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1) Stock R has a beta of 2.4, Stock S has a beta of 0.9, the expected rate of return on an...

Question:

1) Stock R has a beta of 2.4, Stock S has a beta of 0.9, the expected rate of return on an average stock is 11%, and the risk-free rate of return is 7%. By how much does the required return on the riskier stock exceed the required return on the less risky stock? Round your answer to two decimal places.

2) An 8% semiannual coupon bond matures in 5 years. The bond has a face value of $1,000 and a current yield of 8.3832%.What is the bond's YTM?

3)Suppose you are the money manager of a $3.82 million investment fund. The fund consists of 4 stocks with the following investments and betas:

Stock Investment Beta
A $ 500,000 1.50
B 380,000 - 0.50
C 1,140,000 1.25
D 1,800,000 0.75

If the market's required rate of return is 11% and the risk-free rate is 5%, what is the fund's required rate of return?

Capital Asset Pricing Model:

The capital asset pricing model is the model used to calculate the required rate of return on a security. This model provides the rate of return by adding the risk premium of security to the risk-free rate. This is the rate required by the investor for the given level of risk.

Answer and Explanation:

1. Computation of required rate of return

{eq}\begin{align*} {\text{Required Rate of Return}} &= {R_f} + \beta \times \left( {{R_m} - {R_f}} \right)\\ {\text{Stock R}} &= 7\% + 2.4 \times \left( {11\% - 7\% } \right)\\ &= 16.6\% \\ {\text{Stock S}} &= 7\% + 0.9 \times \left( {11\% - 7\% } \right)\\ &= 10.6\% \end{align*} {/eq}

The required return on the riskier stock exceeds the required return on the less risk stock by 6%.

2. Computation of bond YTM

{eq}\begin{align*} {\text{YTM}} &= \dfrac{{{\text{Interest}} + \dfrac{{{\text{Par Value}} - {\text{Selling Price}}}}{n}}}{{\dfrac{{{\text{Par Value}} + {\text{Selling Price}}}}{2}}}\\ &= \dfrac{{\$ 80 + \dfrac{{\$ 1,000 - \$ 954.29}}{5}}}{{\dfrac{{\$ 1,000 + \$ 954.29}}{2}}}\\ &= 9.12\% \end{align*} {/eq}

Computation of selling price of bond

{eq}\begin{align*} {\text{Selling Price of Bond}} &= \dfrac{{{\text{Interest}}}}{{{\text{Current Yield}}}}\\ &= \dfrac{{\$ 80}}{{0.083832}}\\ &= \$ 954.29 \end{align*} {/eq}

3. Computation of fund?s required rate of return

{eq}\begin{align*} {\text{Required Rate of Return}} &= {R_f} + \beta \times \left( {{R_m} - {R_f}} \right)\\ &= 5\% + 0.87 \times \left( {11\% - 5\% } \right)\\ &= 10.22\% \end{align*} {/eq}

Computation of the beta of fund

{eq}\begin{align*} {\text{Beta of Fund}} &= \sum {{\text{Beta of Stock}} \times {\text{Weight of Stock}}} \\ &= \left( {1.5 \times \dfrac{{\$ 500,000}}{{3,820,000}}} \right) + \left( {\left( { - 0.5} \right) \times \dfrac{{\$ 380,000}}{{3,820,000}}} \right) + \left( {1.25 \times \dfrac{{\$ 1,140,000}}{{3,820,000}}} \right) + \left( {0.75 \times \dfrac{{\$ 1,800,000}}{{3,820,000}}} \right)\\ &= 0.87 \end{align*} {/eq}


Learn more about this topic:

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Required Rate of Return (RRR): Formula & Calculation

from Financial Accounting: Help and Review

Chapter 1 / Lesson 29
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