Question

1. The risk-free rate of DAF Digital LLC. is 8 percent. The average expected return for the industry is 16 percent.

a. Using CAPM, what is the expected return of DAF Digital LLC if the beta of its stock is 0.7?
b. What is the beta of a competitor in the same industry that has an expected return of 24 percent?

Answer 1

Using the CAPM, the expected return of DAF Digital LLC with a beta of 0.7 is 13.6%. The beta of a competitor with an expected return of 24% is 2.

Step-by-step explanation:

Calculating the Expected Return using CAPM

For DAF Digital LLC with a beta of 0.7 and a risk-free rate of 8%, you can calculate the expected return using the Capital Asset Pricing Model (CAPM) as follows:

Expected Return = Risk-free Rate + (Beta × (Market Return - Risk-free Rate))

This equation plugs in the given values to find the expected return for DAF Digital LLC:

Expected Return = 8% + (0.7 × (16% - 8%))

Expected Return = 8% + (0.7 × 8%)

Expected Return = 8% + 5.6%

Expected Return = 13.6%

Finding the Beta of a Competitor

For a competitor with an expected return of 24% and the same risk-free rate and average industry return, you can rearrange the CAPM formula and solve for Beta as follows:

Beta = (Expected Return - Risk-free Rate) / (Market Return - Risk-free Rate)

Beta = (24% - 8%) / (16% - 8%)

Beta = 16% / 8%

Beta = 2