Question

In: Finance

Apex Roofings's stock has a beta of 1.50, its required return is 17.00%, and the risk-free...

Apex Roofings's stock has a beta of 1.50, its required return is 17.00%, and the risk-free rate is 5.00%. What is the required rate of return on the stock market?

Solutions

Expert Solution

From the given information on Apex Roofings's,

Beta of the stock(Ba) = 1.50

required return(Ra) = 17.00%

risk-free rate(Rf) = 5.00%

required rate of return on market(Rm) = ?

To solve this we need to use CAPM model,

CAPM model: It is the model developed to describe the relationship between the expected return and the risk of investing into that security. this model is based on the systematic risk and for which investor need to be compensated for in the name of risk-premium.

From the CAPM model, Required rate of return(Ra) = risk-free rate(Rf) + (required return on market(Rm) - riskfree rate(Rf) ) * beta of the stock(Ba)

We have the information from the question and we will put the respective value in the CAPM model to get the required result from it.

therefore, 17.00% = 5.00% + ( Rm - 5.00%) * 1.50

or, 17.00% = 5.00% + Rm * 1.50 - 5.00% * 1.50

or, 17.00% = 5.00% + Rm * 1.50 - 7.5%

or, 17.00% = 5.00% - 7.5% + Rm * 1.50

or, 17.00% + 7.5% - 5.00% = Rm * 1.50

or, 19.5% = Rm * 1.50

Rm = 19.5% / 1.50 = 13%

Hence, the required rate of return on market is 13%.


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