Advanced Financial Management · Discounted cash flow techniques

Project-Specific Discount Rates and Risk-Adjusted WACC

Updated 11 October 2026 · Fact-checked

A project-specific discount rate reflects the project's own business risk and the financing used. Take a proxy company's equity beta, ungear it to an asset beta, regear it to the project's gearing, apply CAPM to get the cost of equity, then weight it with the after-tax cost of debt to get a risk-adjusted WACC.

Understand Project-Specific Discount Rates and Risk-Adjusted WACC

A company's existing WACC reflects its existing business risk and its existing gearing. It is a fair discount rate only if a new project has the same business risk and is financed in the same proportions. In AFM, the scenario often tells you it is neither. You then need a rate built for the project.

Start with the two risks in a share beta. Business risk comes from the nature of the operations: how sensitive cash flows are to the economy and how much operating gearing the business has. Financial risk comes from debt, because interest must be paid before shareholders get anything. An equity beta contains both. An asset beta (also called ungeared beta) strips out the financial risk and shows business risk only.

That is why you cannot just copy a proxy company's equity beta. Its gearing is not the gearing you will use. The method is: find a listed company (a proxy) in the same business, ungear its equity beta to get an asset beta, then regear that asset beta to the gearing that applies to the project or the investing company. Use the regeared equity beta in CAPM to get the cost of equity.

Finally, combine the cost of equity and the after-tax cost of debt using the gearing weights, at market values. This gives a risk-adjusted WACC for the project. It works best when the project is small relative to the company and the company's capital structure will stay broadly the same. If the project changes the capital structure materially, or has special financing such as subsidised loans, the APV method is usually better because it values the financing side effects separately.

Two points the examiner watches. First, the gearing you regear to must be stated and justified: the company's target structure, or the project's own financing. Second, the proxy's debt beta is usually assumed to be zero unless the question gives one or gives enough data to work it out.

Key rules to remember

CAPM cost of equity: Ke = Rf + βe × (Rm − Rf); Rm − Rf is the equity risk premium. Use the regeared equity beta for the project.
Asset beta (ungearing): βa = [Ve × βe + Vd(1 − T) × βd] ÷ [Ve + Vd(1 − T)]; Ve and Vd are market values of equity and debt of the proxy. T is the tax rate. Use the proxy's own gearing and tax.
Asset beta when debt beta is zero: βa = βe × Ve ÷ [Ve + Vd(1 − T)]; The usual simplification in exam questions. Equivalent to βe ÷ [1 + (1 − T) × Vd/Ve].
Equity beta (regearing): βe = βa × [Ve + Vd(1 − T)] ÷ Ve when βd = 0; Use the target gearing, not the proxy's gearing.
Regearing with a debt beta: βe = βa + (βa − βd) × Vd(1 − T) ÷ Ve; Rearranged from the asset beta formula. Use it when a debt beta is given.
Debt beta from the cost of debt: βd = (Kd − Rf) ÷ (Rm − Rf); Only if the question tells you to treat Kd as the CAPM return on debt. Kd is the pre-tax cost of debt.
After-tax cost of debt: Kd after tax = Kd × (1 − T); For irredeemable debt. For redeemable debt, find the pre-tax yield by IRR first, then apply (1 − T) if tax relief is available.
Risk-adjusted WACC: WACC = Ke × Ve ÷ (Ve + Vd) + Kd(1 − T) × Vd ÷ (Ve + Vd); Weights are market values at the gearing you regeared to. Convert a D:E ratio into proportions of total value.

How to solve Project-Specific Discount Rates and Risk-Adjusted WACC questions

Use this order for any question on project-specific rates. It keeps the logic clear and earns method marks even if one number slips.

1Read the scenario and decide whether the existing WACC is suitable. Compare the project's business risk and the financing with the company's current position. State your conclusion in one sentence.
2Pick the proxy company or companies. If you have several, ungear each one and average the asset betas. Note any adjustment the question requires.
3Ungear each proxy equity beta to an asset beta using the proxy's own market-value gearing and tax rate. Assume a zero debt beta unless told otherwise.
4Decide the gearing to regear to. Use the target structure of the investing company or the project's stated financing. Convert D:E into Vd/Ve.
5Regear the asset beta to that gearing using the investing company's tax rate. Then calculate Ke with CAPM.
6Calculate the after-tax cost of debt. Calculate the weights from the target gearing and compute WACC.
7Use the WACC to discount the project cash flows and give the NPV and recommendation, if the question asks for it.
8Comment on limitations: proxy may not match exactly, CAPM assumptions, constant gearing assumed, and whether APV would be better if financing is special.

Quickest way: Ungear, regear and weight in one pass

When to use it: Use this when the question gives proxy data and a target gearing and the debt beta is zero. It is the standard exam case and takes only a few minutes.

Write the factor for the proxy: 1 + (1 − T) × Vd/Ve. Divide the equity beta by it to get βa.
Write the factor for the target: 1 + (1 − T) × Vd/Ve at target gearing. Multiply βa by it to get the new βe.
Ke = Rf + βe × ERP. Kd after tax = Kd × (1 − T).
Convert the target D:E to weights, then WACC = E weight × Ke + D weight × Kd after tax.
Sense-check: more gearing must give a higher equity beta than the asset beta, and the WACC should sit between Kd after tax and Ke.

Common mistakes in Project-Specific Discount Rates and Risk-Adjusted WACC

Using the proxy's equity beta directly in the project's CAPM calculation.
The equity beta looks like a ready-made input and the ungear-regear step feels like extra work.
Fix: Always ask: does the proxy have the same gearing as my target? Even if it does, show the ungear and regear steps or state clearly why they cancel out.
Regearing with the proxy's gearing or tax rate instead of the target's.
Students reuse the ratio from the ungearing line without pausing.
Fix: Label each calculation 'proxy' or 'target' before you start. Proxy data is used only to ungear. Target data is used only to regear.
Forgetting the (1 − T) term in the beta formulas, or applying it twice.
The tax adjustment appears in several formulas and students mix them up.
Fix: In the ungear and regear factors, tax appears once on debt: Vd(1 − T). Using the same factor form in both directions avoids errors.
Using book values or the wrong ratio for gearing weights.
D:E and D/(D+E) are confused, or book values are used because they are easier to find.
Fix: Use market values. If gearing is 1:3 debt to equity, debt is 25% of total value, not 33%. Write the weights down before computing.
Using the pre-tax cost of debt in WACC.
Students remember CAPM and forget the tax shield on interest.
Fix: Multiply Kd by (1 − T) whenever tax relief is available. The exception is the debt beta calculation, which uses pre-tax Kd.
Using a WACC where the question needs APV, or giving no commentary on suitability.
WACC is the more familiar method and students apply it by default.
Fix: State the assumptions behind WACC: same risk, constant gearing, marginal project. If financing is special or the capital structure changes, say APV is more suitable and explain why.

Worked examples

Example 1

Kiran Ltd is a food retailer considering a project in online grocery delivery. Its own WACC is not suitable because the business risk is different. A listed online delivery company, Zest plc, is a good proxy. Zest has an equity beta of 1.50. Its debt to equity ratio is 1:3 by market value. Its debt beta is zero. Corporate tax is 25% for both companies. Kiran will finance the project at 40% debt and 60% equity by market value. Risk-free rate is 4%, equity risk premium is 5%, and Kiran's pre-tax cost of debt is 6%. Calculate a risk-adjusted WACC for the project.

Show the solution

Ungear Zest. Vd/Ve = 1/3. Factor = 1 + 0.75 × 1/3 = 1.25.
Asset beta = 1.50 ÷ 1.25 = 1.20.
Regear to Kiran's target. Debt 40%, equity 60%, so Vd/Ve = 40/60 = 2/3. Factor = 1 + 0.75 × 2/3 = 1.50.
Equity beta = 1.20 × 1.50 = 1.80.
Ke = 4% + 1.80 × 5% = 13%.
Kd after tax = 6% × (1 − 0.25) = 4.5%.
WACC = 0.60 × 13% + 0.40 × 4.5% = 7.8% + 1.8% = 9.6%.

Answer: The risk-adjusted WACC for the project is 9.6%. Use it to discount the project's cash flows, because it reflects Zest's business risk and Kiran's target gearing.

Example 2

Orbit Inc is evaluating a project in a new sector. A proxy company has market value of equity $400m and debt $125m. Its equity beta is 1.25, its debt beta is 0.10, and tax is 20%. Orbit will fund the project so that debt to equity is 1:2 by market value. Risk-free rate is 3% and equity risk premium is 6%. Orbit's debt is priced to give the CAPM return implied by the debt beta. Tax is 20%. Calculate the project discount rate.

Show the solution

Proxy Vd(1 − T) = 125 × 0.80 = 100. Ve + Vd(1 − T) = 400 + 100 = 500.
Asset beta = (400 × 1.25 + 100 × 0.10) ÷ 500 = (500 + 10) ÷ 500 = 1.02.
Target: Vd/Ve = 0.5, so Vd(1 − T)/Ve = 0.5 × 0.80 = 0.40.
Regeared equity beta = 1.02 + (1.02 − 0.10) × 0.40 = 1.02 + 0.368 = 1.388.
Ke = 3% + 1.388 × 6% = 3% + 8.328% = 11.328%.
Pre-tax Kd = 3% + 0.10 × 6% = 3.6%. After tax = 3.6% × 0.80 = 2.88%.
Weights: debt 1/3, equity 2/3. WACC = (2/3) × 11.328% + (1/3) × 2.88% = 7.552% + 0.96% = 8.512%.
Check: asset beta from the new structure with Ve = 100 and Vd(1 − T) = 40 is (100 × 1.388 + 40 × 0.10) ÷ 140 = 142.8 ÷ 140 = 1.02. This matches.

Answer: The project discount rate is about 8.51%. The regeared equity beta is 1.388 and the cost of equity is about 11.33%.

Exam tips

Show every beta step on its own line with the label 'proxy' or 'target'. Markers give credit for method, and clear layout is part of the professional skills marks.
Read the question for the debt beta. If none is given, assume zero and say so. If one is given, use the full formula and do not drop it.
Always add a short comment on suitability. Say whether the proxy truly matches the project, and whether WACC or APV is more appropriate given the financing.
If several proxy companies are given, ungear each separately and then average the asset betas. Do not average equity betas of companies with different gearing.
Keep spare time for the written part. Typical points are business risk versus financial risk, limits of CAPM, and the constant gearing assumption.

Practice questions from Discounted cash flow techniques

Project-Specific Discount Rates and Risk-Adjusted WACC: frequently asked questions

Why do we ungear and regear beta in AFM?

The proxy's equity beta includes its own financial risk, which does not match your project's financing. Ungearing removes that and leaves business risk only. Regearing adds the financial risk of the structure you will actually use.

When should I use WACC and when APV?

Use WACC when the project has similar business risk to the existing business, is small relative to the company, and gearing will stay broadly constant. Use APV when the capital structure changes or there are special financing effects such as subsidised loans or issue costs. APV values these effects separately.

Should I assume the debt beta is zero?

Yes, if the question does not give one and does not ask you to derive one. State the assumption in your answer. If a debt beta is provided, include it in both the ungearing and regearing formulas.

Which gearing do I use to regear the beta?

Use the gearing that the question states for the project or the investing company's target structure, at market values. Convert any debt to equity ratio into proportions of total value before calculating WACC.

What is the difference between business risk and financial risk?

Business risk comes from the operations: demand, costs and operating gearing. Financial risk comes from using debt, which creates fixed interest obligations. The asset beta measures business risk. The equity beta measures both.