and pending variations, claims and open risk, and why a report of agreed changes reads low.
The NEC Option C style calculation: price for work done, share ranges applied in slices, what the client pays, and the overrun at which the contractor's fee disappears.
The all-in labour rate from paid and productive hours, the gang rate and output, waste, and plant spread over the pour, with the two judgment inputs stress-tested.
Labour prime cost is the annual cost of employment over the hours actually worked, and the percentage additions go on that, never on an all-in rate.
A late week costs the contractor its site as well as the damages, and the right answer is rarely to recover every week.
A front-loaded tender matches the cost plan in total. The rates move money forward in time, and the client finances the difference.
The recovery clause decides when the advance comes back, and on an S-curve it comes back out of the contractor's busiest months.
Remeasurement pays for what is built, but a rate with fixed costs spread across the bill quantity stops being fair once the quantity moves far enough.
Companion workbooks: /energy
A retail book hedged with a flat block reports 25,883,698.63; priced in its hours, the load shape takes 22,282,166.81 of it, 86.0857 per cent.
The formula takes three lines. The mistake is applying it to the annual average price when the plant only runs in the hours above its marginal cost.
A solar park sells in the hours the sun shines, and those are the hours everyone else's panels are selling in too. The capture rate measures how much that costs.
One identity turns two quoted forwards into the third price, and the hour count decides whether it is right.
MW times hours, times the move, every morning: why a hedged generator runs out of cash before it runs out of profit.
Power over gas, compared with the plant's own heat rate plus variable cost, hour by hour rather than on the annual average.
Why a generator hedged on its availability is really short, how large the true position is, and what a 10 per MWh rise does to it.
A short baseload strip valued month by month, with the hour counts, the discounting and the two shortcuts that move the answer.
An outage removes particular hours, and the hours decide the bill. The average price of the window says almost nothing about it.
Every start burns fuel, emits carbon and wears the turbine before a single MWh is sold. Short runs that look profitable hour by hour often are not.
Sort the hourly prices, take the round-trip losses off the discharge and haircut for forecasting: a daily high and low are not a revenue model.
A toll is an option on the spark spread in every hour; priced on the flat forward the plant is worthless, priced on the hours it earns a fee.
Intrinsic value is the spread you can lock in today on the forward curve. It is an optimisation over months and rates, not the gap between two seasonal strips.
The switching price is where a gas plant's and a coal plant's marginal costs, fuel, carbon and variable O&M, meet. Above it gas runs first; below it, coal does.
Sorting a year of hourly power prices, reading the averages it hides, and why the top 100 hours matter more to a plant than to the forward.
Why the fuel hedge belongs on the dispatch, not on the availability, and what the surplus gas does to the year and to the margin account.
A gas plant's dispatch right priced as a call on the spread, step by step, and the correlation that decides it.
Short and long volumes cancel over the year. The cost does not, because a wind farm's errors move the system the same way.
Valuing an FTR obligation and an FTR option from the hourly congestion spread, and why most of the value sits in a few hundred hours.
The NBP, TTF and Henry Hub conversion step by step, with the volume match for hedges and the calorific value trap that distorts spark spreads.
Companion workbooks: /edp
A partner’s EDF co-financing is repaid by margin only at a 58.7 per cent procurement probability; holding the prototyping, 86.7 per cent.
Companion workbooks: /contracts
Paying the repair instead of the part is worth 200,336.62, more than the extra warranty year at 196,996.34, which falls to 23,019.80 on a part-only remedy.
Whole-volume or shortfall drafting: one phrase in a volume band clause, a factor of 14.28 in what it costs.
Two base prices, two firm periods, one cap, and the quarter in which the cheaper bid becomes the dearer contract.
Price each clause per unit, probability-weighted, add it to the headline, and solve for the price at which the cheaper bid would really be cheaper.
The formula, the three drafting details that move it, and the expected cost per unit of a weak clause.
Expected recovery at 100, 150, 200 and 300 per cent of the charges, what a higher cap is worth paying for, and why the exclusion decides it.
Two different numbers hide behind the cost of getting out of a contract, and mixing them keeps businesses in contracts that lose money every month.
A contract priced in the supplier's currency is an open foreign exchange position for the whole term, and it can be priced three ways on the same scenario.
A fixed element, a weight per index and a base date: three drafting choices that decide what an indexation clause pays.
A benchmarking clause is an option the buyer holds, and it can be priced before anyone knows whether it will trigger.
A year of on-time-in-full deliveries run through a service credit regime: the monthly credit, the cap, what the buyer actually lost, and the rate and cap that would make the clause compensate.
An evergreen clause priced on one supply contract: the renewal price, the market price, the term, and the switching costs it only defers.
The event list and the exit right, priced as replacement supply on one three-year contract, with the tail the expectation hides.
Material net of scrap, conversion at a machine rate, reject allowance, SG&A and a fair profit, then the gap attributed driver by driver.
Overcharges, unclaimed rebates and credits, index cuts never applied, early payment and off-contract buying, each priced against the contract's own terms.
The statutory rate, the fixed compensation per invoice, and what a weaker contract clause gives up before anyone pays late.
TCV, committed value and the value with options answer three different questions, and the approval threshold depends on which one you use.
A fixed price looks dear against the supplier's estimate plus margin. Against the expected cost of cost-plus, the gap is the price of insurance.
The financing rate in the adder matters, but the unit cap and the true-up clause decide most of the money.
The clause pays the gap to a comparable customer's price, and most of the arithmetic is in making the comparison comparable.
Companion workbooks: /bsb
A 2,600,000 price with two seller notes is worth 2,533,642 in cash to the seller, and paying that in cash lifts year-1 coverage from 0.96 to 1.04.
A broker's multiple of SDE and a lender's multiple of EBITDA are not the same price, and the gap between them is two lines of the earnings bridge.
Turn the lender's coverage ratio around and it gives the most a business can be financed for, and how much of that ceiling the business cannot actually pay.
The multiple gets the attention, but the SDE it multiplies decides the price, and the result has to survive the debt service before it is a value.
Total project cost, the equity injection, pre-closing spend and a reserve, with the one seller note structure that actually reduces the buyer's cheque.
Turn the customer into profit, weight the two outcomes, then find the price at which the loan still gets paid if the customer leaves.
The year-1 return on an illustrative 1,500,000 SBA-financed purchase, measured after paying the owner a market salary.
Two allocations of the same illustrative 2,000,000 asset purchase, valued from both sides of the table.
The payment on an SBA 7(a) acquisition loan follows from three things: the financed guaranty fee, a ten-year term and a variable rate.
A multiple of SDE is not a payback period. The cash that repays the price is what is left after a manager's salary, the equipment and the tax.
Plus inventory or including inventory: the same business costs 180,000 more or less depending on one line of the letter of intent, and the multiple means nothing until it is stated.
The 3-2-1 weighting protects a buyer when earnings rise and works for the seller when they fall. What it replaces is evidence about the latest year.
A broker's add-back schedule tested line by line, the break-even finding, and what the report does to the price and the loan.
Receivables excluded, bought at face or bought at collectible value: the cash each structure costs the buyer, and the shortfall that arrives in the second payroll.
The bank sets your salary before you do. Here is the ceiling a 1.25x coverage test puts on it, what is left for tax, and why taking the full amount leaves no margin.
Owning the premises feels safer than renting from the seller. Priced as its own investment, with the loan, the tax and the exit, it is usually a modest real estate return bought with scarce cash.
A healthy DSCR at closing hides how little revenue the business can lose, because fixed costs stay put when sales fall.
The discount for owner dependence is the profit that leaves with the owner, and a seller transition is the cheapest way to keep it.
A rollover as business start-up defers the income tax rather than avoiding it, so the true saving is the penalty less the fees.
The lender underwrites the guarantor's household as well as the business, and the house and the car go into the denominator.
Companion workbooks: /costing
A bushing quoted at 5.90 against an absorbed 6.53 looks like a 1,162,407 saving and costs 2,857,439 a year; no avoidable share makes buying right.
The same 13,440,000 of overhead, five drivers instead of one, and a profitable part that turns out to lose 25.5 per cent.
Divide overhead by actual hours and the cost of an empty shift disappears into every part the factory did make.
Two formulas that must add back to the total, worked on one month of a moulding line, and the cheaper grade of material that cost more than it saved.
Strike the rate, apply it to actual hours, then split what is left into spending and volume before deciding where it goes.
Two income statements for the same factory, the one-line reconciliation, and how much profit overproduction can manufacture.
The cost-plus formula is one line of arithmetic; the cost it is applied to decides which orders a factory wins and which it loses.
The schedule that turns a factory's costs into cost of sales, and decides how much of them waits on the balance sheet instead.
One machine, five fixed costs, two running costs and the choice of hours that decides the answer.
Setup, order handling and inspection are paid once per order; the minimum quantity is how many units it takes to carry them.
A factory's direct labour line split into a rate and an efficiency variance, then the overhead variance a labour-hour absorption base drags along with every excess hour.
A one-off order priced below absorbed cost, worked through variable cost, order-specific costs, capacity and the opportunity cost of displaced sales, with the minimum price for each route.
Process costing worked both ways, weighted average and FIFO, with the estimate that moves cost between profit and stock.
Three conventions for dividing the cost of one process between its products, and the decision none of them can make.
Three ways to push maintenance and stores costs into production departments, worked on the same factory, and why the step-down order can move cost more than the method does.
The two variable overhead variances, worked on a factory that absorbs on labour hours, and why the efficiency variance says more about the absorption base than about the overhead.
One variance is an overspend someone can explain; the other is output that never absorbed a cost already paid.
Fit the rate to the pilot, cost the increment rather than the average, and know which of the two learning curve models you are using.
Normal spoilage belongs in the product's cost; abnormal spoilage belongs on the income statement, and the equivalent unit count decides whether it gets there.
When production leans on the cheaper ingredient, the usage variance hides a saving and a loss that only the split can separate.
Companion workbooks: /fpa
A revenue commission pays a representative to discount from 4.55 extra units per hundred; the company needs 11.40. Cutting the rate moves neither.
Allocation moves profit between segments without moving a dollar of cash. Before a segment is closed on its allocated loss, the closure test has to be run on contribution and avoidable cost.
MAPE says how far off the forecast is. Bias says which way. A forecast with a large bias is not noisy, it is wrong in a direction you can correct.
Three columns instead of two: the static budget, the budget at actual volume, and actual. The middle one decides who explains what.
Five ways to turn nine months of actuals into a full year, and the fourth quarter each of them quietly promises.
The cost line by line, per year and per productive hour, with why one multiplier misstates junior and senior roles and how to budget a mid-year hire.
Break-even, margin of safety and operating leverage for one illustrative company, and the gross-margin shortcut that gets break-even wrong.
One illustrative quarter's budget-versus-actual report, with costs, losses, a zero budget and a line that changes sign.
A budget split into twelfths reports seasonality as variance. A seasonality index built from two years of history puts each month where it belongs.
A new role costs a fraction of its salary in the year it starts and all of it every year after. The budget needs both numbers.
This year's local revenue at last year's exchange rates, the bridge from reported to constant currency, and the same method used to split a budget variance into trading and FX.
A favourable payroll line is usually empty roles sitting on top of a rising cost per head. The three-way split into headcount, grade mix and pay shows which is which.
A revenue beat should reach profit at a rate you can calculate in advance; the gap is the cost that grew when it should not have.
A two-month shortcut to the cost split every flexible budget needs, tested against the other ten months.
A gross margin percentage bridge for a three-segment business, the two conventions in use, and why they disagree by 0.31 points.
A driver tree for an equipment business with recurring revenue, the next year it forecasts, and the ten per cent test that ranks the drivers.
The vacancy factor built from attrition and time to fill, then netted for the agency cover and recruiter fees that quietly spend it.
Stage percentages are labels. Fit them to history, add timing, set coverage from your own conversion and report a range.
Countback DSO matches receivables to the months that are actually unpaid, so seasonal sales stop looking like slow collections.
A worked depreciation budget: the existing base with its roll-off, new assets from the month they enter service, and the conventions that move the number.
Companion workbooks: /supplychain
A 10 per cent under-forecast costs AF-7 8,952.25 EUR a year; the same over-forecast saves 2,168.93, because it quietly lifts the board’s 98 per cent to the optimum.
Add the variances, not the standard deviations, and find out who really owns the uncertainty: the market or the supplier.
Two measures both called service level, 1,709 units of safety stock apart, and the batch size that links them.
The square-root formula worked on one part number, the cost curve around it, and why the inputs matter more than the formula.
The formula worked on one part number, and the trap that catches it whenever the lead time is longer than the order cycle.
Four regional depots against one central warehouse, worked on one part number: what pools, what does not, and where the real cost of the network sits.
The all-units discount method worked on one part number, and why the deeper discount is not the cheaper one.
The cost-minimising cycle service level for a reorder-point system, worked on one part, and why the newsvendor ratio gives the wrong answer here.
The ratio built from the bottom up on one stocked part, so you can see which decision, the order size, the service level or the supplier's reliability, actually sets the number.
The (R, S) policy worked on one stocked part: the protection interval, the order-up-to level, the order placed at each review, and why the review period costs less buffer than textbooks suggest when the supplier is unreliable.
The holding rate is four costs added up and applied to stock at cost, and on a part where safety stock dominates, three-quarters of the bill is the buffer.
When stock is planned against a forecast, the buffer covers what the forecast misses, and how much a better forecast saves depends on how reliable the supplier is.
Reliability is worth a price premium, and the premium is the annual policy cost it removes divided by the units you buy, not the stock it releases.
The lead-time standard deviation drives most of the safety stock, and it takes far more goods receipts to pin down than most planners use.
The economic order quantity ignores shortages and the optimal service level takes the batch as given. Solved together, the batch grows by a third and the reorder point falls.
A shorter lead time lowers the reorder point by weeks of demand, but stock on hand barely moves unless the supplier's spread shrinks too. The money is in the pipeline, and only on the right delivery terms.
Nobody upstream is irrational. The order-up-to rule itself turns a steady market into lumpy orders, and the size of the swing can be written down before a single week is simulated.
One order, no second chance: how the margin and the loss on leftovers set how far above or below the forecast to buy.
ABC ranking shows where the money is, which is where safety stock is dearest, not where it does most good.
A kanban loop is a reorder point counted in containers, and the flat safety factor in the textbook formula has no idea how variable demand is.
Companion workbooks: /tradefinance
A 6.90 per cent discount on the price costs 72,450 over 90 days; an 8.40 per cent facility on the cost costs 71,883. The lower rate is dearer by 567.
A confirmation is insurance on the issuing bank and its country. Price it like insurance: the fee against the expected loss it takes off your books.
A factor quotes a discount rate and a commission as if they were separate prices. Annualised on the cash actually received, they are one rate, and it is higher than either.
Issuance, acceptance, advising, confirmation, examination: each on its own basis, and the rounding to whole quarters decides more than the rates do.
One open-account export order, priced with and without a policy: the premium, the uncovered tenth, the break-even default probability and the tail the expected loss hides.
The break-even price premium for granting credit, solved in closed form on one export order, and why the shortcut most sales teams use falls short.
Fees, financing and expected loss priced for both instruments on one export order, and the buyer default rate at which the answer flips.
Straight discount and discount to yield on a series of avalised notes, the equivalent yield, and the gross-up that keeps the exporter whole.
Why a confirmed usance credit that costs 5.53 per cent on a large export order costs more than the whole operating margin on a small one, and how to find the line for your own terms.
The refusal rate, the waiver rate and the days lost, turned into money on one fictional export order, and set against the bank and country risk the credit was bought to remove.
Hold the buyer's terms fixed, then price each route as financing, fees and expected loss. On fees alone open account always wins, and that is the wrong test.
The money is out from the first day of production, not from the invoice date, and it is the cost of goods that is financed, not the price.
The extra commission for non-recourse buys the buyer's credit risk and nothing else, so compare it with the expected credit loss you would otherwise keep.
Under a UPAS credit the exporter is paid at sight and the buyer gets its term, so the discount does not disappear: it moves to the applicant.
Both collections leave the exporter without a bank undertaking. The difference is the buyer credit D/A grants, which runs from acceptance, not shipment, and the risk that comes with it.
One is priced on the buyer's credit and funds the whole invoice; the other is priced on your receivables and advances part of it. The headline rates hide most of the difference.
One buyer's credit, one supplier, two ways to pass the payment through: the fees, the blocked cash and the risk the trader carries, priced line by line.
The fee is the small part of the sum. Cash collateral, the expiry clause and the discount the buyer asks for decide whether the advance pays.
The premium is quoted once and paid on day one, so its annual cost depends on how fast the loan amortises, and it is larger than it looks.
The premium is charged on 110 per cent of the CIF price it belongs to, so the price has to be solved, not stacked.
Companion workbooks: /notes
A court timeline takes $45,080 off Harlow Street’s maximum bid, 39.26 per cent of the non-judicial price; 84 per cent of it is waiting, not legal fees.
A worked owner-financed note with a balloon: the price at a required net yield, the yield at the seller's ask, and what payoff and extension do to it.
One non-performing first lien, two paths valued month by month, and why the bid still belongs to the path that needs no cooperation.
A partial buys the next stream of payments and leaves the balloon with the seller; it is safer than the whole note and far more sensitive to fixed costs.
Every note yield is a yield to an assumed payoff month, and which month you assume decides whether you overpay.
A second lien is a levered position in the house, and its price starts with one line: net value less the first lien's payoff.
Gross and net yield worked on one illustrative performing note, then the same fees applied to notes from 15,000 to 160,000.
Eviction against a negotiated exit after foreclosure, priced month by month on one illustrative REO, with the break-even offer by timeline and value.
Investment-to-value is the note buyer's quickest screen, but the right number is not a rule of thumb: it falls out of the foreclosure timeline and your required return.
A default overlay replaces the promised payments with expected ones: survival-weighted payments plus a recovery from the house two years after each default.
A pool has no yield of its own: it is the sum of its loans, and the loans priced as an average are where a tape quietly takes your return.
Borrowing to buy a note raises the return only while the unlevered return beats the all-in cost of the loan, and on a non-performing note the timeline decides which side of that line you are on.
A non-performing first lien bought at a discount, cured by the borrower in month 7: the quote line by line, the payoff it is not, and the return it gives the note buyer.
An owner-financed sale priced the way a note buyer will price it: the rate that lets the seller cash out at face, and what each point below it costs.
The payoff statement a note holder sends when the borrower sells or refinances, built line by line, with the day-count and the good-through date.
A seller-financed note that wraps an existing low-rate mortgage, priced as what it really is: a leveraged position in the seller's own note.
When the borrower stops paying the mortgage, he usually stops paying the taxes and the insurance too. In a foreclosure, the note holder pays them and rarely gets them back.
Buy, modify, season, sell: how the buyer's yield falls with payment history, what that does to the exit price, and what a re-default does to the return.
A borrower's Chapter 13 filing stops the foreclosure and replaces it with a five-year plan. Whether that helps or hurts the note depends on what the foreclosure would have recovered.
The alternative to a short sale is not the value of the house or the debt. It is a year or more of foreclosure, and the price follows from that.
Companion workbooks: /projectfinance
A 1.45 times cover test would lend Northgate 538.1 million; the 65 per cent cost cap lends 427.3, and the 110.7 refused buys 13.6 points of rent cushion.
A cash reserve enlarges the loan that sizes it, and then earns a deposit rate on borrowed money.
The average-balance rule of thumb misses draw timing, compounding and the fee drawn on day one, and the gap travels into every ratio downstream.
Why the energy has to be discounted too, the capital recovery shortcut and where it misses, and how capacity factor and the discount rate move the answer.
One operating year run through every account to the cent, then the same year with 10 per cent less revenue and the distribution gate shut.
Fee, interest during construction and the reserve all grow with the loan. Turn them into one factor and the loop solves in a line, or in six passes.
Sizing DSCR, debt, gearing, equity IRR and covenant headroom worked on one illustrative contracted project, ratio by ratio.
The investment and production tax credits valued side by side on one illustrative solar project, with the break-even capacity factor and cost.
The PPA price a sponsor can bid is an output of the debt sizing, not only of the cost of the plant: solve it with the loan moving, or the answer is wrong.
The tail is the contracted life left after the loan matures. It costs debt on day one and buys the room to restructure later: here is how to price both.
The bridge defers the sponsor's cheque to commercial operation, so the IRR rises whenever the bridge costs less than the equity return; value is created only when it costs less than the sponsor's cost of capital.
The years after the power purchase agreement carry little weight in the project's value and a great deal in the equity's, because the lenders have already been repaid out of the contracted years.
A partnership flip on an illustrative ITC solar project, year by year: what the investor pays, where its return comes from, and why the flip date moves with the sun.
A seven-year loan on an eighteen-year repayment profile: the balance it leaves, what step-ups and a cash sweep do to it, and the refinancing rate at which the plan fails.
The cash a refinancing releases is not the gain: the higher debt service and the lost tail years have to be netted off first.
A holdco loan sits behind the senior debt, so its cover ratio looks generous and is not: distributions fall several times faster than revenue.
The reserve is one PMT on an inflated net cost. When you start funding it is worth more to equity than the deposit rate it earns.
Curtailment removes revenue but leaves the operating costs in place, so the loan falls faster than the megawatt-hours.
The gain on a sale at commercial operation is two things: time at the construction-stage rate, and a lower rate once completion risk has gone.
Two numbers decide whether a fire during construction becomes a debt default: the indemnity period and the basis of the sum insured.
Companion workbooks: /immobilienfonds
Unter der Kreditgrenze ist der faire Rücknahmeabschlag genau der Verkaufsabschlag von 12 Prozent, an der Grenze 17,14; ein pauschaler Abschlag von 5 Prozent lässt die Bleibenden 3,18 Millionen tragen.
Companion workbooks: /pricing
Distributors buy 8.67 weeks ahead of a 2.5 per cent increase, taking back 59,840.25: exactly a fifth of what they owed. Their volume then falls 67 per cent.
The invoice admits 12.8 points of discount. The pocket price waterfall finds 24.0, and more than half of the contribution.
Five effects, one check line that must read zero, and a volume year that turns out to be a price year.
The midpoint formula, a control region and a contribution check, worked on one price test, and why an elastic reading can still mean the rise paid.
The four profit levers moved one per cent each on one company's books, why price beats volume by 3.63 to one, and the base most people compute it on wrongly.
The rebate cliff worked on one account: the effective price of the units that cross the tier, the two thresholds where they become free or loss-making, and what an incremental scheme changes.
Match or hold, priced on one product family: the cost of matching, the defection that would justify it, and the elasticity at which the answer flips.
From the increase the board announced to the one the invoices collected, split into rate, timing and concessions.
Three accounts, one product, and the ranking that inverts when orders, visits and payment terms are charged to the customer who causes them.
The spread of what customers pay for the same item, once every deduction is off, is the cheapest place to find price.
Four things a price increase can protect, four different rates, and the volume each one can afford to lose.
A skipped increase lowers every later price, while costs keep rising on schedule. Worked over five years, with the volume a lower price keeps.
A discount authority matrix built from the extra volume each discount needs, instead of flat 5, 10 and 15 per cent bands.
Fit a logistic win curve to past quotes, multiply it by the margin each discount leaves, and solve for the peak; then see what a revenue commission does to it.
Value-based pricing as a cost-of-ownership comparison run backwards: the parity price, the components of differentiation value, and how much of it to keep.
A discount ranking by salesperson is mostly a ranking of account mix. Adjust for the accounts, then test what is left against chance.
The annual discount buys retention and early cash. Price both, and two months free turns out to be a giveaway.
A bundle discount converts customers who buy one product, and is handed for nothing to those who already buy both. The right depth balances the two.
Four questions, four curves and four crossing points, worked through on an illustrative survey, with the cleaning step and the segment split most analyses skip.
Part-worth utilities become money through the price coefficient; a logit share simulator then turns that money into a price.
Companion workbooks: /financialmodeling
A 9.0x exit after a 10.0x entry implies 4.10 per cent perpetual growth; at the DCF’s own 6.97x the buyout returns 1.75x, not 2.35x.
Companion workbooks: /tax-liens
A homestead certificate clears 8 per cent down to a 4.25 per cent bid; vacant land needs 17.75. Bid at every floor, the sixty certificates still earn 7.99 per cent.
Companion workbooks: /buyouts
A 17.05 per cent buyout leaves the investor 12.70 per cent: the fee takes 1.90 points, the carry 2.44.
The interview test in four steps, sources and uses to IRR, with the shortcuts that keep you within a few hundredths of the full model.
The exact grid by holding period, the logarithm shortcut for doing it in your head, and why the same 2.20x can be 17.1 or 23.9 per cent.
Interest limitation rules turn excess leverage into deferred deductions. Whether they cost real money depends on whether the company grows out of the cap before exit.
The entry price sensitivity worked on a five-year buyout, with the debt held constant so that the table measures price and nothing else.
A recap brings cash forward and pays for it with interest, so the rate of return and the multiple move in opposite directions, and the trade only works while the deal earns more than the debt costs.
The sweep decides who holds the cash, the lender or the company, and that moves leverage far more than it moves the sponsor's return.
The maximum price is not a guess at the multiple. It is the exit equity discounted at the return the fund needs, plus whatever the lenders will put in.
The only clean way to measure leverage is to run the identical deal without it. The answer depends on one spread: the unlevered return over the after-tax cost of debt.
The exit multiple moves equity by exactly one year of exit EBITDA per turn, and how many IRR points that buys depends on leverage and the holding period.
Uses first, debt second, equity as the plug: a buyout's sources and uses worked line by line, and the 25.0 of non-price uses that a quick EV minus debt forgets.
The interest bill is the smaller channel. The larger one is how much the lenders will still advance, and the equity that has to replace it.
Why management and sponsor can pay the same price per ordinary share and still enter at prices twenty times apart, and what that does to each side's multiple at exit.
A vendor loan note is a second layer of leverage that the seller provides: the arithmetic of what it adds to the sponsor's return, where it starts to hurt, and what it costs the seller.
Work the LBO backwards from the return: the equity the target demands, the debt still owed, and the EBITDA that has to sit under them at exit.
The IRR and the multiple disagree about when to exit. The marginal return of one more year of ownership settles it, and it is a calculation, not a preference.
Fees raise the equity cheque on day one and shrink the proceeds at exit. The shorter the hold, the more of the IRR they take.
A holdco PIK note cuts the equity cheque and compounds quietly to exit. Whether it helps the sponsor comes down to one comparison.
Working capital costs an LBO the change, not the level, so the faster the plan grows, the more cash it never sees.
An IPO sells the first tranche of the stake at a discount and leaves the rest to a sell-down priced by the market, which a valuation headline does not show.
Companion workbooks: /creditinvesting
A CCC bond quoting 10.06 per cent is expected to earn 1.06 after default losses, below a 4.00 per cent Treasury bill.
Three fictional BDCs, one income stack each, and the leverage that makes a high dividend yield the one the income does not pay.
A fictional BDC bought at 80 per cent of NAV, its return split into dividends, NAV and discount, and the exit discount that decides it.
Duration is a weighted average of when the money comes back; modified duration turns it into the percentage the price moves for one point of yield, and convexity fixes the rest.
One equation, solved by trial and error or by RATE(). The bond's coupon and its current yield are both lower, and the return actually earned can be far lower still.
The distribution rate is a payout. The return is gross income on levered assets, less borrowing, three layers of fees and credit losses, and half of the gross never reaches the investor.
Yield to maturity, yield to each call and the minimum, worked on one illustrative callable high-yield bond, with the price at which the worst date changes.
Attachment, detachment, loss given default and the annualised default rate, worked tranche by tranche on one illustrative CLO, with the loss grid and a recovery stress.
The arithmetic takes one formula; deciding which yield to weight decides whether the answer means anything.
The payout floats with SOFR, the defaults come out of the share price: a three-year worked case, with rates up, rates down and a recession.
Yield to maturity assumes you hold to the end and reinvest at the same yield. The holding period return uses the assumptions you actually expect.
The fill ratio is one division. What it does to the investor's return depends on the NAV path during the wait, not on the delay itself.
A $125,000 investment-grade ladder bought at par: income, the reinvestment rule, six years of income when rates move, and the price risk against one long bond.
Price from the discount rate, then the bond-equivalent yield, the money market yield and the effective annual yield, with the quadratic the Treasury uses for bills longer than six months.
The four letters of the prescribed formula, why it differs from the distribution yield, and what it leaves out.
Why tax on the inflation part of the coupon takes most of a bond's real income, line by line from a Treasury bill to a high-yield bond.
The quoted margin is the spread only at par. The discount margin adds the pull to par, and it is the number to compare across floaters.
There are two recovery dates, not one. The first depends on the loss and the new yield; the second is the fund's duration, almost to the decimal.
The two measures agree only at par. Below it current yield understates the return, above it overstates it, and the gap is the gain or loss to redemption spread over the remaining years.
Duration is the slope of the price-yield curve; convexity is its bend, and it is worth having the formula and the Excel version to hand.
Companion workbooks: /digitalinfra
A second tower tenant pays back in 0.71 years; no new tenants cuts equity IRR from 10.06 to 5.72 per cent.
Fibre is built per home passed and paid for per home connected, so penetration decides whether the first spend is ever repaid.
The year-one yield leaves out the escalator and the tower multiple, which together are most of the return.
The formula that turns a fibre build cost into the capital behind each paying customer, and the penetration a target yield on cost requires.
The PUE-capped power clause as a small business inside the lease, and the price at which it starts losing money.
The share of a data centre deal that is credit, and the share that is a bet on the building's second life.
One formula turns a kW-month rent into a price per MW. The harder question is which MW the price is divided by.
The formula is a geometric series. What it shows is that monthly churn outweighs the cost of capital, and why an open-access line can be worth more than a retail one.
The same fibre network modelled twice, once selling broadband to households and once selling lines to internet providers, with the penetration, wholesale price and exit multiple each model needs.
Why tower portfolios change hands at multiples that look indefensible on year-1 EBITDA, and how much of that multiple rests on tenants not yet signed and on the exit multiple.
An IRU is a lease prepaid at the buyer's cost of capital, with the maintenance still to pay; price both streams and the upfront figure follows.
Renew, retrofit or re-let: value each option per MW from the expiry date, and the rent of the next lease turns out to matter far more than the cost of the works.
When two tenants on the same towers merge, one of the two antennas comes down. The rent goes, the costs stay, and the exit multiple turns the gap into the real loss.
Price per home passed is the headline of every fibre deal and the output of none of them. It is what is left after penetration, the build still to come and the exit multiple have been priced.
Rent that starts late is deferred, not cancelled, but the whole value of the phase moves back with it, and past the long-stop date the lease itself is at risk.
Data centre debt is sized on the lease, and the lease has an end date. Refinanced a year before expiry, the same building borrows like a bond or like a construction site.
Tower debt is sized on EBITDA and tested on covenants, and both look comfortable. The binding constraint is the cash left after the owner buys the land under its towers.
Amendments are the quiet half of tower growth: small tickets, almost no cost, and a large share of the organic growth figure if the master lease allows them to be charged.
Interconnection is the high-margin line in retail colocation. Valued on its own margin, it explains why two buildings with the same rent roll can be worth very different amounts.
Start from the server, not the chip: each layer between the GPU and the meter multiplies the load.
Reading guides: which book to read first, field by field →
Ten of the books come with companion files — working models, empty templates and checklists, with every published figure reproduced in a formula. They are free, and they need no account and no email address.
See all companion files → · All titles by Julian R. Sterling →