Question

Movie Part’s bonds have 9 years remaining to maturity. The bonds have a face value of $1,000 and a yield to maturity of 8%. They pay interest annually and have a 9% coupon rate. What is their current yield?

b. Assume that the risk-free rate is 5% and that the market risk premium is 6%. What is the required return on the market, on a stock with a beta of 1.0, and on a stock with a beta of 1.2?

c. Assume that the risk-free rate is 6% and that the expected return on the market is 13%. What is the required rate of return on a stock that has a beta of 0.7?

d. One of your friends has $35,000 invested in a stock with a beta of 0.8 and another $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio’s beta?

Answer 1

The current yield of the bond is 9%. The required return on the market using the given rates is 11%, 11% for a stock with beta 1.0, and 12.2% for a beta of 1.2. The required return on a stock with a beta of 0.7 is 10.9%, and the portfolio's beta with the given investment is 1.12.

Step-by-step explanation:

To calculate the current yield of Movie Part's bonds, you would use the annual interest payment and the current price of the bond. Since we know the annual interest payment is a 9% coupon on a $1,000 face value bond, it is $90 per year. Assuming the bonds are selling at face value since no market price is given, the current yield would be ($90 / $1,000) = 9%.

For the second question, the required return on the market is calculated using the risk-free rate plus the market risk premium. The required return on the market is thus (5% risk-free rate + 6% market risk premium) = 11%. A stock with a beta of 1.0 would have the same required return as the market, 11%, and a stock with a beta of 1.2 would have a higher required return: (5% + 1.2 * 6%) = 12.2%.

Now, to find the required rate of return on a stock with a beta of 0.7 given the new conditions (6% risk-free rate and 13% expected return on the market), we use the Capital Asset Pricing Model (CAPM), which gives us (6% + (13% - 6%) * 0.7) = 10.9% as the required return.

Last, to calculate the portfolio’s beta, we use the formula for the weighted average of the betas of the individual stocks in the portfolio. It is calculated as follows: (0.8 * $35,000 + 1.4 * $40,000) / ($35,000 + $40,000) = (28,000 + 56,000) / 75,000 = 84,000 / 75,000 = 1.12.