Question

Linke Motors has a beta of 1.30, the T-bill rate is 3.00%, and the T-bond rate is 6.5%. The annual return on the stock market during the past 3 years was 15.00%, but investors expect the annual future stock market return to be 13.00%. Based on the SML, what is the firm's required return?

Answer 1

To calculate Linke Motors' required return based on the SML, we use the CAPM formula with a beta of 1.30, a T-bill rate of 3.00%, and an expected market return of 13%. The calculation leads to a required return of 16% for the firm.

Step-by-step explanation:

The student is asking how to calculate the firm's required return using the Security Market Line (SML) which is part of the Capital Asset Pricing Model (CAPM). The beta of Linke Motors is 1.30, reflecting how much more volatile the stock is compared to the market. With a risk-free rate, represented by the T-bill rate of 3.00%, and the market risk premium, which is the difference between the expected market return (13%) and the risk-free rate (3%), we can calculate the required return.

The formula for CAPM is:

Required Return = Risk-Free Rate + (Beta * Market Risk Premium)

So, we use:

• Risk-Free Rate: 3.00%
• Beta: 1.30
• Market Risk Premium: 13% - 3% = 10%

Now plug these values into the formula:

Required Return = 3.00% + (1.30 * 10%)

Required Return = 3.00% + 13%

Required Return = 16%

Therefore, based on the SML, the firm's required return is 16%.