Cost of Capital in Project Finance: Why a Constant WACC Is Wrong by Construction
Take the project this series has been building. Compute its net present value three defensible ways:
Constant WACC at financial close (7.62%) NPV = $31,559,737
Adjusted present value NPV = $21,950,544
Time-varying WACC NPV = $17,116,886
A spread of $14.4m on identical cash flows, from nothing but the choice of discounting method. And the highest answer — the one most commonly produced, because a single WACC is what a spreadsheet defaults to — overstates the time-varying result by 84%.
The problem is not that the WACC was estimated badly. It is that project finance guarantees the capital structure changes. The debt amortises to zero by design. A weighted average cost of capital weighted on a mix that exists only at financial close is describing a structure that stops existing the following year.
This post covers why the textbook approach breaks here, what the WACC path actually looks like, the two methods that handle it, and why the industry's habit of reporting an equity IRR rather than an NPV turns out to be the right one.
ℹ️ Note: All figures are labelled assumptions carried forward from the Series E capital structure. The three methods make different assumptions about the tax shield and are not expected to agree exactly; the direction and magnitude of the spread is the point.
What Is the Cost of Capital Here?
The return required by the providers of the project's funding, weighted by how much each provides. In principle:
WACC = (D / (D+E)) × Kd × (1 − tax) + (E / (D+E)) × Ke
At financial close, on the worked structure:
Debt $203,649,376 75%
Equity $67,883,125 25%
Cost of debt 6.50%
Tax rate 21%
Cost of equity 15.07%
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WACC 7.62%
That number is correct for one day.
Why the Textbook Approach Breaks
Four reasons, and the first is decisive.
The capital structure is designed to change. A corporate WACC assumes a target capital structure the company maintains. A project finance structure amortises its debt to zero over the facility term — that is the entire point of the sculpting, the sweep and the waterfall. Gearing at close is 75%; by final maturity it is zero.
There is no traded equity. CAPM requires a beta, and a single project has no observable one. The standard workaround — take a listed comparable's beta, unlever it, relever at the project's gearing — imports the comparable's business mix along with its beta, and a listed renewables developer is not a single contracted asset.
The risk profile changes over the life. Construction risk, ramp risk and operating risk are genuinely different, and a single discount rate applied to all three periods prices them identically. The Series E posts are full of reasons why they are not the same.
The debt is non-recourse and covenant-heavy. The cost of debt is not just the margin. It includes the reserve carry, the lock-up's effect on distribution timing, and the sweep's effect on their amount — none of which appears in Kd and all of which reduces what equity receives.
What the WACC Path Actually Looks Like
As the debt amortises, the weighting shifts toward equity and the WACC rises toward the cost of equity:
| Point | Gearing | WACC |
|---|---|---|
| Financial close | 75% | 7.62% |
| Year 10 | ~57% | 8.54% |
| Year 18 | ~10% | 12.96% |
| After repayment | 0% | 15.07% |
That is not a forecast or a scenario. It is arithmetic that follows from the amortisation schedule, and it is knowable at financial close.
Discounting twenty years of cash flow at 7.62% therefore applies the financial-close cost of capital to years in which the project is substantially or entirely equity funded. The later cash flows — which in a project with a merchant tail or a long contracted life are a large share of the value — are discounted far too lightly.
The result is the $14.4m gap in the opening table, and it is directional: a constant close-date WACC always overstates the value of a self-amortising structure, because the true rate only ever rises.
What Should You Use Instead?
Two methods handle a changing capital structure properly, and a third avoids the question entirely.
Adjusted present value. Value the project as if unlevered, then add the present value of the financing benefits separately:
Unlevered cost of equity (Ku) 9.04%
Unlevered NPV at Ku $1,486,253
PV of interest tax shield (discounted at Kd) $20,464,290
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APV $21,950,544
APV's advantage is transparency: it separates what the asset is worth from what the financing contributes, which is exactly the separation the three-IRR post argued for. The tax shield is $20.5m of the $22.0m total, which is a striking and useful disclosure — on these assumptions nearly all the value of this project to equity comes from the deductibility of interest rather than from the operating asset.
A time-varying WACC. Compute the weighting each period from the actual debt and equity balances, and discount each period's cash flow at its own rate. More laborious, conceptually straightforward, and it produces the $17.1m figure.
Flow to equity — discount equity cash flows at the cost of equity. This sidesteps the weighting problem entirely, because there is nothing to weight: the cash flows are already after debt service, and the cost of equity is the only rate involved.
That last method is what project finance actually does, and it is why a project finance model reports an equity IRR rather than an NPV at WACC. The convention that looks like a quirk of the industry is in fact the method that handles the structure correctly, arrived at by practice rather than by theory.
Does the Tax Shield Really Belong to Equity?
A figure of 93% demands scrutiny, and scrutinising it exposes an assumption the APV calculation makes silently.
An interest tax shield is worth something only if there is taxable income to shield and a taxpayer able to use the deduction. In a corporate context those are usually safe assumptions. In renewable project finance neither is.
There may be no taxable income. A project with a hundred percent bonus depreciation deduction in year one, as the depreciation post described, generates a very large loss before any interest is considered. Interest deductions in the early years therefore add to a loss rather than shielding income, and their value is deferred to whenever the loss is actually used — if it ever is.
The deduction may be allocated elsewhere. In a partnership flip, tax benefits including the interest deduction are allocated ninety-nine percent to the tax equity investor in the early years. The shield is real and it is not the sponsor's, which means an APV computed at the project level attributes value to equity that a different partner receives.
The user may be gated. The four gates from the outside basis post — §704(d), §465, §469 and §461(l) — determine whether an allocated deduction is usable at all, and a suspended deduction is worth nothing until it is released, and nothing at all if it is extinguished on exit.
Back-leverage moves it again. Interest at the holding company level is deductible to a different entity from the project, and the project-level APV does not see it.
So the honest statement about the worked figure is narrower than it first appears: 93% of this project's APV is the tax shield, assuming the deduction is usable in the period it arises by the party holding the equity. In a partnership flip with bonus depreciation, that assumption is wrong in at least two ways.
The practical instruction is to compute the tax shield against the actual taxpayer and the actual gates, not against the project's own interest expense — and to be suspicious of any valuation where the shield is most of the answer, because that is a valuation resting almost entirely on a set of tax facts the operating model never examines.
Real or Nominal?
A smaller point that produces large errors when it goes wrong.
A discount rate and the cash flows it discounts must be on the same basis. A nominal rate discounts cash flows that include inflation; a real rate discounts cash flows expressed in constant money. Mixing them is a common and expensive error.
Two features of renewable projects make the mix easy to produce accidentally.
Revenue and costs escalate differently. A PPA may have a fixed price with no escalation, a fixed escalator of two percent, or full CPI indexation — and the operating cost base escalates at whatever the market does, which is a different number. A model with a non-escalating PPA and an escalating cost base has a real margin that declines every year, and that is a genuine feature rather than an error. But it must be modelled in nominal terms for the effect to appear at all.
Debt is nominal. Debt service is fixed in cash terms, so it is a nominal quantity by construction. A real-terms model has to convert it, and the conversion is a frequent source of mistakes.
The practical rule is to build in nominal terms throughout for a project financing, because the debt service, the tax calculation and the covenant tests are all nominal quantities and converting them introduces error for no benefit. Real-terms analysis has its place in long-horizon policy work; it has very little place in a model whose central output is a coverage ratio against a fixed payment.
Where a real discount rate is quoted — as it sometimes is for infrastructure hurdle rates — convert it properly rather than approximately: (1 + nominal) = (1 + real) × (1 + inflation), not nominal = real + inflation, which on a 9% real rate and 2.5% inflation is out by 22.5 basis points.
How Is the Cost of Equity Actually Set?
Rarely by CAPM, in practice.
Target returns. Most sponsors and funds operate with a required return by asset class and risk profile — a contracted operating asset at one level, a merchant development project several hundred basis points higher. These are set by what capital is available at, which is a market observation rather than a model output.
Build-up. A risk-free rate plus a series of stated premiums: country, market, technology, construction, offtake, merchant exposure. It is transparent about what is being charged for and is honest that the components are judgements.
Relevered comparable betas. The CAPM route, used mostly where a formal valuation requires it. The difficulties above apply.
The pragmatic observation is that the cost of equity in project finance is closer to a hurdle set by capital availability than to a computed required return — and treating it as the latter lends a precision the number does not have.
The useful discipline, from the debt sizing post, is the same here: express it as a spread over the cost of debt rather than as an absolute. On the worked structure that spread is 857 basis points, and it is a more stable quantity across a rate cycle than either component.
One Rate, or One Rate Per Phase?
The third of the four objections above, and the one with the clearest fix.
A project passes through phases with genuinely different risk. Construction carries execution, cost overrun and completion risk and generates no revenue. Ramp carries performance risk against untested equipment. Steady-state operations under a contract carry counterparty and availability risk. A merchant tail carries price risk of an entirely different order.
Applying one discount rate to all four prices them identically, which no analyst would defend if asked directly and which almost every model does by default.
A staged rate is straightforward to implement and forces a useful conversation:
Construction Ke + construction premium
Ramp Ke + reduced premium
Contracted operation Ke
Merchant tail Ke + merchant premium
The sizes of those premiums are judgements, and making them explicit is most of the benefit — a model that charges 300 basis points for merchant exposure has stated a view that can be examined, while one applying a flat rate has stated the same view invisibly and set the premium to zero.
Two cautions. Staged rates interact awkwardly with an IRR, since an IRR produces a single rate by construction and cannot be compared to a schedule of hurdles; the natural output is an NPV. And the premiums should not double-count risks already reflected in the cash flows — a merchant tail already haircut on price and volume, as the merchant tail post described, should not also carry a full merchant discount rate premium, or the same risk is charged twice.
The cleanest arrangement is to take risk out of the cash flows where it can be quantified — basis, curtailment, availability, all of which Series C addressed — and to use the discount rate only for risk that cannot be, which is mostly the residual uncertainty about whether the quantification is right.
How Do You Build This in Excel?
As a path, not a constant, with the method stated.
The WACC path
For each period t:
Gearing(t) = Debt_Balance(t) / (Debt_Balance(t) + Equity_Book)
WACC(t) = Gearing(t) × Kd × (1 − Tax) + (1 − Gearing(t)) × Ke
Cumulative discount factor:
DF(t) = DF(t−1) / (1 + WACC(t))
Note the cumulative construction. Discounting each period's cash flow at that period's WACC raised to the power of t is wrong — the discount factor must compound the sequence of rates actually applying.
The three methods, side by side
PF_NPV_ConstantWACC $31,559,737
PF_NPV_APV $21,950,544
PF_NPV_TimeVaryingWACC $17,116,886
PF_MethodSpread $14,442,851
Publishing all three is more useful than choosing one, because the spread is information: a project whose value depends heavily on the discounting method is a project whose value depends heavily on the financing, and that is worth knowing.
The APV decomposition
PF_UnleveredNPV $1,486,253
PF_TaxShieldPV $20,464,290
Tax shield as % of APV 93.2%
That percentage is the single most useful output in this post. A project whose value is 93% tax shield is not primarily an operating asset — it is a financing structure attached to one, and its value is exposed to tax policy in a way the operating model never shows.
The flow-to-equity check
Equity cash flows discounted at Ke = 15.07%
NPV should be approximately zero if Ke was derived from the equity IRR
If the cost of equity was taken as the equity IRR, the flow-to-equity NPV is zero by construction — which is a useful check that the inputs are internally consistent, and a reminder that a hurdle rate set equal to the modelled return produces no information.
ℹ️ Note: Never apply a single discount rate across construction, ramp and operations. Those periods carry different risks, and the Series E material is largely an explanation of why. Where a single rate is required for simplicity, say so and test the alternative.
To build the WACC path, the three methods and the APV decomposition, prompt Dezzmond with your capital structure and cost inputs.
What Do Analysts Actually Check?
- Is the WACC constant? If so, it is describing a capital structure that exists for one day.
- What does the WACC path look like, and how much of the value sits in the years where it has risen?
- What share of value is the tax shield? On the worked case, 93%.
- Is the cost of equity a computed rate or a market hurdle? Usually the latter, and it should be said.
- Is the same rate applied to construction and operations?
- Is the hurdle expressed as a spread over the cost of debt rather than as an absolute?
- Has the discount factor been built cumulatively where the rate varies?
Frequently Asked Questions
Why is a constant WACC wrong in project finance?
Because the capital structure is designed to change. The debt amortises to zero, so gearing falls from 75% to nothing and the true WACC rises from 7.62% to the cost of equity. A close-date WACC applied across twenty years discounts later cash flows far too lightly.
How much does it matter?
On the worked project, a constant WACC produces an NPV of $31.6m against $17.1m on a time-varying basis — an 84% overstatement, and it is always in that direction for a self-amortising structure.
What is adjusted present value?
Valuing the project unlevered and adding the present value of financing benefits separately. It produced $22.0m here, of which $20.5m is the interest tax shield — a separation that makes visible how much of the value comes from the financing rather than the asset.
Why do project finance models report an equity IRR instead of an NPV?
Because discounting equity cash flows at the cost of equity avoids the changing capital structure entirely. The industry convention turns out to be the method that handles the problem correctly.
Is the tax shield really worth 93% of the value?
Only if the deduction is usable, in the period it arises, by the party holding the equity. With bonus depreciation there may be no income to shield; in a partnership flip the deduction is allocated to the tax equity investor; and the §704(d), §465, §469 and §461(l) gates may suspend it entirely.
Should the model be in real or nominal terms?
Nominal, for a project financing. Debt service, tax and covenant tests are all nominal quantities, so a real-terms model has to convert them and introduces error for no benefit. Convert any real hurdle rate multiplicatively, not by addition.
How is the cost of equity set in practice?
Usually as a target return by asset class, reflecting what capital is available at, rather than as a CAPM output. Expressing it as a spread over the cost of debt is more stable than quoting an absolute rate.
Closing: The Rate Is an Output, Not an Input
The cost of capital is taught as something you determine and then apply. In project finance it is closer to a result of the structure than an input to it.
The gearing comes out of the debt sizing, which comes out of the coverage tests, which come out of the cash flows. The cost of debt comes out of the market and the covenant package. The cost of equity is whatever capital is available at. And the weighting between them changes every year, by design, according to an amortisation schedule that the coverage tests determined.
So a WACC in a project finance model is a derived quantity that describes a moment, and using it as though it described the life of the asset produces an error of eighty-four percent in the direction of optimism — reliably, because the true rate only ever moves one way.
The industry mostly avoids this by accident. Project finance reports equity IRRs, not NPVs at WACC, and the flow-to-equity method that convention implies is the one that handles a changing capital structure correctly. The practitioners were right and the textbook was wrong, which is unusual enough to be worth saying plainly.
Where an NPV is required — for a valuation, an impairment test, a comparison against a corporate hurdle — the honest approach is to produce all three, publish the spread, and report what share of the value is the tax shield. On the worked project that share is ninety-three percent, which reframes the asset entirely and is invisible in every other presentation of the same numbers.
The final post in this series takes the cases all of this gets run through: base case, banking case and downside case, and what distinguishes them.
Sources: Edward Bodmer — Project Finance Exercises · Wall Street Prep — Distinctive Features of a Project Finance Model · Energy IB Guide — Renewable Energy Valuation Methods · Ryan O'Connell, CFA — Building a Project Finance Financial Model