IDNLearn.com: Where your questions are met with thoughtful and precise answers. Our experts provide timely and precise responses to help you understand and solve any issue you face.
Certainly! Let's solve the given problem step-by-step:
### Part (a): Calculate Stock A's beta.
We are given the following information: - Risk-free rate [tex]\(\operatorname{rRF} = 5\%\)[/tex] - Market return [tex]\(\operatorname{rM} = 10\%\)[/tex] - Return on Stock A [tex]\(\operatorname{rA} = 12\%\)[/tex]
We use the Capital Asset Pricing Model (CAPM) formula to calculate the beta of Stock A. The CAPM formula is: [tex]\[
rA = rRF + \beta_A \times (rM - rRF)
\][/tex]
So, Stock A's beta ([tex]\(\beta_A\)[/tex]) is approximately 1.4.
### Part (b): Calculate A's new required rate of return if Stock A's beta were 2.0
Now, we are given the new beta value for Stock A: - New [tex]\(\beta_A = 2.0\)[/tex]
We need to calculate the new required rate of return ([tex]\(rA_{new}\)[/tex]) using the CAPM formula again: [tex]\[
rA_{new} = rRF + \beta_{new} \times (rM - rRF)
\][/tex]
Substitute the given values: [tex]\[
rA_{new} = 5\% + 2.0 \times (10\% - 5\%)
\][/tex]
Break it down step-by-step: 1. Calculate the excess market return (market risk premium): [tex]\[
10\% - 5\% = 5\%
\][/tex]
2. Multiply this with the new beta: [tex]\[
2.0 \times 5\% = 10\%
\][/tex]
3. Add this to the risk-free rate: [tex]\[
rA_{new} = 5\% + 10\% = 15\%
\][/tex]
So, the new required rate of return for Stock A ([tex]\(rA_{new}\)[/tex]) is approximately 15%.
### Summary of results: - Stock A's beta ([tex]\(\beta_A\)[/tex]) is approximately 1.4. - New required rate of return for Stock A ([tex]\(rA_{new}\)[/tex]) is approximately 15%.
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.
