You are analyzing a disressed bond with one year to maturity. The bond has a fac

Question

You are analyzing a disressed bond with one year to maturity. The bond has a face value of $100 and pays a coupon rate 5 percent per year, with annual coupons. The bond is currently trading at $80. What is the yield to maturity on the bond? If the probability of default is 35 percent, what is the cost of debt? Assume that upon default, only 50 percent of face value will be recovered and that remaining coupons will not be paid. If the probability of default rises to 40 percent but the expected pay out in default remains at 50 percent, what do you think will happen to the yield to maturity and the cost of debt? Why?

Explanation / Answer

YTM can be calculated using I/Y function on a calculator

N = 1, PMT = 5, PV = -80, FV = 100 => Compute I/Y = 31.25%

If there is 35% probability of default, then

N = 1, PMT = 5 x 0.65 = 3.25, FV = 100 x 65% + 50% x 100 x 35% = 82.5, PV = -80

=> Compute I/Y = 7.19%

If there is 40% probability of default, then I/Y = 3.75%

YTM will decline due to increase in higher probability of default.

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