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Gardner Electric has a beta of 0.88 and an expected dividend growth rate of 4.00% per year. The T-bill rate is 4.00%, and the T-bond rate is 5.25%. The annual return on the stock market during the past 4 years was 10.25%. Investors expect the average annual future return on the market to be 12.50%. Using the SML, what is the firm's required rate of return?

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Answer:

11.48%

Explanation:

The SML (Security Market Line) is a graphical representation of the CAPM model. The x-axis is risk (in terms of Beta) and the y-axis is the expected return.

The CAPM expected return formula is:

[tex]R_s=R_f+\beta(R_m - R_f)[/tex]

Where

[tex]R_s[/tex]  is the expected return

[tex]R_f[/tex]  is the risk-free return

[tex]R_m[/tex]  is the average return (market return)

[tex]\beta[/tex]  is the systematic risk factor

We need to firm firm's required rate of return, or  [tex]R_s[/tex].

From the given problem, we have:

  • The risk free rate is the dividend growth rate, given as 4% or 4/100 = 0.04
  • The market return (average return) is given as 12.50% or 12.50/100 = 0.125
  • The systematic risk factor, or Beta, is given as 0.88

Now, we simply plug in the known values and find the required rate of return for the firm. Shown below:

[tex]R_s=R_f+\beta(R_m-R_f)\\R_s=0.04+0.88(0.125-0.04)\\R_s=0.1148[/tex]

So, in percentage, that would be:

0.1148 * 100 = 11.48%

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