Question

1. You are purchasing a 20-year, semi-annual bond with a current market price of $973.64. If the yield to maturity is 8.68 percent and the face value is $1,000, what must the coupon payment be on the bond?

2.Collingwood Homes has a bond issue outstanding that pays an 8.5 percent coupon and has a yield to maturity of 9.16%. The bonds have a par value of $1,000 and a market price of $944.30. Interest is paid semiannually. How many years until the bond matures?

Answer 1

1. Ytm half yearly = 8.68%/2 = 4.34%
Number of Periods = 2*20 = 40
PV = 973.64
PV of Bond = PV of Coupons + PV of par Value
973.64 = Coupon*(1-(1+4.34%)^-400/4.34% + 1000/(1+4.34%)⁴⁰
973.64 - 182.796 = Coupon *18.83
Coupon = (973.64 - 182.796)/18.83 = 42
Coupon rate =42*2/1000 = 8.4%

2. Coupon = 8.5%*1000/2 = 42.50
Par Value = 1000
Semi annual YTM = 9.16%/2 = 4.58%
PV = 944.30

Using Financial calculator
I/Y = 4.58%, PMT = 42.50; PV = - 944.30; FV = 1000; CPT N = 33.163
Number of years = 33.163/2 = 16.56 years

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