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At t = 0, a 3-year, 7% coupon corporate bond with face value $1,000 is trading at a credit spread of 15%. The risk free rate is constant and equal to 4% for all maturities. The recovery rate on the corporate bond is 40% if a default occurs. At t = 0, the market believes that the probability of default in the first year, P1, is 20%, and the probability of default in the second year, P2, is 30%. Assume investors are risk neutral. a) At t = 0, what is the price of the bond? b) At t = 0, what is the market's belief about the default probability in the third year, P3? c) If you buy $10,000 present value worth of the bond at t = 0, and you will liquidate the position at t = 1, what is the expected total amount of money you will have at t = 1? (Note: you may answer this question using a long way or a very short way.) d) Suppose the same company also has a 3-year zero coupon bond outstanding with face value $500. The bond is junior to the previous bond, and the recovery rate is therefore 0%. What is the value of this junior bond at t = 0? (Hint: you need to use P1, P2, and P3.)
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