Question

A 10% semi-annual coupon bond currently sold at $950 will mature after 20 years. Investors expect that the firm will be able to make good on the remaining interest payments but that at the maturity date bondholders will receive full $1000 par value with 0.5 probability and 70% of par value with 0.5 probability. Compute the expected bond equivalent YTM.

Answer 1

Scenario 1: Bondholders will receive full par value. FV = 1000

Scenario 2: Bondholders will receive 70% of par value. FV = 70%*1000 = 700

But given that, investors expect that the firm will be able to make good on the remaining interest payments, there will not be any change in the coupons paid.

Therefore coupon payment, PMT = (10%*1000) / 2 = 50 [Coupons are paid semiannually] , in both scenarios

PV = 950, n = 20*2 = 40

Scenario 1:

FV = 1000

Using RATE function in Excel,

42 Today's price (PV) IS 950.00 43 Face value [$ 1,000.00] 44 Coupon rate 10.00% 45 Coupon payment Semiannual 46 Remaining coupon I 40 47 PMT I 50 48 IVY 5.303602% 49 =RATE/B46, 147,-B42,343) 50 RATE(nper, pmt, pv, [fv], [type], (guess]) 51 YTM 10.61% "=B48*2 52

We get the rate = 5.30%.

Since it is semiannual compounding, YTM = 5.30%*2 = 10.61%

Scenario 2:

FV = 700 (As discussed in the beginning)

Using RATE function in Excel,

42 Today's price (PV) I$ 950.00 43 Face value [$ 700.00 44 Coupon rate 10.00% 45 Coupon payment Semiannual 46 Remaining coupon I 40 47 PMT 50 48 IN 5.047842% 49 =RATE D46,047,-D42,D43) 50 RATE(nper, pmt, pv, [fv], [type], (guess]) 51 YTM 10.10% 52 =D482

We get the rate = 5.048%.

Since it is semiannual compounding, YTM = 5.048%*2 = 10.10%

Calculation of expected bond equivalent YTM:

Probability that YTM = 10.61% is 0.5

Probability that YTM = 10.10% is 0.5

Expected YTM, using weighted average mean = (0.5*10.61%) + (0.5*10.10%) = 10.35%