Advanced Financial Management · Impact of financing on investment decisions and adjusted present values

Ungeared Cost of Equity and Business Risk Adjustment in APV

Updated 11 October 2026 · Fact-checked

The ungeared cost of equity is the return shareholders would require if the business had no debt. You find it by degearing a proxy company's equity beta into an asset beta, or by using the Modigliani and Miller formula. You then use it to discount the base-case cash flows in APV.

Understand Ungeared Cost of Equity and Business Risk Adjustment

APV splits a project into two parts. First you value it as if it were all-equity financed. Then you add the value of financing side effects, such as the tax shield on debt. The first part needs a discount rate that reflects only business risk. That rate is the ungeared cost of equity.

Your company's own cost of equity does not work. It includes financial risk from its current gearing. It may also reflect a different business. So you look for a proxy company in the same line of business as the project. Its equity beta mixes business risk and financial risk. You strip out the financial risk to leave the asset beta, which measures business risk only. This is called degearing.

Once you have the asset beta, put it into CAPM. That gives the ungeared cost of equity: risk-free rate plus asset beta times the equity risk premium. You use this rate to discount the project's after-tax operating cash flows. These cash flows are treated as if no debt existed.

The other route is the Modigliani and Miller (MM) formula with tax. It starts from the company's own geared cost of equity, its cost of debt, its tax rate and its market value gearing. It gives the ungeared cost of equity directly. Use it when the question gives a cost of equity, not a beta.

In APV you do not regear to the project's gearing. The financing effects are valued separately. You regear only if the question asks for a geared cost of equity or a risk-adjusted WACC.

Key rules to remember

CAPM: Ke = Rf + β × (Rm − Rf); Rm − Rf is the equity risk premium. Check whether the question gives Rm or the premium.
Asset beta (general form): βa = βe × E ÷ [E + D(1 − T)] + βd × D(1 − T) ÷ [E + D(1 − T)]; E and D are market values. T is the tax rate. βd is the debt beta.
Asset beta (debt beta zero): βa = βe × E ÷ [E + D(1 − T)]; This is the usual exam form. Use it unless a debt beta is given.
Regearing the beta: βe = βa × [1 + (1 − T) × D/E]; Assumes a zero debt beta. Use only if the question asks for a geared beta or WACC.
Ungeared cost of equity from CAPM: Ke(u) = Rf + βa × (Rm − Rf); This is the APV base-case discount rate.
MM with tax: geared cost of equity: Ke = Ke(u) + (Ke(u) − Kd) × (1 − T) × D/E; Kd is the pre-tax cost of debt. Use market value D/E.
MM with tax: ungeared cost of equity: Ke(u) = [Ke × E + Kd × (1 − T) × D] ÷ [E + D(1 − T)]; Use when you are given the geared cost of equity, not a beta.

How to solve Ungeared Cost of Equity and Business Risk Adjustment questions

Use this method whether the question gives betas or costs of capital. Decide first which route the data points to.

1Identify the project's business risk. Decide whether your own company's risk applies or you need a proxy company in the project's industry.
2List the proxy's equity beta, market value of equity, market value of debt and tax rate. If you are given a debt-to-equity ratio, convert it to E and D values, such as 3:1 meaning E = 3 and D = 1.
3Degear: calculate βa = βe × E ÷ [E + D(1 − T)]. Include a debt beta only if the question gives one.
4If several proxies are given, degear each one and average the asset betas, unless told otherwise.
5Put the asset beta into CAPM to get Ke(u) = Rf + βa × (Rm − Rf). If no beta is given, use the MM formula with Ke, Kd, T, E and D instead.
6Discount the base-case after-tax cash flows at Ke(u) to get the base-case NPV.
7Only if asked for a geared figure, regear using the project's financing. Otherwise move on to the financing side effects of APV.
8State your assumptions briefly, such as a zero debt beta and market value weights, and comment on how reliable the proxy is.

Quickest way: Degear, CAPM, discount

When to use it: Use this when the question gives a proxy beta and gearing and asks for the APV base-case rate. It is the fastest route in a time-pressed Section A or B question.

Write E = 1 style weights first. For D/E of 0.25, use E = 1 and D = 0.25.
Compute the divisor: 1 + (1 − T) × D/E. Divide the equity beta by it to get βa.
Compute Ke(u) = Rf + βa × premium in one line.
Discount the cash flows at Ke(u) and stop. Do not regear unless the requirement says so.

Common mistakes in Ungeared Cost of Equity and Business Risk Adjustment

Using the company's own equity beta or cost of equity to discount the base case.
It is already in the question and looks convenient.
Fix: Check whether it reflects the project's business risk and no financial risk. Usually you need a proxy asset beta or the MM ungeared rate.
Leaving out (1 − T) when degearing.
Students remember the shape βe × E ÷ (E + D) from basic theory.
Fix: Write the divisor as E + D(1 − T) every time. The tax shield on debt reduces its effect on equity risk.
Using book values of debt and equity.
The balance sheet figures are the first ones in the data.
Fix: Use market values. If only a market ratio is given, use that ratio.
Regearing the asset beta to the project's gearing in an APV question.
Students mix up the WACC method with APV.
Fix: In APV, discount the base case at Ke(u) and value financing effects separately. Regear only when asked.
Using D/(D + E) in a formula that needs D/E.
Gearing is quoted in different ways.
Fix: Convert to D and E values first, then plug in. For example, 25% debt in total capital means D = 25 and E = 75.
Putting the after-tax cost of debt in the MM formula where the pre-tax cost belongs.
The (1 − T) already appears in the formula and gets applied twice.
Fix: Enter the pre-tax Kd. The formula applies (1 − T) itself.

Worked examples

Example 1

Quoted company P is in the same business as a proposed project. P has an equity beta of 1.35. Its debt to equity ratio at market values is 1:3. The tax rate is 25%. The risk-free rate is 4% and the market return is 10%. Debt beta is zero. Calculate the asset beta and the ungeared cost of equity to use in an APV base case.

Show the solution

Set E = 3 and D = 1. So D/E = 1/3.
Divisor: E + D(1 − T) = 3 + 1 × 0.75 = 3.75.
βa = 1.35 × 3 ÷ 3.75 = 4.05 ÷ 3.75 = 1.08.
Equity risk premium = 10% − 4% = 6%.
Ke(u) = 4% + 1.08 × 6% = 4% + 6.48% = 10.48%.

Answer: Asset beta = 1.08. Ungeared cost of equity = 10.48%.

Example 2

A company has market value of equity $60m and debt $20m. Its cost of equity is 13%, pre-tax cost of debt is 6% and tax rate is 25%. A new project has the same business risk as the company. It needs an investment of $75m now and gives a perpetual after-tax operating cash flow of $9.28m a year. Using the MM formula, find the ungeared cost of equity and the base-case NPV.

Show the solution

Ke × E = 13% × 60 = 7.8.
Kd × (1 − T) × D = 6% × 0.75 × 20 = 0.9.
Numerator = 7.8 + 0.9 = 8.7.
Denominator = E + D(1 − T) = 60 + 20 × 0.75 = 75.
Ke(u) = 8.7 ÷ 75 = 11.6%.
Check: Ke = 11.6% + (11.6% − 6%) × 0.75 × (20/60) = 11.6% + 1.4% = 13.0%. This matches.
Base-case PV = 9.28 ÷ 0.116 = $80m.
Base-case NPV = 80 − 75 = $5m.

Answer: Ungeared cost of equity = 11.6%. Base-case NPV = $5m. The financing side effects are then added to get the APV.

Exam tips

Read the data for hints on the route. A beta and a proxy company point to degearing and CAPM. A geared cost of equity with Kd points to the MM formula.
Show the degearing line clearly, with E + D(1 − T) written out. Method marks are awarded even if a number slips.
State your assumptions, such as a zero debt beta and market values. These gain professional skills credit in Section A.
Add a short comment on the proxy's limits. No company has exactly the same risk, gearing or project mix, and a single proxy is a weak estimate.
Do not regear in an APV question unless the requirement asks for it. Move straight on to the tax shield and issue costs.

Practice questions from Impact of financing on investment decisions and adjusted present values

Ungeared Cost of Equity and Business Risk Adjustment: frequently asked questions

What is the difference between an equity beta and an asset beta?

An equity beta reflects both business risk and the financial risk from the company's debt. An asset beta removes the financial risk, so it measures business risk only. You compare projects and companies on asset betas.

Why do we use a proxy company in APV?

The project may carry business risk different from your company's existing activities. A quoted company in the same industry gives an observable beta. You degear it so that its financial risk does not distort the base-case rate.

Do I regear the asset beta in APV?

No, not for the base case. APV discounts at the ungeared cost of equity and values debt effects separately. Regear only when the question asks for a geared beta or a risk-adjusted WACC.

When should I use the MM formula instead of asset beta?

Use MM when you are given a cost of equity, a cost of debt, a tax rate and gearing, but no beta. It gives the ungeared cost of equity directly. If a beta is given, the CAPM route is quicker.