Indexed infrastructure cash flows invite real models, and the discount rate on the committee paper is almost always nominal.
Discount real cash flows at a real rate and nominal cash flows at a nominal rate, and convert between them with the Fisher equation: (1 + nominal) = (1 + real) x (1 + inflation). Done consistently, an illustrative 25-year indexed asset is worth 140.94 either way. Mix them and the error is large: real cash flows at the nominal rate understate value by 21.8 per cent, and nominal cash flows at the real rate overstate it by 31.6 per cent.
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 →
Infrastructure revenue is often indexed: availability payments, regulated tariffs and many tolls rise with a price index. That makes a real model natural, since the cash flow is flat in today's money. It also makes the mismatch easy, because the discount rate the investment committee quotes, a target return or a WACC built from bond yields, is almost always nominal. Every figure below is illustrative.
| Input | Value |
|---|---|
| Cash flow, real, every year | 10.0 |
| Remaining life, years | 25 |
| Real discount rate | 5.0% |
| Inflation, per year | 2.5% |
| Nominal discount rate (Fisher) | 7.625% |
Fisher: nominal = (1 + real) x (1 + inflation) - 1 = 1.05 x 1.025 - 1 = 7.625%
Back again: real = (1 + nominal) / (1 + inflation) - 1
Nominal cash flow in year t = real cash flow x (1 + inflation)t: 10.25 in year 1, 18.54 in year 25
Real route: PV of 10.0 a year for 25 years at 5.0% = 140.94
Nominal route: PV of the indexed series at 7.625% = 140.94
In Excel: =PV(5%,25,-10) for the real route; for the nominal route, cash flows in B2:Z2 built as =10*1.025^t, then =NPV(1.05*1.025-1,B2:Z2).
The two routes agree exactly because inflation appears in the numerator and the denominator and cancels year by year. That identity is the test: if a real model and a nominal model of the same asset do not give the same value, one of them has mixed its units.
| Cash flow | Discount rate | Value | Error |
|---|---|---|---|
| Real | Real, 5.0% | 140.94 | 0.0% |
| Nominal | Nominal, 7.625% | 140.94 | 0.0% |
| Real | Nominal, 7.625% | 110.26 | -21.8% |
| Nominal | Real, 5.0% | 185.54 | 31.6% |
| Nominal | Additive, 7.5% | 142.68 | 1.2% |
The two big errors are not symmetric. Discounting real cash flows at a nominal rate deflates them twice, which is the conservative mistake and tends to show up as a bid that never wins. Discounting nominal cash flows at a real rate counts inflation as a gift, which is the expensive mistake and tends to show up as a bid that wins. In both cases the error is larger than most of the judgement calls an investment committee spends its time on.
The additive shortcut, real rate plus inflation, gives 7.5 per cent instead of 7.625. The difference looks like rounding, but at 25 years it is worth 1.2 per cent of value, enough to lose a tight auction or explain an unexplained gap between two models.
The error compounds with time, because the gap between real and nominal cash flows widens every year. Longer concessions and higher inflation both make it worse.
| Remaining life, years | Correct value | Real CF at nominal rate | Nominal CF at real rate | Additive shortcut |
|---|---|---|---|---|
| 10 | 77.22 | -11.6% | 13.7% | 0.59% |
| 25 | 140.94 | -21.8% | 31.6% | 1.23% |
| 40 | 171.59 | -27.6% | 47.8% | 1.69% |
| Inflation | Nominal rate | Real CF at nominal rate | Nominal CF at real rate |
|---|---|---|---|
| 2.0% | 7.100% | -18.1% | 24.4% |
| 2.5% | 7.625% | -21.8% | 31.6% |
| 3.5% | 8.675% | -28.4% | 47.9% |
A 40-year asset valued on nominal cash flows at a real rate is overstated by almost half. That is why the mistake matters most for the long-dated, indexed assets where real models are most popular.
The inflation assumption is itself a source of value. If the model is nominal and the market's expected inflation differs from the one used to index the cash flows, the two routes stop agreeing and the difference is a bet on inflation, often an unintended one. A practical check is to compare the inflation in the model with the breakeven inflation implied by index-linked government bonds of similar maturity, and to state any difference as a deliberate view rather than leave it buried in the cash flow line.
The clean cases above are rare. The real-world mismatch is a model that is mostly real but contains nominal items: fixed-rate debt service, tax depreciation on historical cost, a fixed-price operations contract or a tariff that is only partly indexed. Deflating those items is easy to forget, and discounting them at a real rate overstates their value just as the full mismatch does. The safer practice is to model in nominal terms, with each line indexed at its own contractual rate, and to discount at a nominal rate. Where a real rate is quoted, convert it with Fisher, not by subtraction: a nominal 8.0 per cent with 2.5 per cent inflation is a real 5.366 per cent, not 5.5.
Match the units, convert with Fisher, and check that the real and nominal routes give the same value. On this asset the right answer is 140.94; the wrong ones range from 110.26 to 185.54. The book's valuation workbook values a regulated utility twice and reconciles the two routes, and is in the free workbooks for this book. For the related error of holding the discount rate constant as debt amortises, see whether a constant WACC overstates value.
Divide, do not subtract: real = (1 + nominal) / (1 + inflation) - 1. A nominal 8.0 per cent with 2.5 per cent inflation is a real 5.366 per cent, not 5.5. Discounting 10.0 a year of real cash flow for 25 years at 5.5 per cent instead of 5.366 understates value by 1.3 per cent, enough to separate two bids.
Either gives the same value if every line is consistent, which is the test: the illustrative asset is worth 140.94 both ways. In practice nominal is safer, because debt service, tax depreciation and fixed-price contracts are nominal by nature and are easy to leave undeflated in a real model.
The gap between real and nominal cash flow widens every year, so the error compounds. Discounting nominal cash flows at a real rate overstates value by 13.7 per cent on a 10-year life, 31.6 per cent on 25 years and 47.8 per cent on 40 years, at 2.5 per cent inflation.
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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