Sculpting to a Target DSCR: The Mechanics, and the Circularity That Is Not Where You Think
The FAST standard is unambiguous: never release a model with purposeful use of circularity. Almost every project finance model in existence ignores that instruction, and the reason usually given is debt sculpting.
That reason is wrong, and the correction is worth having because it removes most of the problem.
Sculpting itself is not circular. The sized debt is the present value of the sculpted debt service stream discounted at the debt rate, which is a closed-form expression that resolves in one pass and amortises to exactly zero. What makes project finance models circular is everything around the sculpt — tax, interest during construction, fees calculated on the facility, and a debt service reserve funded from the debt it is sized against.
This post separates the two, shows the closed form, quantifies the tax circularity that genuinely cannot be avoided, and sets out what the available solutions actually cost.
ℹ️ Note: All figures are labelled assumptions. The arithmetic is exact within the stated assumptions and is intended to be reproducible.
What Is Debt Sculpting?
Shaping principal repayment so the coverage ratio is constant. Instead of a level repayment schedule that produces a DSCR which rises and falls with cash flow, sculpting sets debt service in each period equal to that period's CFADS divided by the target ratio — so the ratio is the target in every period.
Debt service(t) = CFADS(t) ÷ target DSCR
Interest(t) = opening balance(t) × rate
Principal(t) = Debt service(t) − Interest(t)
The rationale is that project cash flows are not level. A wind or solar asset degrades; an availability-based asset has a maintenance cycle; a project with a merchant tail has a step change. A level repayment schedule against a declining cash flow produces a DSCR that falls every year, so the facility must be sized against the worst year and the earlier years are over-covered. Sculpting removes that waste, which is why it raises debt capacity.
The Mechanics, Worked
Assumptions, labelled as such:
CFADS, year 1 $26,000,000
CFADS decline 1.0%/year
Target DSCR 1.30×
Debt rate 6.5%
Tenor 18 years
Sized debt, as the present value of the debt service stream:
Sized debt = Σ (CFADS(t) ÷ 1.30) ÷ 1.065^t = $195,034,301
And the schedule that follows:
| Year | CFADS | Debt service | Interest | Principal | Closing balance |
|---|---|---|---|---|---|
| 1 | $26,000,000 | $20,000,000 | $12,677,230 | $7,322,770 | $187,711,530 |
| 2 | $25,740,000 | $19,800,000 | $12,201,249 | $7,598,751 | $180,112,780 |
| … | |||||
| 17 | $22,137,902 | $17,029,155 | $2,005,483 | $15,023,672 | $15,829,919 |
| 18 | $21,916,523 | $16,858,864 | $1,028,945 | $15,829,919 | $0.00 |
The closing balance in year 18 is exactly zero. Not approximately, not after iteration — exactly, in one pass.
What Does Sculpting Actually Buy?
Worth quantifying, because it is the reason anyone accepts the extra complexity.
Take the same CFADS profile and size it with a level repayment schedule instead. Level debt service against declining cash flow produces a DSCR that falls every year, so the binding year is the last one, and the facility must be sized so that year still clears 1.30×.
Level debt service = CFADS(18) ÷ 1.30 = $16,858,864
Level-sized debt = 16,858,864 × 10.4325 = $175,879,531
Sculpted debt = $195,034,301
------------
Uplift from sculpting = $19,154,770 (+10.9%)
Nearly eleven percent more debt on identical cash flow. And the reason is visible in the wasted coverage: under the level schedule, year one's DSCR is 1.54× against a 1.30× requirement — a quarter of a turn of coverage the project is providing and not being paid for.
That is the whole case for sculpting. It does not make the project better; it stops the structure discarding coverage the project already has. On a declining-CFADS asset, which is most renewables, the waste compounds across the tenor.
The corollary is that sculpting is worth least where cash flow is flat. A fully availability-based asset with level payments gains almost nothing, because a level schedule already produces a near-constant ratio. The complexity is only justified by the shape of the cash flow, and a model that sculpts a flat profile has taken on circularity risk for a rounding difference.
Why Is the Sculpt Not Circular?
Because the present value relationship is an identity, not an equation to be solved.
The circularity people describe is real as a dependency: interest depends on the balance, the balance depends on principal repaid, and principal is debt service less interest. That is genuinely a loop if you try to compute the opening balance from the schedule.
But you do not have to. An amortising loan's opening balance is the present value of its payment stream discounted at its own interest rate — that is what an amortising loan is. So if you know the payment stream, which sculpting gives you directly from CFADS and the target ratio, you know the balance without iterating.
B(0) = Σ DS(t) × (1 + r)^−t
Run the recursion B(t) = B(t−1) × (1 + r) − DS(t) forward from that starting balance and it terminates at zero. The table above is that recursion, and the final row is the proof.
So a model that enables iterative calculation in order to sculpt has enabled it unnecessarily. That matters beyond elegance, because once iteration is on it becomes very difficult to distinguish deliberate circular references from accidental ones, and a model that silently converges on the wrong answer looks exactly like one that converges on the right one.
So Where Does the Circularity Come From?
Four places, and they are separable.
1. Tax. Interest is deductible, so taxable income depends on the debt balance; tax reduces CFADS; CFADS sizes the debt. This is the one that cannot be removed by reordering, and it is quantified below.
2. Interest during construction. IDC is capitalised into project cost. Where debt is sized as a percentage of project cost, more debt means more IDC means higher project cost means more debt. As the standard description has it: with higher IDC and fees the project cost increases, with the increase in project cost the debt increases if measured on debt-to-capital, and when the debt goes up the IDC and fees go up, and around it goes.
3. Fees. Arrangement, commitment and agency fees calculated as a percentage of the facility are funded from the facility, so they enlarge the project cost that sizes the facility.
4. The debt service reserve account. The DSRA is sized off debt service, funded from the debt, and included in project cost. As one description puts it, because the size of the DSRA is affected by the fees and the fees depend on debt, "a nasty circular reference arises."
Note what these four have in common and what separates them from sculpting. Each is a case where the size of the debt appears on both sides of the equation for the size of the debt. Sculpting is not; it is a case where the schedule is determined by cash flow and the balance follows.
The Tax Circularity, Quantified
This is the one worth measuring, because the error from ignoring it is large and one-directional.
Assumptions, labelled as such:
EBITDA, year 1 $30,000,000
EBITDA decline 1.0%/year
Depreciation $12,500,000/year
Tax rate 21%
Target DSCR 1.30×
Debt rate / tenor 6.5% / 18 years
Size the debt on pre-tax CFADS and you get one answer. Size it on post-tax CFADS, where tax depends on the interest deduction which depends on the debt, and it converges to another:
| Iteration | Sized debt | Change |
|---|---|---|
| 0 (pre-tax) | $225,039,578 | — |
| 1 | $215,684,415 | −$9,355,163 |
| 2 | $214,760,288 | −$924,128 |
| 3 | $214,697,978 | −$62,310 |
| 4 | $214,694,704 | −$3,274 |
| 5 | $214,694,561 | −$143 |
| 6 | $214,694,556 | −$5 |
Sizing on pre-tax CFADS overstates the facility by $10.3m — about 4.8%.
Three observations that matter for how a model is built.
It converges fast. The first correction does 90% of the work and the result is stable to the dollar by iteration six. This is a well-behaved contraction, not a pathological loop, which is why iterative calculation appears to work.
It converges downward, always. More debt means more interest, more interest means less tax, less tax means more CFADS — but the effect on the sizing runs the other way, because the additional debt service consumes the additional cash. A pre-tax start therefore always overstates, and by a predictable order of magnitude.
The convergence path is information. A model that converges in six iterations is well conditioned. One that oscillates, or takes hundreds of iterations, has a structural problem — usually a tax loss carry-forward, a cash sweep or a DSRA rule that switches behaviour — and the right response is to find it, not to raise the iteration limit.
That last point deserves expanding, because it is where models go quietly wrong. The tax loop above is smooth: every function in it is continuous, so each iteration moves the answer a little less than the last and the sequence contracts. Introduce a MAX(0, ...) on a tax loss carry-forward, or a cash sweep that triggers above a threshold, and the function acquires a kink. A loop containing a kink can oscillate between two values indefinitely, or settle on whichever side of the discontinuity the calculation happened to approach from.
Excel will not tell you which happened. It will report a number, the same number every time, and that number will depend on the order cells were last calculated in. This is the substantive reason the FAST standard's prohibition exists — not that circular references are inelegant, but that a circularity crossing a discontinuity produces an answer with no defined value, presented with exactly the same confidence as one that has.
The practical test is cheap: change an unrelated input, change it back, and check the answer returns to where it was. If it does not, the loop is not converging — it is landing.
What About a Curved or Stepped Target?
A refinement that matters more than it sounds, and it removes a common objection to sculpting.
A single target DSCR across the whole tenor assumes the risk profile is constant. It rarely is. A project with a fifteen-year PPA and an eighteen-year facility is contracted for the first fifteen years and merchant for the last three, and applying 1.30× uniformly prices those two periods identically — which no credit committee actually believes.
The answer is a target that varies by period: 1.25× while contracted, stepping to 1.45× or higher once the offtake ends. The sculpt handles this without modification, because debt service is CFADS divided by that period's target:
DS(t) = CFADS(t) ÷ Target_DSCR(t)
and the present value identity still holds, so the closed form survives intact. The tail years simply contribute less debt capacity per dollar of cash flow, which is the intended result.
Two practical points follow. A stepped target makes the merchant tail's contribution explicit rather than buried in an average, which is what the next post is about. And it removes the temptation to solve the contracted/merchant problem by shortening the tenor — shortening loses the cash flow entirely, while a stepped target keeps it at a discount.
When Should You Not Sculpt?
Three situations where a level or minimum-amortisation schedule is preferable, and it is worth knowing them because sculpting is not free.
Where the lender imposes minimum amortisation. Many credit agreements require principal to reduce by at least a stated percentage per year regardless of cash flow, to avoid a back-ended profile that leaves a large balance exposed to late-life risk. That floor overrides the sculpt in the affected periods, breaks the constant-DSCR property, and — importantly — breaks the closed form, because debt service is no longer a simple function of CFADS. This is a real circularity, and it is one of the few that justifies iteration.
Where the cash flow profile is rising. Sculpting against rising CFADS back-ends the repayment, which increases the balance outstanding in later years and the exposure to anything that goes wrong late. Lenders often resist, and a level or lightly sculpted schedule is the compromise.
Where refinancing is intended. If the plan is to refinance at year seven, the shape of years eight to eighteen is largely theoretical, and optimising it with a sculpt adds complexity to a schedule nobody expects to run. What matters is the balance outstanding at the refinancing point, which a simpler structure makes easier to see and to negotiate.
What Are the Solutions?
Four, and the trade-offs are real.
| Approach | How it works | Cost |
|---|---|---|
| Algebraic | Reorder or solve in closed form so no loop exists | Not always possible; can be opaque |
| User-defined function | A UDF computes the converged value inside one cell | Requires VBA; the logic leaves the grid |
| Macro (copy-paste) | Iterate manually, paste values | Static — must be re-run whenever an input changes |
| Iterative calculation | Excel resolves the loop itself | Hides accidental circularity; results depend on calculation order |
Two of those deserve a stronger view than they usually get.
Iterative calculation is the worst option and the most used. The objection is not that it fails to converge — it usually does. It is that once enabled, every accidental circular reference in the workbook also silently resolves instead of raising an error, and the single most useful diagnostic in Excel is gone. A model with iteration enabled cannot tell you that you have made a mistake of exactly the kind iteration was enabled to accommodate.
Macros and Goal Seek are static procedures. If the inputs change, the procedure has to be repeated — and nothing in the workbook indicates that it has not been. A sensitivity table run over a macro-broken circularity produces numbers that look fine and are wrong, because the macro ran once at the base case.
Where a loop genuinely cannot be removed — the tax case above — the recommendation in practice is a user-defined function or parallel model, precisely because multiple circular references arising from taxes, interest income, fees and DSRA movements are too many for copy-and-paste to manage reliably.
How Do You Build This in Excel?
Closed form where possible, controlled iteration where not, and never iteration as a default.
The sculpt, with no circularity
DS(t) = CFADS(t) / Target_DSCR
DF(t) = 1 / (1 + Rate)^t
Sized_Debt = SUMPRODUCT(DS_range, DF_range)
Opening(1) = Sized_Debt
Interest(t) = Opening(t) * Rate
Principal(t) = DS(t) - Interest(t)
Closing(t) = Opening(t) - Principal(t)
The check that proves it
Closing(final) = $0.00
Put that cell somewhere visible with a hard test. If the sculpt is correct it is exactly zero; if it is not, something upstream has broken and the model should say so loudly.
The tax loop, handled explicitly
Iteration 0: size on pre-tax CFADS
Iteration n: interest(n) from schedule(n−1)
tax(n) = MAX(0, EBITDA − Dep − Interest(n)) × Rate
CFADS(n) = EBITDA − tax(n)
Debt(n) = SUMPRODUCT(CFADS(n)/Target, DF)
Stop when |Debt(n) − Debt(n−1)| < $1,000
Report the number of iterations taken and the final change as model outputs. Six iterations and a five-dollar residual is a healthy model; forty iterations is a warning.
The construction-phase loop, separated
During construction there is no CFADS, so IDC logic is built separately from the sculpt. Keeping the two apart is the single most useful structural decision in this part of a model: the construction funding loop is a genuine algebraic circularity that can often be solved in closed form, and mixing it with the operating-phase sculpt guarantees that neither can be.
ℹ️ Note: If a model requires iterative calculation to be enabled, document why — which specific dependency, and what the converged value is at the base case. A reviewer who finds iteration enabled with no explanation is entitled to assume the model has an accidental circular reference somewhere, and is usually right.
To build the closed-form sculpt, the zero-balance check and a controlled tax iteration, prompt Dezzmond with your CFADS profile and term sheet.
What Do Modellers and Lenders Actually Check?
- Does the final closing balance equal exactly zero? If not, the sculpt is broken.
- Is iterative calculation enabled, and is there a documented reason?
- Is the debt sized on post-tax CFADS? Pre-tax overstates, on the worked case by 4.8%.
- How many iterations does the tax loop take, and is that number reported?
- Is the construction funding loop separated from the operating sculpt?
- If a macro breaks the circularity, has it been re-run since the last input change?
- Do sensitivity tables respect the break? A table run over a static macro is unreliable.
Frequently Asked Questions
What is debt sculpting?
Setting principal repayment so that the debt service coverage ratio equals a target in every period, rather than using a level repayment schedule. Debt service in each period is CFADS divided by the target ratio.
Is sculpting circular?
No. The sized debt is the present value of the sculpted debt service stream discounted at the debt rate, which resolves in one pass and amortises to exactly zero. The circularity in project finance models comes from tax, IDC, fees and the DSRA.
Why does tax create a circular reference?
Because interest is tax-deductible. Taxable income depends on the debt balance, tax reduces CFADS, and CFADS sizes the debt. On the worked example, sizing on pre-tax CFADS overstates the facility by about 4.8%.
Should I enable iterative calculation?
Only as a last resort and with documentation. Once enabled, accidental circular references resolve silently instead of raising an error, which removes the most useful diagnostic in the workbook.
How much extra debt does sculpting raise?
On the worked example, 10.9% — $195.0m sculpted against $175.9m on a level schedule with the same cash flow. The gain comes from not discarding coverage: the level schedule delivers 1.54× in year one against a 1.30× requirement.
Can the target DSCR vary by period?
Yes, and it often should. A stepped target — lower while contracted, higher in merchant years — passes straight through the sculpt formula and keeps the closed form, because debt service is CFADS divided by that period's target.
What is wrong with a copy-paste macro?
It is a static procedure. If any input changes the macro must be re-run, and nothing in the model indicates that it has not been — so sensitivity tables run over a macro-broken loop produce plausible, wrong numbers.
Closing: Separate the Loops You Cannot Avoid from the Ones You Invented
The instruction to never release a model with purposeful circularity is often treated as unrealistic advice from people who have not had to size project finance debt. It is better read as an instruction to be precise about which loops are unavoidable.
Sculpting is not one of them. The present value identity resolves it, and a model that iterates to sculpt has taken on a diagnostic cost for no benefit. Construction funding is usually solvable algebraically with effort. Fees and reserve accounts often can be too, by reordering.
Tax is the genuine case, and it converges in six iterations to a number 4.8% below the pre-tax answer — which is a large enough difference that no model should be sizing on pre-tax cash flow, and a well-enough behaved loop that it can be handled deliberately rather than by switching on a setting that suppresses errors across the whole workbook.
The distinction matters because the cost of getting it wrong is not a wrong number. It is a model that cannot tell you it is wrong.
The next post takes the sizing question into the hardest revenue case: what happens when the PPA runs out before the debt does, and how lenders haircut a merchant tail.
Sources: Edward Bodmer — Project Finance Structuring with Sculpting · Edward Bodmer — Philosophy of Circular References · Forvis Mazars — Managing Circular References in Project Finance Models · Wall Street Prep — Debt Sizing in Project Finance