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