Project-Specific Cost of Capital and Adjusted WACC

A company that sells groceries decides to open a pharmacy chain. The new business has different customers, different costs and a different sensitivity to the economy. Shareholders will ask for a return that reflects the risk of pharmacies, not the risk of groceries, and a project appraised at the company’s own cost of capital will be judged against the wrong yardstick.

It will be too easy to pass if pharmacies are riskier, and too hard if they are safer.

The way to find the right rate is to look at the quoted companies that already do the new business, learn the systematic risk of that business from their share prices, strip out the effect of how they are financed, and then put back the effect of how the new project will be financed.

This topic explains the beta factors (equity, asset and debt), the factors that affect beta, when a project-specific rate is required, the steps of degearing and regearing with the formulae, how to use a proxy company that has more than one business, why proxy companies are an imperfect guide, and the adjusted present value method when the financing changes a great deal, with worked examples.

The next topic examines how gearing affects risk and the cost of capital.

The skill was tested in November Diet, 2025, Question 3 (20 marks) (the asset beta, the re-geared beta and the project cost of capital, then why asset betas differ and the difficulties of using proxy companies) and in May Diet, 2026, Question 3(a) (10 marks) (a risk-adjusted divisional cost of capital compared with an internal rate of return). Read the weighted average cost of capital first.

Beta factors and what affects them

The capital asset pricing model needs a beta for the project, and a project has no shares of its own. The company’s own equity beta measures the systematic risk of its existing business and its existing gearing. There are three kinds of beta:

• Equity (geared) beta (β_e): the market risk of the shares, which includes the business risk of the company’s activities and the financial risk from its borrowing.
• Asset (ungeared) beta (β_a): the market risk of the business with the effect of debt removed; it measures only the business risk of the assets.
• Debt beta (β_d): the systematic risk of the debt; usually assumed to be zero because debt is almost default-free.

Beta depends on the nature of the business (cyclical businesses and luxury goods have higher betas than utilities), on operating gearing (a high proportion of fixed costs magnifies the effect of sales on profit), on financial gearing (more debt, higher equity beta), on size and growth style, on the market conditions, and on how it was measured (the market index used and the period and frequency of the returns).

When a project-specific rate is needed

The company’s WACC can be used only if the project leaves business risk and financial risk unchanged. A risk-adjusted rate is needed when:

• the business risk of the project differs from that of the company: degear and regear to get a cost of equity for the business risk of the project;
• the capital structure will change because of the project: if the change is small, use the new weights in a risk-adjusted WACC; if it is large, use the adjusted present value.

The same applies to a divisional cost of capital. A division in a riskier industry should be appraised at a higher rate than one in a safer industry. A single group rate would make the group favour projects in the riskier division and starve the safer one.

The steps: degear, regear, then the rate

The formulae (given on the formula sheet) with tax at t, market value of equity V_e and market value of debt V_d:

β_a = β_e × V_e ÷ [V_e + V_d(1 − t)] + β_d × V_d(1 − t) ÷ [V_e + V_d(1 − t)]

With a debt beta of zero the second term disappears: β_a = β_e × V_e ÷ [V_e + V_d(1 − t)], and the regeared beta is β_e = β_a × [V_e + V_d(1 − t)] ÷ V_e.

A worked example: from groceries to pharmacies

Delta, a grocery retailer, is considering a pharmacy business. A quoted pharmacy company has an equity beta of 1.4 and a debt to equity ratio of 25% (market values). Tax is 30%, the debt beta is zero, the risk-free rate is 8% and the market risk premium is 7%. Delta expects to finance the project so that its debt to equity ratio is 40%. The pre-tax cost of debt is 14%.

1. Degear the proxy.
   Take V_e = 100, V_d = 25: V_d(1 − t) = 17.5. β_a = 1.4 × 100 ÷ 117.5 = 1.19.
2. Regear to Delta’s gearing.
   V_e = 100, V_d = 40: V_d(1 − t) = 28. β_e = 1.1915 × 128 ÷ 100 = 1.525.
3. Cost of equity.
   8 + 1.525 × 7 = 18.7%.
4. Weights.
   Equity 100 ÷ 140 = 71.4%; debt 28.6%.
   After-tax cost of debt 14% × 0.70 = 9.8%.
5. Risk-adjusted WACC.
   0.714 × 18.7% + 0.286 × 9.8% = 13.34% + 2.80% = 16.1%.

A project with an internal rate of return of 15% would pass at a group rate of 12% but fails at 16.1%, which is the rate that reflects the risk of pharmacies financed in this way.

When the proxy has more than one business

A proxy company may also run other businesses. Two things must be removed: the proxy’s financial risk (degearing) and the unwanted business. If both betas are at the same level (both equity betas or both asset betas), remove the unwanted business first, by weighting by value, and then degear. If they are at different levels, degear first.

Example: a proxy has an equity beta of 1.5 and is 65% pharmacies and 35% beverages, whose equity beta at the same gearing is 0.9. Then 1.5 = 0.35 × 0.9 + 0.65 × β_pharmacy, so β_pharmacy = (1.5 − 0.315) ÷ 0.65 = 1.82 (an equity beta). Degear at a debt to equity ratio of 30%: β_a = 1.8231 × 100 ÷ 121 = 1.507; regear at 40%: 1.507 × 128 ÷ 100 = 1.93, and the cost of equity is 8 + 1.93 × 7 = 21.5%.

Reasons asset betas differ and problems with proxy companies

Two companies in similar businesses can have different asset betas because of differences in the type of business (the product and its sensitivity to the economy), operating gearing (fixed against variable costs), the ability to pass on cost changes to customers, size and diversification, and the regulation of prices. The difficulties of using a proxy company are:

• there may be no quoted company in exactly the same business (no “pure” proxy), and a proxy with other businesses must be adjusted;
• the proxy’s capital structure and the way it measures its debt (including the debt beta and the tax position) are assumptions;
• the proxy may have a different operating gearing, size, market position or geography;
• betas are estimates that depend on the index, the period and the frequency used, and a thinly traded share gives an unreliable beta;
• the proxy’s beta reflects its existing mix of businesses, which may change; and
• the model itself rests on the capital asset pricing model’s assumptions.

Adjusted present value

If a project changes the capital structure a great deal, a WACC based on one set of weights is not right.

The adjusted present value (APV) method values the project in two steps: the base-case NPV, as if the project were financed entirely by equity, discounted at the ungeared cost of equity (from the asset beta); then the present value of the financing side effects, mainly the tax relief on the interest (the tax shield), discounted at the cost of debt, less issue costs.

Example: the pharmacy project costs ₦100m and produces after-tax cash flows of ₦38m a year for four years. The ungeared cost of equity is 8 + 1.1915 × 7 = 16.34%; the annuity factor for four years is 2.779, so the base-case NPV = 38 × 2.779 − 100 = +₦5.61m. It is financed partly by a ₦40m loan at 14%; the annual tax shield is 40 × 0.14 × 0.30 = ₦1.68m; at 14% for four years (factor 2.914) its present value is ₦4.90m; issue costs are ₦1m. APV = 5.61 + 4.90 − 1.00 = +₦9.51m: accept.

The ideas in more depth

Why degear at all

A proxy’s equity beta is inflated by its borrowing. Using it directly would give the project a financial risk that belongs to another company’s balance sheet. By stripping out the proxy’s gearing we obtain a measure of the risk of the business itself, which can then be combined with the gearing that the project will really have.

Why the tax term (1 − t) appears

Interest is tax-deductible, so a naira of debt costs the company (1 − t), and the effective weight of debt in the risk is reduced by the tax shield. The formula therefore uses the after-tax value of debt. Some textbooks omit tax in the formula; follow the formula given in the paper and say which assumption you use.

Sources and references

• No accounting standard governs the choice of discount rate. The asset beta and equity beta formulae are on the formula sheet of the paper; the Nigeria Tax Act 2025 sets the rate of tax (30% for companies other than small companies).

These points are stated as at 5 November 2026.

Worked examples

1. Denominator.
   100 + 25 × 0.70 = 117.5.
2. Asset beta.
   1.4 × 100 ÷ 117.5 = 1.19.

1. Factor.
   (100 + 28) ÷ 100 = 1.28.
2. Equity beta.
   1.1915 × 1.28 = 1.525.

1. Cost.
   8 + 1.525 × 7 = 18.7%.

How to answer in the exam

• List the steps and show each formula with the numbers.
• State your assumptions: the debt beta, the tax rate and the use of market values.
• Compare the project’s internal rate of return (IRR) with the risk-adjusted rate and say what would have happened at the group rate.
• Discuss the limits of the proxy and of the model when asked.

Common mistakes in the exam

• Using the proxy’s equity beta without degearing.
• Regearing with the proxy’s gearing instead of the company’s.
• Forgetting (1 − t) on the debt.
• Using book values for the gearing ratio.
• Eliminating an unwanted business and degearing in the wrong order.
• Using the company’s own WACC for a project in a different industry.

Quick revision

• Equity beta = business + financial risk; asset beta = business risk only.
• Degear: β_a = β_e × V_e ÷ [V_e + V_d(1 − t)]; regear by inverting.
• Then the capital asset pricing model (CAPM) for the cost of equity and a WACC at the new weights.
• Large financing change: adjusted present value.

Practice questions

These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.

Recall check: multiple choice

Section B style: written questions

A further written question

Model answers

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