Final answer:
The expected rate of return for DAF Digital LLC using CAPM cannot be calculated without the actual values for the risk-free rate and market return. Likewise, the beta of a competitor with an expected return of 24% depends on these values, but a hypothetical calculation with assumed rates shows it to be 4.2, indicating higher volatility.
Step-by-step explanation:
The student's question pertains to the calculation of the expected rate of return using the Capital Asset Pricing Model (CAPM), and the determination of beta for a competitor's stock given its expected return.
Part a: Expected Return of DAF Digital LLC Using CAPM
To calculate the expected return of DAF Digital LLC using CAPM, we would use the formula:
Expected Return = Risk-Free Rate + Beta * (Market Return - Risk-Free Rate)
Without the actual percentage values for the risk-free rate and the average market return, we cannot calculate a specific number. If these values were provided, for instance, as 3% (risk-free rate) and 8% (market return), the calculation for a beta of 0.7 would be:
Expected Return = 3% + 0.7 * (8% - 3%) = 3% + 0.7 * 5% = 3% + 3.5% = 6.5%
Part b: Beta of a Competitor
To find the beta of a competitor in the same industry with an expected return of 24%, we can rearrange the CAPM formula:
Beta = (Expected Return - Risk-Free Rate) / (Market Return - Risk-Free Rate)
Again, with the actual risk-free rate and market return, the beta could be calculated precisely. If we assume a risk-free rate of 3% and market return of 8%, as before:
Beta = (24% - 3%) / (8% - 3%) = 21% / 5% = 4.2
This beta indicates that the competitor's stock is significantly more volatile compared to the market.