CAPM & WACC: practice problems with step-by-step solutions

Free CAPM & WACC practice problems with diagrams, hints and full worked solutions. New values every time, at three levels: CAPM, WACC, WACC with CAPM and market values.

Free practice problemEasy
βr (%)SMLrf​ = 1.5%β = 1rm​ = 8%β = 0.8re​ = ?

The risk-free rate is 1.5%, the expected market return is 8% and a share has a beta of 0.8. Use CAPM to find the required return on the share re.

rf = 1.5%rm = 8%β = 0.8
%
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What you practise

  1. EasyCAPM
  2. MediumWACC
  3. HardWACC with CAPM and market values

Key formulas

CAPM
re = rf + β·(rm − rf)
WACC
E/V·re + D/V·rd·(1 − T)
Firm value
V = E + D

Learn CAPM & WACC from scratch

1What the cost of capital is

A company finances itself with two kinds of money. Equity comes from shareholders. Debt comes from banks and bondholders.

Neither is free. Lenders want interest, and shareholders want a return for the risk they take. That required return is the cost of capital.

The company uses it as the minimum return on new projects, for example as the rate in an NPV calculation.

This topic has two parts:

  • CAPM tells you what return shareholders require: the cost of equity re.
  • WACC mixes the cost of equity and the cost of debt into one rate for the whole company.
Self-check Why is equity more expensive for a company than debt, as a rule?
  1. Dividends are tax-deductible
  2. Equity has to be repaid sooner
  3. Shareholders are always paid first
  4. Shareholders carry more risk, so they require a higher return

Answer: Shareholders carry more risk, so they require a higher return. Lenders are paid before shareholders and get fixed interest. Shareholders only get what is left, so they take more risk and want more return. Interest, not dividends, is tax-deductible.

2CAPM: the cost of equity

The capital asset pricing model (CAPM) starts from a safe return and adds extra return for risk.

  • The risk-free rate rf: the return on a safe government bond.
  • The market return rm: the expected return on the stock market as a whole.
  • The market risk premium rm − rf: the extra return investors want for holding shares instead of safe bonds.
  • Beta β: how strongly the share moves with the market. β = 1 moves like the market, β = 1.5 moves 50% more, β = 0.8 moves less.
re = rf + β · (rm − rf)

Example: rf = 2%, rm = 8% and β = 1.5. The premium is 6%, so re = 2% + 1.5 · 6% = 11%.

βrrf​ = 2%rm​ = 8%11%11.50

The figure shows the required return rising in a straight line with beta. At β = 0 it is the risk-free rate, at β = 1 it is the market return.

Self-check rf = 3%, rm = 8% and β = 1.2. What is the cost of equity?
  1. 12.6%
  2. 6%
  3. 9%
  4. 9.6%

Answer: 9%. 3% + 1.2 · (8% − 3%) = 3% + 6% = 9%. 12.6% multiplies β by the market return instead of the premium, 6% forgets to add rf, and 9.6% is β · rm.

3WACC: one rate for the company

The weighted average cost of capital (WACC) averages the two costs. Each one counts in proportion to its market value.

V = E + D
WACC = (E/V) · re + (D/V) · rd · (1 − T)

E is the market value of equity, D the market value of debt, rd the interest rate on the debt (before tax) and T the tax rate.

Why (1 − T)? Interest is a cost that lowers taxable profit. With 25% tax, €4 of interest saves €1 of tax, so debt at 4% really costs 3%.

Market values: E = number of shares × share price. D = number of bonds × bond price. Book values from the balance sheet are not used.

Self-check A company has equity worth €3 000 000 and debt worth €1 000 000. What is the weight of equity E/V?
  1. 0.25
  2. 0.75
  3. 1.33
  4. 3

Answer: 0.75. V = 3 000 000 + 1 000 000 = 4 000 000, so E/V = 3/4 = 0.75. Dividing equity by debt (3) is not a weight: weights are shares of the total and add up to 1.

4The method step by step

  1. If the cost of equity is not given, find it with CAPM: re = rf + β · (rm − rf).
  2. Find the market values E and D. If shares and bonds are given, multiply number by price.
  3. Add them, V = E + D, and find the weights E/V and D/V. They add up to 1.
  4. Find the after-tax cost of debt: rd · (1 − T).
  5. WACC = (E/V) · re + (D/V) · rd · (1 − T). Check that it lies between the two costs.

5A worked example

Follow every step. Try to predict the next one before you open it.

Worked example

A company has equity worth €6 000 000 and debt worth €2 000 000. Its cost of equity is 10%, its pre-tax cost of debt is 4% and the tax rate is 25%. Find the WACC.

1

Total value

V = E + D = 6 000 000 + 2 000 000 = 8 000 000
2

Weights

E/V = 6/8 = 0.75 D/V = 2/8 = 0.25

Check: 0.75 + 0.25 = 1.

3

After-tax cost of debt

rd · (1 − T) = 4% · 0.75 = 3%
4

Weighted average

WACC = 0.75 · 10% + 0.25 · 3% = 7.5% + 0.75% = 8.25%
5

Check the answer

8.25% lies between 3% and 10%, and closer to 10%, because most of the money is equity. That fits.

Answer

WACC = 8.25%

6Common mistakes

  • Forgetting the tax shield: use rd · (1 − T), not rd.
  • Weighting the two costs equally instead of by market value.
  • Using book values from the balance sheet instead of market values.
  • In CAPM, multiplying β by the market return rm instead of by the premium rm − rf.
  • In CAPM, forgetting to add the risk-free rate.
Self-check E = €3 000 000, D = €1 000 000, re = 12%, rd = 6% and T = 25%. What is the WACC?
  1. 10.125%
  2. 10.5%
  3. 8.25%
  4. 9.375%

Answer: 10.125%. 0.75 · 12% + 0.25 · 6% · 0.75 = 9% + 1.125% = 10.125%. 10.5% forgets the tax, 8.25% weights both costs equally, and 9.375% uses rd · T instead of rd · (1 − T).

7How exam questions look

  • Easy: CAPM. Find the cost of equity from rf, rm and β.
  • Medium: WACC. The values of equity and debt and both costs are given.
  • Hard: WACC with CAPM and market values. Work out E and D from shares and bonds, and the cost of equity with CAPM, then the WACC.

Give the WACC in percent and check that it lies between the after-tax cost of debt and the cost of equity.

Learn it step by step in the appLearn it step by step in the app

Worked examples

Example 1Easy
βr (%)SMLrf​ = 2%β = 1rm​ = 6.5%β = 0.6re​ = ?

The risk-free rate is 2%, the expected market return is 6.5% and a share has a beta of 0.6. Use CAPM to find the required return on the share re.

rf = 2%rm = 6.5%β = 0.6

Find re (%)

Show hints
  1. CAPM: required return = risk-free rate + β × market risk premium.
  2. market risk premium = 6.5% − 2% = 4.5%.
  3. β·(4.5%) = 2.7%.
Show the answer and the step-by-step solution

Cost of capital: CAPM gives the return shareholders require: re = rf + β·(rm − rf). The weighted average cost of capital mixes equity and debt by their market values: WACC = E/V·re + D/V·rd·(1 − T), with V = E + D. Interest is tax-deductible, hence the (1 − T).

CAPM

re = 2% + 0.6·(6.5% − 2%) = 4.7%

Answer

re = 4.7%
Example 2Medium
WACC = ?equity€5 000 000re​ = 8%debt€4 000 000rd​ = 7%T = 21%

A company has equity worth €5 000 000 and debt worth €4 000 000. Its cost of equity is 8%, its pre-tax cost of debt is 7% and the tax rate is 21%. Find the WACC.

E = €5 000 000D = €4 000 000re = 8%rd = 7%T = 21%

Find WACC (%)

Show hints
  1. Weights: E/V and D/V, with V = E + D.
  2. E/V = 0.5556, D/V = 0.4444.
  3. After-tax cost of debt: 7%·(1 − 0.21) = 5.53%.
Show the answer and the step-by-step solution

Cost of capital: CAPM gives the return shareholders require: re = rf + β·(rm − rf). The weighted average cost of capital mixes equity and debt by their market values: WACC = E/V·re + D/V·rd·(1 − T), with V = E + D. Interest is tax-deductible, hence the (1 − T).

Weights

V = €9 000 000, E/V = 0.5556, D/V = 0.4444

WACC

WACC = 0.5556·8% + 0.4444·7%·(1 − 0.21) = 6.902%

Answer

WACC = 6.902%
Example 3Hard
rf​ = 4%, rm​ − rf​ = 4.5%no debtequityβU​ = 0.7D/E = 0.6equityre​ = ?debtT = 25.8%

A company's business has an unlevered (asset) beta of 0.7. It plans a debt-to-equity ratio of 0.6. The tax rate is 25.8%, the risk-free rate is 4% and the market risk premium is 4.5%. Find the cost of equity re at the new capital structure.

βU = 0.7D/E = 0.6T = 25.8%rf = 4%rm − rf = 4.5%

Find re (%)

Show hints
  1. Relever the beta with Hamada's formula.
  2. βL = 0.7·(1 + (1 − 0.258)·0.6) = 1.012.
  3. Then use CAPM with the levered beta.
Show the answer and the step-by-step solution

Levered beta (Hamada): debt makes equity riskier. βL = βU·(1 + (1 − T)·D/E), where βU is the beta of the business without debt. To move a beta to another capital structure, unlever it first and then relever it at the new D/E.

Levered beta

βL = 0.7·(1 + 0.742·0.6) = 1.012

Cost of equity (CAPM)

re = 4% + 1.012·4.5% = 8.552%

Answer

re = 8.552%

Questions and answers

What is CAPM & WACC?

A company finances itself with two kinds of money. Equity comes from shareholders. Debt comes from banks and bondholders.

Neither is free. Lenders want interest, and shareholders want a return for the risk they take. That required return is the cost of capital.

How do I solve CAPM & WACC problems step by step?

Cost of capital: CAPM gives the return shareholders require: re = rf + β·(rm − rf). The weighted average cost of capital mixes equity and debt by their market values: WACC = E/V·re + D/V·rd·(1 − T), with V = E + D. Interest is tax-deductible, hence the (1 − T).

What are common mistakes in CAPM & WACC?
  • Multiply β by the market risk premium (rm − rf), not by the market return.
  • Add the risk-free rate: re = rf + β·(rm − rf).
  • Use the after-tax cost of debt: rd·(1 − T). Interest is tax-deductible.
What do the CAPM & WACC exercises cover?
  • Easy: CAPM
  • Medium: WACC
  • Hard: WACC with CAPM and market values

Every problem has new values, so you learn the method instead of an answer. Stuck? Open a small hint first, and the full explanation only when you need it.

How practising works

  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Your progress, mistakes and saved problems are kept, so you can review before the exam.

Calculators

WACC calculatorCAPM calculator

Courses with this topic

Corporate FinanceInvestments and ValuationCFA Level I quantitative methods and fixed income practice

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Time value of moneyNPV & IRRBond pricing & yieldPrice elasticity of demandEconomics conceptsBreak-even analysisFinancial accountingDepreciationMarketing principles

Printable worksheet

CAPM & WACC worksheet with answers
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