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.
A concession ends, so it has no terminal value: its value at exit is the present value of the cash flow over the years that remain, and nothing after. An illustrative toll concession bought at 11.2 times EBITDA with 25 years left is worth 8.2 times forward EBITDA after a ten-year hold, at the same 7.0 per cent discount rate. Modelling the exit at the entry multiple overstates exit value by 36.2 per cent; modelling it as a perpetuity nearly doubles it.
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 →
The asset is an illustrative toll road concession with 25 years to run, handed back to the grantor for nothing at the end. Cash flow before financing is a constant 80 per cent of EBITDA, and both grow at 2.0 per cent a year. The buyer pays exactly the present value of the cash flow at 7.0 per cent, so the fair return is 7.0 per cent by construction. All figures are in millions and unlevered.
| Input | Value |
|---|---|
| EBITDA, year 1 | 50.0 |
| Cash flow as share of EBITDA | 80% |
| Cash flow, year 1 | 40.0 |
| Growth, per year | 2.0% |
| Concession remaining at entry, years | 25 |
| Discount rate | 7.0% |
| Hold, years | 10 |
Entry value = Σt=1..25 CFt / 1.07t = 558.2, or 11.2 times year-1 EBITDA of 50.0
Exit value at year 10 = Σt=11..25 CFt / 1.07t−10 = 499.5
Exit multiple = 499.5 / forward EBITDA of 60.9 = 8.2 times
In Excel, with cash flows in D5:AB5 and the exit at the end of year 10 (column M): =NPV(7%,N5:AB5). The range stops at the last year of the concession; it is never followed by a terminal value cell.
EBITDA has grown 21.9 per cent over the hold, to 60.9 in the first year of the buyer's ownership, yet the asset is worth less than it cost: 499.5 against 558.2. Nothing has gone wrong. The fund has received 438.0 of cash over ten years, and the next buyer is purchasing fifteen years of cash flow, not twenty-five. Discount the 438.0 and the 499.5 back at 7.0 per cent and the IRR is exactly 7.00 per cent.
| Exit method | Exit value | Exit multiple | Overstatement | IRR |
|---|---|---|---|---|
| Present value of the 15 years left | 499.5 | 8.2x | 7.0% | |
| Entry multiple applied to exit EBITDA | 680.4 | 11.2x | 36.2% | 9.2% |
| Growing perpetuity at 7.0% less 2.0% | 975.2 | 16.0x | 95.2% | 12.0% |
The entry-multiple exit adds 180.9 of value the asset cannot produce and 2.2 points of IRR. The perpetuity adds 475.7 and five points. Both are returns the concession cannot earn, because both pay the buyer for years after the handback.
An exit at the entry multiple always implies an IRR of cash yield plus growth: 40.0 over 558.2 is 7.17 per cent, plus 2.0 per cent growth, gives 9.2. That holds whatever the hold period, which is why the error survives every sensitivity on the exit year.
The fair exit multiple is a function of the years left, not of the asset's quality. At the same 7.0 per cent and 2.0 per cent growth:
| Years left at exit | Fair exit multiple |
|---|---|
| 25 | 11.2x |
| 20 | 9.9x |
| 15 | 8.2x |
| 10 | 6.1x |
| 5 | 3.4x |
Hold for five years and the fair exit is 9.9 times; hold for fifteen and it is 6.1 times. In every case the true IRR is 7.0 per cent and the entry-multiple model reports 9.2. The longer the hold, the larger the gap in exit value, and the more the model depends on a buyer who ignores the calendar.
The mistake is importing corporate private equity habits: an exit multiple copied from the entry, or a Gordon growth terminal value on the last explicit year. Both treat the concession as a going concern. On a contract with a handback date, the only defensible exit value is the discounted cash flow to that date, less any handback obligations, which grow in present value as the end approaches. A secondary check is to state the implied exit multiple and the years remaining side by side in the investment committee memo: 8.2 times with 15 years left is a coherent pair, 11.2 times with 15 years left is not.
The same logic sits behind other concession valuation errors, such as holding a constant WACC while the debt amortises; see whether a constant WACC overstates value. For going-concern assets, where a terminal value is legitimate, see what share of a DCF the terminal value should be.
Value the exit as the present value of the years left and nothing more. Here that is 499.5, or 8.2 times, against 680.4 at the entry multiple and 975.2 as a perpetuity. The book's toll road case, whose exit after an eight-year hold is valued on the eighteen years of concession that actually remain, is in the free workbooks for this book.
Because fewer years of cash flow remain to be bought. In the illustrative case EBITDA grows 21.9 per cent over ten years, but the remaining life falls from 25 to 15 years, so the fair multiple falls from 11.2 to 8.2 times forward EBITDA at a constant 7.0 per cent discount rate.
The cash yield plus growth, whatever the hold. Bought at 558.2 for 40.0 of cash flow growing 2.0 per cent, an exit at the entry multiple implies a 9.2 per cent IRR after five, ten or fifteen years. The asset earns only the 7.0 per cent at which it was priced.
Only for assets with no contractual end, such as a freehold regulated network whose licence rolls over. On a concession with 15 years left, a perpetuity at 7.0 per cent less 2.0 per cent growth gives 975.2 against a fair 499.5, nearly double, and lifts the IRR to 12.0 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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