Question

Use the basic equation for the capital asset pricing model(CAPM) to work each of the following problems.

a. Find the required return for an asset with a beta of 1.51 when the risk-free rate and market return are 8% and 10% respectively.

b. Find the risk-free rate for a firm with a required return of 9.791% and a beta of 0.97 when the market return is 10%.

c. Find the market return for an asset with a required return of 14.010% and a beta of 1.01 when the risk-free rate is 9 %.

d. Find the beta for an asset with a required return of 19.993% when the risk-free rate and market return are 7% and 14.1 %, respectively.

Answer #1

Answer a:

Required Return = Risk-free Rate + Beta * (Market Return -
Risk-free Rate)

Required Return = 8.00% + 1.51 * (10.00% - 8.00%)

Required Return = 8.00% + 1.51 * 2.00%

Required Return = 11.02%

Answer b.

Required Return = Risk-free Rate + Beta * (Market Return -
Risk-free Rate)

9.791% = Risk-free Rate + 0.97 * (10.00% - Risk-free Rate)

9.791% = Risk-free Rate + 9.70% - 0.97 * Risk-free Rate

0.091% = 0.03 * Risk-free Rate

Risk-free Rate = 3.03%

Answer c.

Required Return = Risk-free Rate + Beta * (Market Return -
Risk-free Rate)

14.010% = 9.00% + 1.01 * (Market Return - 9.00%)

5.010% = 1.01 * (Market Return - 9.00%)

4.96% = Market Return - 9.00%

Market Return = 13.96%

Answer d.

Required Return = Risk-free Rate + Beta * (Market Return -
Risk-free Rate)

19.993% = 7.00% + Beta * (14.10% - 7.00%)

12.993% = Beta * 7.10%

Beta = 1.83

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