Every model that pairs an amortising debt schedule with a single blended discount rate carries the same error, and it always points the same way.
Discounting unlevered free cash flow at a constant weighted average cost of capital and subtracting debt values this concession asset at 263.05 against a correct 242.18 — an overstatement of 8.6 per cent. The blended rate of 6.01 per cent is right for an asset financed at 65 per cent gearing, and this one is financed that way on the first day only. As the debt amortises the true cost of capital rises, and the later years are discounted too lightly.
Worked in full in The Infrastructure Investment Analyst by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Calder Water is a regulated water utility with twenty-five years left on its concession. Year-one revenue is 100, indexed at 2.0 per cent. Operating costs start at 38 and escalate at 2.5 per cent, so margins compress slowly. Lifecycle capital expenditure starts at 6 and escalates with costs. The regulated asset base is 900, depreciated straight-line to expiry, and tax is 25 per cent. The unlevered cost of capital is 7.0 per cent, debt costs 5.5 per cent, and the asset is financed at 65 per cent gearing with debt amortising straight-line over twenty years.
Discounting unlevered free cash flow at 7.0 per cent gives an unlevered value of 646.68. Debt of 449.76 generates interest tax shields worth 45.25, discounted at the cost of debt. Enterprise value is 691.93, and equity is 691.93 less 449.76, or 242.18. Run the same asset as an equity discounted cash flow, with the cost of equity relevered year by year as the debt falls, and the answer is 242.1768. Two independent routes agreeing to six decimal places is the test that a model is internally consistent.
Two of the mismatches are the ones every textbook names. The third is the one that ships in production models.
| Route | Cash flow and discount rate | Equity value | Error, per cent |
|---|---|---|---|
| Correct, by either route | Rate matched to the cash flow | 242.18 | — |
| Equity cash flow at the blended rate | Distributable cash flow at 6.01 per cent | 323.23 | +33.5 |
| Unlevered cash flow at the cost of equity | Unlevered cash flow at 9.51 per cent, less debt | 66.91 | −72.4 |
| Unlevered cash flow at a constant blended rate | Unlevered cash flow at 6.01 per cent, less debt | 263.05 | +8.6 |
The first two errors announce themselves. Discounting distributable cash flow to equity at the weighted average cost of capital overstates equity by 33.5 per cent. Discounting unlevered free cash flow at the cost of equity and subtracting debt understates it by 72.4 per cent — an error larger than the answer. Neither survives a review.
The third does not look like a mistake. Unlevered cash flow discounted at a weighted average cost of capital computed at target gearing, then debt subtracted, is what most infrastructure models do, and it prints 263.05 against 242.18. Nothing in the model flags it, because every step is the step the analyst was taught.
The weighted average cost of capital of 6.01 per cent is the correct rate for an asset financed at 65 per cent gearing. This asset is financed that way on the first day and never again. Debt amortises straight-line over twenty years, so leverage falls every year, so the cost of equity falls with it and the blended rate rises. By year ten the debt is under half its opening balance and the true cost of capital has risen substantially.
| Point in the debt schedule | Cost of equity, per cent |
|---|---|
| Year one, at opening gearing | 9.51 |
| Year ten | 8.03 |
| At expiry, debt repaid | 7.00 |
Holding the rate at its opening value discounts the later years too lightly, and on a twenty-five-year concession the later years are where most of the value sits. The error is structural, not a rounding artefact. It scales with the speed of amortisation and with the length of the forecast, which makes infrastructure — long-dated and fully amortising — the asset class where it bites hardest.
The relevering itself has a trap of its own. The formula consistent with discounting the tax shield at the cost of debt sets the cost of equity as the unlevered rate plus the spread between the unlevered rate and the cost of debt, multiplied by net debt — debt less the present value of the remaining tax shields — over equity. The commonly quoted textbook version, one minus the tax rate times debt over equity, assumes something different about the tax shield and does not reconcile. It produces 249.80 against 242.18, a discrepancy of 3.1 per cent with no economic content at all.
Three checks catch the whole family of errors.
An analyst who has reconciled the two routes to the last decimal understands what the discount rate is doing. One who has only been told they should agree does not, and will not notice when a model quietly stops being consistent.
Because the weighted average cost of capital is fixed at opening gearing while the debt amortises. Adjusted present value gives an unlevered value of 646.68 plus tax shields of 45.25, so enterprise value of 691.93 and equity of 242.18. The constant-rate route gives 263.05, an overstatement of 8.6 per cent.
Set the cost of equity as the unlevered rate plus the spread between the unlevered rate and the cost of debt, multiplied by net debt over equity, with net debt taken after the remaining tax shields. That path runs 9.51 per cent in year one to 7.00 per cent at expiry. The textbook alternative gives 249.80 against 242.18, a gap of 3.1 per cent.
It overstates equity badly. Distributable cash flow to equity discounted at 6.01 per cent gives 323.23 against 242.18, an overstatement of 33.5 per cent. The opposite mismatch is worse: unlevered cash flow discounted at the cost of equity, less debt, gives 66.91, an understatement of 72.4 per cent.
This article is one calculation from The Infrastructure Investment Analyst. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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