Porter Plumbing's stock had a required return of 11.75% last year, when the risk-free rate was 5.50% and the market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%. The risk-free rate and the firm's beta remain unchanged. What is the company's new required rate of return

New required rate of return = 11.88%

Explanation:

The capital asset pricing model is a risk-based model. Here, the return on equity is dependent on the level of reaction of the the equity to changes in the return on a market portfolio. These changes are captured as systematic risk. The magnitude by which a stock is affected by systematic risk is measured by beta.  

Under CAPM, Ke= Rf + β(Rm-Rf)  

Ke- required rate of return, Rf-risk-free rate (treasury bill rate), β= Beta, Rm= Return on market.

Using the model, we work out  Beta which is not given and then re-calculate the required rate of return of the new stock

Ke- 11.75 % Rf- 5.5, Rm-Rf = 4.75%,  β= ?

11.75% = 5.50% + β(4.75%)

11.75% -5.50% =  β(4.75%)

(11.75-5.50)/4.75= β

1.315789474 = β

1.315 = β

New required rate of return

5.50% + 1.315(1.02×4.75)

11.875

New required rate of return = 11.88%

Explanation:

Given

Required rate of return,  (Re) = 11.75%

Risk-free rate (Rf) = 5.50%

Market risk premium (Rm - Rf) = 4.75

Let's calculate beta (b) first, by using below formula.

Re = Rf + b (Rm - Rf)

11.75 = 5.50 + b ( 4.75)

By solving, we get beta (b) = 1.3157 = 1.32

Now, market risk premium is increased by 2%.

So, new market risk premium (Rm - Rf) = 6.75%. Beta and Rf values are same.

New Required rate of return (Re) = 5.50 + 1.32 * 6.75

By solving, we get Re = 14.41 %

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