Consider the following information regarding corporate bonds and answer the following questions:RatingAAAAAABBBBBBCCCAverage Default Rate0.0%0.1%0.2%0.5%2.2%5.5%12.2%Recession Default Rate0.0%1.0%3.0%3.0%8.0%16.0%48.0%Average Beta0.050.050.050.100.170.260.31Smartline Corp plans to issue 10-year bonds that it believes will have a B rating. Suppose AAA bonds with the same maturity have a 5% yield. Assume that the market risk premium is 6% and the expected loss rate in the event of default on the bonds is 65%. What is the yield that these bonds will have to pay during recession times? (3 marks)Your firm is considering expanding its consumer division. You identify Negtle as a comparable firm. Suppose Negtle has a market capitalization of 120 billion and a beta of 1.27. Negtle also has $30 billion of BBB-rated debt outstanding, with an average yield of 4.3%. Estimate the cost of capital of your firm’s investment given the risk-free rate of 4% and a market risk-premium of 6% (3 marks).
Question
Consider the following information regarding corporate bonds and answer the following questions:RatingAAAAAABBBBBBCCCAverage Default Rate0.0%0.1%0.2%0.5%2.2%5.5%12.2%Recession Default Rate0.0%1.0%3.0%3.0%8.0%16.0%48.0%Average Beta0.050.050.050.100.170.260.31Smartline Corp plans to issue 10-year bonds that it believes will have a B rating. Suppose AAA bonds with the same maturity have a 5% yield. Assume that the market risk premium is 6% and the expected loss rate in the event of default on the bonds is 65%. What is the yield that these bonds will have to pay during recession times? (3 marks)Your firm is considering expanding its consumer division. You identify Negtle as a comparable firm. Suppose Negtle has a market capitalization of 120 billion and a beta of 1.27. Negtle also has $30 billion of BBB-rated debt outstanding, with an average yield of 4.3%. Estimate the cost of capital of your firm’s investment given the risk-free rate of 4% and a market risk-premium of 6% (3 marks).
Solution
The first question is asking for the yield that the B-rated bonds from Smartline Corp will have to pay during recession times.
Step 1: We first need to find the expected loss rate in the event of default. This is given as 65%.
Step 2: Next, we need to find the default rate for B-rated bonds during a recession. This is given as 16.0%.
Step 3: We then multiply the expected loss rate by the default rate to find the expected loss during a recession. This is 0.65 * 0.16 = 0.104 or 10.4%.
Step 4: The yield that these bonds will have to pay is then the yield on AAA bonds plus the expected loss. This is 5% + 10.4% = 15.4%.
The second question is asking for the cost of capital for your firm's investment.
Step 1: We first need to find the equity cost of capital. This is given by the risk-free rate plus the beta times the market risk premium. This is 4% + 1.27 * 6% = 11.62%.
Step 2: Next, we need to find the debt cost of capital. This is given as the yield on BBB-rated debt, which is 4.3%.
Step 3: We then need to find the weights of equity and debt in the firm's capital structure. The equity weight is the market capitalization divided by the total capital, which is 120 billion / (120 billion + 30 billion) = 0.8. The debt weight is the debt divided by the total capital, which is 30 billion / (120 billion + 30 billion) = 0.2.
Step 4: The cost of capital is then the equity cost of capital times the equity weight plus the debt cost of capital times the debt weight. This is 11.62% * 0.8 + 4.3% * 0.2 = 9.696%.
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