Question

A stock has a required return of 12%, the risk-free rate is 5.5%, and the market risk premium is 3%.

1. What is the stock's beta? Round your answer to two decimal places.
2. If the market risk premium increased to 6%, 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.
   1. 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

   -Select-IIIIIIIVVItem 2

   Stock's required rate of return will be   %.

Answer 1

a. required return = risk-free rate + (stock's beta*market risk premium)

12% = 5.5% + (stock's beta*3%)

12% - 5.5% = stock's beta*3%

6.5% = stock's beta*3%

stock's beta = 6.5%/3% = 2.17

the stock's beta is 2.17.

b. Stock's required rate of return = 5.5% + 2.17*6% = 5.5% + 13.02% = 18.52%

Stock's required rate of return will increase and it will be 18.52%.

Correct statement is statement III. 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.

let assume stock's beta is 1.5.

required return without increase in market risk premium:

required return = 5.5% + 1.5*3% = 5.5% + 4.5% = 10%

required return with increase in market risk premium:

required return = 5.5% + 1.5*6% = 5.5% + 9% = 14.5%

increase in required return = 14.5% - 10% = 4.5%

increase in market risk premium = 6% - 3% = 3%

rest all the statements are incorrect.

if stock's beta is equal to 1 then change in required rate of return and the change in the market risk premium will also be equal.

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

let assume stock's beta is 0.8.

required return without increase in market risk premium:

required return = 5.5% + 0.8*3% = 5.5% + 2.4% = 7.9%

required return with increase in market risk premium:

required return = 5.5% + 0.8*6% = 5.5% + 4.8% = 10.3%

increase in required return = 10.3% - 7.9% = 2.4%

increase in market risk premium = 6% - 3% = 3%