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?

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%