The problem requires using the Capital Asset Pricing Model (CAPM) to solve for different variables in different scenarios. The CAPM formula is: $Required Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)$ a. Find the required return given beta = 2.2, risk-free rate = 5%, and market return = 32%. b. Find the risk-free rate given required return = 23.75%, beta = 1.25, and market return = 20%. c. Find the market return given required return = 18%, beta = 1.2, and risk-free rate = 8%. d. Find beta given required return = 15%, risk-free rate = 3%, and market return = 15%.

1. Problem Description

The problem requires using the Capital Asset Pricing Model (CAPM) to solve for different variables in different scenarios. The CAPM formula is:

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

a. Find the required return given beta = 2.2, risk-free rate = 5%, and market return = 32%.

b. Find the risk-free rate given required return = 23.75%, beta = 1.25, and market return = 20%.

c. Find the market return given required return = 18%, beta = 1.2, and risk-free rate = 8%.

d. Find beta given required return = 15%, risk-free rate = 3%, and market return = 15%.

2. Solution Steps

a. Find the required return:

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

$Required Return = 5\% + 2.2 * (32\% - 5\%)$

$Required Return = 5\% + 2.2 * (27\%)$

$Required Return = 5\% + 59.4\%$

$Required Return = 64.4\%$

b. Find the risk-free rate:

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

$23.75\% = Risk-Free Rate + 1.25 * (20\% - Risk-Free Rate)$

$23.75\% = Risk-Free Rate + 25\% - 1.25 * Risk-Free Rate$

$23.75\% - 25\% = Risk-Free Rate - 1.25 * Risk-Free Rate$

$-1.25\% = -0.25 * Risk-Free Rate$

$Risk-Free Rate = -1.25\% / -0.25$

$Risk-Free Rate = 5\%$

c. Find the market return:

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

$18\% = 8\% + 1.2 * (Market Return - 8\%)$

$18\% - 8\% = 1.2 * (Market Return - 8\%)$

$10\% = 1.2 * (Market Return - 8\%)$

$10\% / 1.2 = Market Return - 8\%$

$8.33\% = Market Return - 8\%$

$Market Return = 8.33\% + 8\%$

$Market Return = 16.33\%$

d. Find beta:

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

$15\% = 3\% + Beta * (15\% - 3\%)$

$15\% - 3\% = Beta * (12\%)$

$12\% = Beta * (12\%)$

$Beta = 12\% / 12\%$

$Beta = 1$

3. Final Answer

a. Required Return = 64.4%

b. Risk-Free Rate = 5%

c. Market Return = 16.33%

d. Beta = 1