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CAPM worksheet

Grades 7–8

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Risk-free rate: 4%
- Beta (β): 1.4
- Expected market return: 12%
Find: Expected return (cost of equity)
Answer
2.
Problem 2.
- Risk-free rate: 3%
- Beta (β): 1
- Expected market return: 7%
Find: Expected return (cost of equity)
Answer
3.
Problem 3.
- Risk-free rate: 4%
- Beta (β): 0.9
- Expected market return: 8%
Find: Expected return (cost of equity)
Answer
4.
Problem 4.
- Risk-free rate: 4%
- Beta (β): 1.2
- Expected market return: 14%
Find: Expected return (cost of equity)
Answer
5.
Problem 5.
- Risk-free rate: 5%
- Beta (β): 1.5
- Expected market return: 11%
Find: Expected return (cost of equity)
Answer
6.
Problem 6.
- Risk-free rate: 5%
- Beta (β): 1
- Expected market return: 11%
Find: Expected return (cost of equity)
Answer
7.
Problem 7.
- Risk-free rate: 5%
- Beta (β): 1.2
- Expected market return: 10%
Find: Expected return (cost of equity)
Answer
8.
Problem 8.
- Risk-free rate: 3%
- Beta (β): 1.1
- Expected market return: 9%
Find: Expected return (cost of equity)
Answer
9.
Problem 9.
- Risk-free rate: 5%
- Beta (β): 1.1
- Expected market return: 9%
Find: Expected return (cost of equity)
Answer
10.
Problem 10.
- Risk-free rate: 4%
- Beta (β): 1
- Expected market return: 12%
Find: Expected return (cost of equity)
Answer

Answer key: CAPM worksheet

1. Expected return (cost of equity): 15.2%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $12% - 4%$ $= 8%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.4 \times 8%$ $= 11.2%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 4% + 1.4 \times (12% - 4%)$ $= 15.2%$
2. Expected return (cost of equity): 7%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $7% - 3%$ $= 4%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1 \times 4%$ $= 4%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 3% + 1 \times (7% - 3%)$ $= 7%$
3. Expected return (cost of equity): 7.6%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $8% - 4%$ $= 4%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $0.9 \times 4%$ $= 3.6%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 4% + 0.9 \times (8% - 4%)$ $= 7.6%$
4. Expected return (cost of equity): 16%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $14% - 4%$ $= 10%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.2 \times 10%$ $= 12%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 4% + 1.2 \times (14% - 4%)$ $= 16%$
5. Expected return (cost of equity): 14%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $11% - 5%$ $= 6%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.5 \times 6%$ $= 9%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 5% + 1.5 \times (11% - 5%)$ $= 14%$
6. Expected return (cost of equity): 11%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $11% - 5%$ $= 6%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1 \times 6%$ $= 6%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 5% + 1 \times (11% - 5%)$ $= 11%$
7. Expected return (cost of equity): 11%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $10% - 5%$ $= 5%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.2 \times 5%$ $= 6%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 5% + 1.2 \times (10% - 5%)$ $= 11%$
8. Expected return (cost of equity): 9.6%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $9% - 3%$ $= 6%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.1 \times 6%$ $= 6.6%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 3% + 1.1 \times (9% - 3%)$ $= 9.6%$
9. Expected return (cost of equity): 9.4%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $9% - 5%$ $= 4%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1.1 \times 4%$ $= 4.4%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 5% + 1.1 \times (9% - 5%)$ $= 9.4%$
10. Expected return (cost of equity): 12%
1. Find the market risk premium, the extra return for owning the market instead of a safe investment: market return minus the risk-free rate
  $12% - 4%$ $= 8%$
2. Multiply that premium by beta, because a riskier asset should earn a bigger reward. This is the asset's own risk premium
  $1 \times 8%$ $= 8%$
3. Add the asset's premium to the risk-free rate to get its expected return, E(R)
  $E(R)$ $= 4% + 1 \times (12% - 4%)$ $= 12%$