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.
The asset, and the value it is actually worth
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.
Three ways to mismatch the rate
Two of the mismatches are the ones every textbook names. The third is the one that ships in production models.
Calder Water, a twenty-five-year concession. Equity value under four discounting routes.
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.
Why the discount rate has to move
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.
Cost of equity on the relevered path, as the debt amortises.
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.
What to do with it
Three checks catch the whole family of errors.
Build the value twice. Adjusted present value on one side, relevered equity discounted cash flow on the other. If they do not agree to several decimal places, the discount rate and the cash flow are not describing the same asset.
Read the debt schedule before fixing the rate. A bullet structure holds gearing roughly constant and a single blended rate is defensible. A fully amortising structure does not, and it is not.
Size the gap before arguing about it. On this asset the constant-rate shortcut adds 8.6 per cent to equity value. In a competitive bid process that is the difference between a disciplined price and an overpayment nobody can trace afterwards.
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.
The workbooks behind this article
Every figure above is a live formula in the free companion files for
The Infrastructure Investment Analyst. Each workbook ends with a Checks sheet
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