Energy at P90 is a little lower than at P50; cash flow after fixed costs is a lot lower, and that sets the debt.
Debt is sized on whichever case gives the smaller debt service: P50 cash flow divided by its DSCR, or P90 cash flow divided by a lower one. On an illustrative 100 MW wind farm, a one-year P90 at 1.20 times binds ahead of P50 at 1.30 times and cuts debt from 97.1 to 88.0, 9.4 per cent less. Energy at P90 is only 11.8 per cent below P50, but fixed operating costs turn that into a 16.4 per cent fall in cash flow available for debt service.
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 wind farm sells at a fixed price under a fifteen-year offtake, so revenue moves only with energy. The energy yield assessment gives a P50 of 300 GWh a year and two sources of uncertainty: inter-annual variability of the wind, and the uncertainty of the assessment itself (measurement, modelling, losses). Lender terms are illustrative but typical in shape: one coverage ratio on the central case, a lower one on the downside. Money figures are in millions.
| Input | Value |
|---|---|
| P50 annual energy, GWh | 300 |
| Offtake price, $ per MWh | 60 |
| Operating costs, $ million a year, fixed | 5.0 |
| Inter-annual variability, one standard deviation | 6% |
| Assessment uncertainty, one standard deviation | 7% |
| DSCR required on P50 | 1.30x |
| DSCR required on one-year P90 | 1.20x |
| Tenor and rate | 15 years, 6.0% |
A P90 is the level exceeded in nine years out of ten. For a normal distribution it sits 1.2816 standard deviations below the P50. The two uncertainties are independent, so they combine as the square root of the sum of squares.
One-year uncertainty = √(6%² + 7%²) = 9.22%
One-year P90 energy = 300 × (1 − 1.2816 × 9.22%) = 300 × 88.2% = 264.6 GWh
CFADS: P50 = 300 × 60 / 1,000 − 5.0 = 18.00 − 5.0 = 13.00; P90 = 15.87 − 5.0 = 10.87
Debt service capacity: P50 test 13.00 / 1.30 = 10.00; P90 test 10.87 / 1.20 = 9.06
Debt = smaller capacity × annuity factor (9.71 at 6.0 per cent over fifteen years) = 9.06 × 9.71 = 88.0
In Excel: =MIN(CF50/1.3, CF90/1.2)*PV(6%,15,-1), with =NORM.S.INV(0.9) returning the 1.2816.
Because the cash flow here is flat, an annuity and a sculpted profile give the same debt; with growing cash flow the same test is applied year by year to a sculpted schedule.
| Case | Energy, GWh | CFADS | DSCR | Debt service | Debt |
|---|---|---|---|---|---|
| P50 | 300 | 13.00 | 1.30 | 10.00 | 97.1 |
| One-year P90 | 264.6 | 10.87 | 1.20 | 9.06 | 88.0 |
| One-year P99 | 235.7 | 9.14 | 1.00 | 9.14 | 88.8 |
The P90 test binds. It removes 9.1 of debt, and at the debt it allows, the P50 case runs at 1.43 times rather than 1.30. Had the loan been sized on P50 alone, a P90 year would cover debt service only 1.09 times. A P99 test at 1.00 times, which some lenders use instead, lands close to the P90 result here at 88.8.
Operating leverage does the damage. Energy falls 11.8 per cent from P50 to P90, but the 5.0 of operating costs does not fall with it, so CFADS falls 16.4 per cent. The higher the cost base relative to revenue, the more the downside case dominates sizing.
| Case | P90 debt | Binding debt |
|---|---|---|
| Assessment uncertainty 5%, P90 DSCR 1.20x | 90.6 | 90.6 |
| Assessment uncertainty 7%, P90 DSCR 1.20x | 88.0 | 88.0 |
| Assessment uncertainty 9%, P90 DSCR 1.20x | 85.0 | 85.0 |
| Assessment uncertainty 7%, P90 DSCR 1.10x | 96.0 | 96.0 |
| Assessment uncertainty 7%, P90 DSCR 1.25x | 84.5 | 84.5 |
On these terms the P50 test binds only if one-year uncertainty is below 4.3 per cent, which is to say almost never for a wind asset. That makes the yield assessment the main lever on debt. Each two points of assessment uncertainty that a better measurement campaign removes is worth roughly 2.6 to 3.0 of debt here, which is why a sponsor will pay for a longer met mast record before financial close.
The common error is using the wrong P90. A ten-year P90 averages the inter-annual variability over a decade, so it divides that term by ten before combining: √(6%²/10 + 7%²) = 7.25%, and the ten-year P90 is 90.7 per cent of P50, not 88.2. Applying the one-year coverage ratio of 1.20 to the ten-year P90 gives 91.7 of debt instead of 88.0, an overstatement of 3.7, or 4.2 per cent. The two P90s answer different questions. The ten-year figure suits a test of whether the loan is repaid over its life; the one-year figure suits a test of whether a single bad year can pay its debt service. Mixing the long-run energy with the single-year ratio passes a loan that a bad year will breach.
The same logic applies beyond wind. A toll road sized on the traffic consultant's central case carries more debt than one sized on a downside, and the book's companion case on traffic below the consultant shows the gap on its own road: 154.1 of debt sized on the downside against 171.3 on the base.
Size on the minimum of P50 cash flow over the P50 ratio and P90 cash flow over the P90 ratio, and match the P90's horizon to the ratio's. Here that is 88.0 of debt, not 97.1. The sculpting mechanics that apply when cash flow grows are in sculpted debt against an annuity, and the toll road downside case is in the free workbooks for this book.
The ten-year P90 averages inter-annual variability over a decade, dividing its variance by ten before combining with assessment uncertainty. With 6 per cent variability and 7 per cent uncertainty, the one-year P90 is 88.2 per cent of P50 and the ten-year P90 is 90.7 per cent. Single-year DSCR tests should use the one-year figure.
Operating costs are largely fixed, so a fall in revenue passes straight to cash flow available for debt service. In the illustrative case P90 energy is 11.8 per cent below P50, but CFADS falls 16.4 per cent, from 13.00 to 10.87, because 5.0 of operating costs does not move.
When uncertainty is low enough that P90 cash flow divided by its lower ratio exceeds P50 cash flow divided by the higher one. With a 1.30 times P50 test and a 1.20 times P90 test on this asset, that requires one-year uncertainty below 4.3 per cent, which few wind assessments achieve.
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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