Purchase accounting values the same balance sheet again, and the answer is not the one in the capital ratio.
A buyer would pay 278,809 for Sagebrook, against published CET1 capital of 639,600 and book common equity of 533,765 — 56.4 per cent below the reported capital. The gap is not a valuation opinion. Purchase accounting records every asset and liability at fair value, so the fixed-rate loan book takes a mark of 319,543 and the deposit franchise the accounts never recorded is added back as a core deposit intangible of 435,094. Strip that intangible out and the price is negative.
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Sagebrook reports common equity tier one capital of 639,600 and carries book common equity of 533,765 at the year end. An acquirer running purchase accounting arrives at 278,809. Nothing about the bank changes between the top and the bottom of that table — same loans, same deposits, same building, same year.
| Reading | Amount |
|---|---|
| Published CET1 capital | 639,600 |
| Book common equity, year end | 533,765 |
| What a buyer would pay | 278,809 |
The price is 56.4 per cent below the published capital and 47.8 per cent below the book value of the equity. What changes is that the buyer pays cash and therefore does not get to use the filter. An accounting convention that permits a bank to carry an asset at cost is a convention about the bank’s own reports. It is not a convention the market participates in. The buyer marks, because the buyer’s own auditors require it.
| Line | Amount |
|---|---|
| Tangible common equity, both marks recognised | 156,890 |
| Fixed-rate loan portfolio, marked | −319,543 |
| Time deposits, marked | 6,369 |
| Core deposit intangible | 435,094 |
| Purchase price | 278,809 |
The loan mark is the largest negative item and the one sellers dispute hardest. A bank that wrote 2,850,000 of fixed-rate loans at 4.35 per cent when the market paid 4.35 per cent holds an asset worth less than par once the market pays 8.60 per cent. The borrower is not in difficulty. The loan is money-good. It is still worth 319,543 less, because the buyer could originate the same loan tomorrow at the higher rate. The seller’s argument — these loans will pay in full — is true and irrelevant to price.
The only positive line is the one no accounting system records while the bank is a going concern. The core deposit intangible of 435,094 is what the buyer pays for the right to fund itself at 18 basis points while the market charges 580. It is larger than the 156,890 of tangible common equity the accounts do record. Strip it out and the price is negative.
435,094 works out at 8.70 per cent of the non-maturity deposit base of 5,000,000. Deposit premiums in American bank transactions have ranged from roughly 1 per cent to 10 per cent of core deposits over the last two decades, with the middle of the distribution nearer 3 to 6 per cent in ordinary conditions, and rising with the level of interest rates, because a cheap deposit base is worth more when money is expensive.
8.70 per cent sits at the top of that range, and the point is worth stating plainly: this is a franchise value a real buyer might well decline to pay. Two adjustments are available and both reduce it — a shorter assumed deposit life, and a beta that rises over time as competitors’ offers accumulate. The conservative corner of those assumptions produces a price below zero.
An acquirer paying 278,809 does not simply own the franchise. It amortises it. A core deposit intangible is written off over the estimated life of the deposits, conventionally ten years, sometimes faster. At ten years the charge is 43,509 a year. Sagebrook’s net income in the shock year was 27,600.
The annual amortisation is 1.58 times the acquired bank’s entire annual profit. The buyer acquires an institution earning 27,600 and immediately books a non-cash charge larger than that against it. The transaction only works if the deposits are worth more in the buyer’s hands — a lower cost base, cross-selling, or the removal of the target’s overheads. That is why bank acquisitions are announced with a cost-synergy number, and why the number is approximately the target’s non-interest expense multiplied by a third. The premium and the amortisation are one transaction described twice: paid once as a price, recognised ten times as a charge.
The question in front of a seller’s board is not whether to sell. It is whether the deposits will stay long enough to earn back the difference between 278,809 and 639,600. If they will, the bank should not sell: the accounting pulls back to par as the securities mature, and the published ratio of 11.40 per cent was right all along. If they will not, the bank should sell now, because the price falls as the deposits leave, and the franchise that supports the price is the thing a run destroys.
Both answers are defensible from the same table. The failure is not choosing wrongly. The failure is a board that never sees the table, because the only capital number put in front of it was 11.40 per cent, and 11.40 per cent does not prompt anybody to ask what the bank is worth.
One line, applied to each category of deposit: value = balance × (1 − beta) × life × rate change. For Sagebrook’s non-maturity deposits, 5,000,000 × 0.65 × 4.2 × 0.0425 = 580,125 before tax, or 435,094 after. Three of the four inputs are facts; the assumed life is the judgement.
Deposit premiums in American bank transactions have run from roughly 1 per cent to 10 per cent of core deposits over the last two decades, with the middle nearer 3 to 6 per cent. Sagebrook’s core deposit intangible of 435,094 is 8.70 per cent of a 5,000,000 base, which sits at the top of that range.
Because the buyer can originate the same loan today at the current rate. Sagebrook wrote 2,850,000 of fixed-rate loans at 4.35 per cent; with the market at 8.60 per cent, the portfolio marks down by 319,543. The borrower is not in difficulty and the loan pays in full, which is true and irrelevant to price.
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