Same asset, same cash flow, two returns: the gap is the debt, and it is not the textbook leverage formula.
Project IRR is the internal rate of return of the total capital cost against the cash flow before any financing; equity IRR is the IRR of the equity cheque against the cash flow left after debt service. On an illustrative 200 concession that produces 20.0 in year one, the project IRR is 10.7 per cent and the equity IRR 19.3 per cent at 80 per cent gearing. The 8.6-point gap is the debt, and it is smaller than the textbook leverage formula predicts.
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 availability-payment concession, already built, bought for 200 with 25 years left. Its cash flow before financing grows with indexation at 2.0 per cent a year. The senior loan is a level annuity. To keep the comparison clean the cash flow is post-tax and the interest tax shield is ignored; including it widens the gap a little. All figures are in millions.
| Input | Value |
|---|---|
| Purchase price (total capital) | 200 |
| Cash flow before financing, year 1 | 20.0 |
| Indexation, per year | 2.0% |
| Remaining concession, years | 25 |
| Gearing (debt / total capital) | 80% |
| Senior debt | 160 |
| Equity | 40 |
| Interest rate, all-in | 6.0% |
| Tenor, years | 18 |
Project IRR: solve for r in −200 + Σ CFt / (1 + r)t = 0, where CFt is cash flow before financing.
Debt service = debt / annuity factor = 160 / 10.83 = 14.78 a year for 18 years.
Equity cash flow = CFt − debt servicet; year 1: 20.00 − 14.78 = 5.22.
Equity IRR: solve for r in −40 + Σ equity CFt / (1 + r)t = 0.
In Excel, with the year-0 outflow in C5 and the 25 years in D5:AB5: =IRR(C5:AB5) on the project row, and the same formula on the equity row, where D7 is =D5-PMT(6%,18,-160) for the loan years and =D5 after maturity.
The two rows share the same top line. Only the first figure and the deduction differ: the project row starts at the full 200 and deducts nothing, the equity row starts at 40 and deducts every payment to the lender.
| Year | Project cash flow | Debt service | Equity cash flow |
|---|---|---|---|
| 0 | −200.00 | −40.00 | |
| 1 | 20.00 | 14.78 | 5.22 |
| 2 | 20.40 | 14.78 | 5.62 |
| 5 | 21.65 | 14.78 | 6.87 |
| 10 | 23.90 | 14.78 | 9.12 |
| 18 | 28.00 | 14.78 | 13.23 |
| 19 | 28.56 | 0.00 | 28.56 |
| 25 | 32.17 | 0.00 | 32.17 |
| Sum of years 1 to 25 | 640.6 | 266.0 | 374.6 |
The project row returns 10.71 per cent; the equity row returns 19.28 per cent. The minimum DSCR, the year-one cash flow divided by debt service (20.00 / 14.78), is 1.35 times, a level an availability-payment lender would accept in many markets, illustratively. The equity multiple is 9.37 times against 3.20 for the project, which says more about the small cheque and the long tail than about value: seven years of debt-free cash flow after maturity carry much of the equity return.
The equity IRR is higher only because the debt costs less than the asset earns. Borrow 160 at 6.0 per cent to fund an asset yielding 10.7, and the spread on 160 flows to 40 of equity. Reverse the inequality and gearing destroys equity return.
The project IRR does not move with the financing; the equity IRR moves with every term of it.
| Gearing | Debt | Equity | Equity IRR | Minimum DSCR |
|---|---|---|---|---|
| 0% | 0 | 200 | 10.7% | n/a |
| 60% | 120 | 80 | 14.7% | 1.80 |
| 70% | 140 | 60 | 16.4% | 1.55 |
| 80% | 160 | 40 | 19.3% | 1.35 |
| 85% | 170 | 30 | 21.7% | 1.27 |
At 80 per cent gearing, a debt rate of 5.0 per cent lifts the equity IRR to 21.3 and the DSCR to 1.46; 7.0 per cent cuts them to 17.3 and 1.26; 8.0 per cent to 15.4 and 1.17. Gearing amplifies the downside too. A permanent 10 per cent fall in cash flow, 18.0 in year one instead of 20.0, costs the project 1.3 points of IRR, down to 9.5 per cent, and costs the equity 4.0 points, down to 15.3, with the DSCR at 1.22.
The tempting shortcut is the corporate finance identity: equity return = project return + (project return − debt rate) × debt / equity. With 10.7, 6.0 and a ratio of 160 to 40, it gives 29.6 per cent, more than ten points above the 19.3 the cash flows actually produce. The formula assumes the debt-to-equity ratio stays at 4.0 forever. An amortising project loan does the opposite: gearing falls every year, reaches zero after 18 years, and the last seven years are earned on an unlevered asset. The only reliable equity IRR is the IRR of the equity cash flow row.
The second error is comparing the wrong pair of numbers. The project IRR is compared with a WACC, the equity IRR with the cost of equity. A 10.7 per cent project IRR set against a 12 per cent equity hurdle looks like a reject; the deal may in fact clear it comfortably once financed, or fail it once the lender's coverage floor caps the gearing.
Build two rows from one top line: the full capital cost against cash flow before financing, and the equity cheque against cash flow after debt service. Here they return 10.7 and 19.3 per cent. The debt sizing that sits between them, sculpted to a coverage floor on the book's toll road, is reproduced in the free workbooks for this book; for how the top line itself is built, see how to calculate CFADS, and for a full model, the project finance model template.
Because the debt costs less than the asset earns. Debt at 6.0 per cent funds 80 per cent of an asset returning 10.7 per cent, and the spread on 160 of borrowing accrues to 40 of equity. If the debt cost more than the project IRR, gearing would lower the equity IRR instead of raising it.
The equity IRR, because both describe the return on the equity cheque after debt. The project IRR is compared with the WACC. In the illustrative case the 19.3 per cent equity IRR is the figure set against an equity hurdle, the 10.7 per cent project IRR against a blended cost of capital.
Arithmetically yes while the project IRR exceeds the debt rate: moving from 60 to 85 per cent gearing takes the illustrative equity IRR from 14.7 to 21.7 per cent. The limit is the lender's coverage test, as the minimum DSCR falls from 1.80 to 1.27 over the same range.
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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