We have a 5% 1-year bond. The bond’s par is $1000. There is a 20% chance the company will go into bankruptcy and only pay $500
1,What is the bond’s value? Assume that the company’s possible default is totally unrelated to other events in the economy and risk-free interest rate is 5%. 2,If on top of default risk, investors require an additional 3 percent market risk premium, what are the price value and YTM?
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| Solution | |||||||||
| Expected Payoff | = | Sum of probability x value | = | 80% x 1000 + 20% x 500 | = | 900 | |||
| Coupon payment | = | par x coupon% | = | 1000 x 5% | = | 50 | |||
| Total Payoff | = | 900 + 50 | = | 950 | |||||
| 1 | Bond Value | = | Total payoff | = | 950 | = | 950 | = | $904.76 |
| 1+return | 1+5% | 1.05 | |||||||
| 2 | Bond Value | = | Total payoff | = | 950 | = | 950 | = | $879.63 |
| 1+return | 1+5%+3% | 1.08 | |||||||
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