An annuity fixes debt service and lets coverage drift upwards; sculpting fixes coverage and borrows against the drift.
Sculpting sets each year's debt service to that year's cash flow available for debt service divided by the target DSCR, and sizes the debt as the present value of that profile at the loan rate. On an illustrative toll road with CFADS of 20.0 growing 2.5 per cent a year, a 1.25 times DSCR and a fifteen-year tenor at 5.5 per cent, sculpting raises 187.3 of debt against 160.6 for a level annuity, 16.6 per cent more from the same cash flow and the same coverage floor.
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 road is illustrative. Its cash flow available for debt service, revenue less operating costs, tax and maintenance, starts at 20.0 and grows with traffic and tolls. The lender requires 1.25 times coverage in every year, the floor the book uses for its own toll road case. All figures are in millions.
| Input | Value |
|---|---|
| CFADS in year 1 | 20.0 |
| CFADS growth, per year | 2.5% |
| Debt tenor, years | 15 |
| All-in interest rate | 5.5% |
| Target minimum DSCR | 1.25x |
An annuity fixes debt service and lets coverage float. Sculpting fixes coverage and lets debt service float. The two produce different debt amounts because the lender's constraint binds differently.
Sculpted debt service in year t = CFADSt / 1.25
Sculpted debt = Σ debt servicet / 1.055t = 187.3
Annuity debt service = lowest CFADS / 1.25 = 20.0 / 1.25 = 16.00 a year
Annuity debt = 16.00 × annuity factor (10.04 at 5.5 per cent over fifteen years) = 160.6
In Excel, with CFADS in C5:Q5: debt service row =C5/1.25, sculpted debt =NPV(5.5%,C6:Q6), annuity debt =PV(5.5%,15,-MIN(C5:Q5)/1.25).
The annuity is sized on its tightest year. With growing CFADS that is year 1, so every later year carries coverage above 1.25 that the lender does not need and the sponsor cannot borrow against. Sculpting converts that surplus coverage into debt.
| Year | CFADS | Sculpted debt service | Sculpted DSCR | Annuity debt service | Annuity DSCR |
|---|---|---|---|---|---|
| 1 | 20.00 | 16.00 | 1.25 | 16.00 | 1.25 |
| 2 | 20.50 | 16.40 | 1.25 | 16.00 | 1.28 |
| 5 | 22.08 | 17.66 | 1.25 | 16.00 | 1.38 |
| 10 | 24.98 | 19.98 | 1.25 | 16.00 | 1.56 |
| 15 | 28.26 | 22.61 | 1.25 | 16.00 | 1.77 |
| Debt raised | 187.3 | 160.6 |
The sculpted loan pays 16.00 in year 1, exactly what the annuity pays, but its interest is higher, 10.30 against 8.83, because the balance is larger. Principal starts at 5.70 and rises to 21.43 in the final year, so the loan repays more slowly: a weighted average life of 9.7 years against 9.0. Total debt service over the tenor is 286.9 against 240.0, out of 358.6 of CFADS.
Sculpting adds 26.7 of debt, 16.6 per cent more, and every unit of it reduces the equity cheque one for one at a given purchase price. On a bid where the equity return is the competitive variable, that is frequently the difference between winning and losing. The lender is no worse off on its own test: the minimum DSCR is 1.25 in both structures.
The gain comes entirely from growth. If CFADS were flat, the annuity would already hold 1.25 in every year and the two structures would raise identical debt. Sculpting is worth most where cash flow rises fastest: indexed tolls, ramping traffic, availability payments with step-ups.
| Case | Sculpted | Annuity | Sculpting adds |
|---|---|---|---|
| Growth 0.0%, DSCR 1.25x | 160.6 | 160.6 | 0.0% |
| Growth 1.5%, DSCR 1.25x | 176.0 | 160.6 | 9.6% |
| Growth 2.5%, DSCR 1.25x | 187.3 | 160.6 | 16.6% |
| Growth 4.0%, DSCR 1.25x | 206.2 | 160.6 | 28.4% |
| Growth 2.5%, DSCR 1.20x | 195.1 | 167.3 | |
| Growth 2.5%, DSCR 1.30x | 180.1 | 154.4 | |
| Growth 2.5%, DSCR 1.40x | 167.3 | 143.4 |
Debt is inversely proportional to the DSCR under either structure, so tightening the floor from 1.25 to 1.40 cuts sculpted debt from 187.3 to 167.3. Growth affects only the sculpted column.
The mistake is to read the sculpted structure's coverage as comfortable because it never dips below 1.25. It never rises above 1.25 either. Sculpting removes the cushion that an annuity builds up in later years, by construction. If CFADS comes in 10 per cent below the case, the sculpted loan runs at 1.125 times in every single year, below a typical lock-up test in each of them. The annuity also starts at 1.12 in year 1, but its coverage climbs back to 1.59 by year 15 on the same stressed cash flow, so the lock-up lasts a few years rather than the whole tenor.
That is why lenders who allow sculpting usually size it on a base case and then test it against a downside case, and why the sculpted debt quantum depends so heavily on whose traffic forecast is used. The second, quieter mistake is circularity: in a real model CFADS is after tax, tax depends on interest, and interest depends on the debt being sized. Break the loop with a copy-paste macro or an iterative calculation and check that the closing balance reaches zero in the final year; a sculpt that leaves a residual balance is not sculpted.
Divide each year's CFADS by the target DSCR and discount the result at the loan rate. On this road that is 187.3 of debt against 160.6 for an annuity, bought at the price of zero coverage headroom in every year. The book's own toll road is sculpted to 1.25 times in the free workbooks for this book, where leverage comes out of the calculation rather than going into it. For the discount-rate side of the same asset class, see whether a constant WACC overstates value, and for a full template, the project finance model.
Set each year's debt service equal to CFADS divided by the target DSCR, then size the loan as the present value of that debt service at the loan's all-in rate. Principal each year is debt service less interest on the opening balance. With CFADS of 20.0 and a 1.25 times DSCR, year-one debt service is 16.00, of which 10.30 is interest and 5.70 principal.
When CFADS is flat. An annuity sized to the lowest year then already holds the target coverage in every year, and both structures raise the same amount: 160.6 in the illustrative case at 0 per cent growth. The faster CFADS grows, the larger the gain, rising to 28.4 per cent more debt at 4.0 per cent growth.
Its minimum DSCR is the same, but it has no headroom in later years. A 10 per cent shortfall in CFADS puts a loan sculpted to 1.25 times at 1.125 times in every year, while an annuity on the same stressed cash flow recovers to 1.59 by year 15. Sculpted loans also repay more slowly, with a weighted average life of 9.7 years against 9.0.
Debt sculpting and the DSCR are the subject of Chapter 4 of 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.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: infrastructure, data centres and energy → · All 324 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.