The airline industry is capital intensive and often funded with debt. Consider a two - year coupon bond issued by an airline with a face value of $1,000, a coupon rate of 3%, an annual default probability of 5%, and a risk-free interest rate of 3% per year. Show work for all of the questions?

1. Use a binomial tree to value the bond assuming no recovery. The value (price, expected present value, etc.) of the bond is ___

2. Calculate the yield to maturity of the bond from question 1? Provide your answer as a percentage with two decimal places. The yield to maturity is ____%

3. Assume the recovery rate is 60% so that bondholders recover 60% of the face value upon default. Use the binomial tree to calculate the value (price, expected present value, etc.) The value of the bond is ____

4.What should it cost to insure the bond of question 3 against default? You can use the binomial tree or the law of one price answer the question. Calculation of the binomial tree is complicated by the need to incorporate the recovery into the payoff from insurance. The law of one price is simpler and what I recommend. Use the value of the risky and risk-free bonds to infer the value of the insurance. The price of the insurance should be ___

5.The two-year coupon bond of question 1 trades in the market at a price of $900. Assume recovery is 50% (half). Calculate the yield to maturity of the bond and use the credit triangle formula to approximate the probability of default.Provide your answer as a percentage with two decimal places. The default probability implied by the credit triangle using a recovery rate of 50% is ___