Question

A stock has a required return of 8%, the risk-free rate is 3%, and the market risk premium is 3%.

What is the stock's beta? Round your answer to two decimal places.

If the market risk premium increased to 8%, what would happen to the stock's required rate of return? Assume that the risk-free rate and the beta remain unchanged. Do not round intermediate calculations. Round your answer to two decimal places.
If the stock's beta is less than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
If the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.
If the stock's beta is equal to 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
If the stock's beta is equal to 1.0, then the change in required rate of return will be less than the change in the market risk premium.
If the stock's beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.

Answer 1

If the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.

Step-by-step explanation:

1.)

Use Capital Asset Pricing Model (CAPM) formula to find the stock beta;

CAPM r = rf + beta (MRP)

whereby rf = risk free rate

MRP = Market risk premium

Next, plug in the numbers to the formula;

0.08 = 0.03 + beta (0.03)

Subtract 0.03 from both sides;

0.08 - 0.03 = 0.03 beta

0.05 = 0.03beta

Divide both sides by 0.03 to solve for beta;

0.05/0.0.3 = beta

beta = 1.67

2.)

Calculate the new rate of return and find the % change and compare with % change in market risk premium;

r = riskfree + beta(market risk premium)

Market risk premium is given as 8%

r = 0.03 + 1.67(0.08)

r = 0.03 + 0.1336

r = 0.1636 or 16.36% as a percentage

Therefore, the new rate of return is 16.36%

Change in required return = (0.1636- 0.08)/ 0.08] *100 = 104.5%

Change in market risk premium = (0.08- 0.03)/ 0.03] *100 = 166.7%

From the above analysis, if the stock's beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.