A 2-year corporate bond has a coupon rate of 4 percent. The one-year spot rate i
ID: 2726839 • Letter: A
Question
A 2-year corporate bond has a coupon rate of 4 percent. The one-year spot rate is 3 percent and the forward rate is 5 percent. The bond credit spread is 1 percent for both the one-year and the two-year maturities. What is the price of the bond expressed as a percentage of its face value
a. What is the price of the bond expressed as a percentage of its face value?
b. What is the bond yield to maturity?
c. What is the bond price calculated with the bond's yield to maturity?
d. Calculate the bond duration first with the duration formula and then with duration as the weighted average maturity of the bond cash flow.
e. What would be the maturity of a zero-coupon bond with the same interest-rate risk as the two-year corporate bond assuming that the two bonds have the same credit risk.
f. Calculate the percentage change in the bond price if the yield rises by 20 base points.
g. Calculate the percentage change in the bond price if the yield rises by 20 base points using the bond duration and compare your answer to the one in the previous question
Explanation / Answer
The rate in year 1 = 3+ 1 =4% and that in year 2 = 5+1 = 6%
The YTM of the bond is (1.04*1.06)^(1/2) - 1 = 4.995% = 5%
The price of the bond is given by the formula =pv(rate,nper,pmt,fv) where rate = 0.05/2 (Semiannual rate), nper = 2*2 (semi annual periods), pmt =4% of 10000 = 40 (annual) and 20 (semi annual). FV =1000
The price of the bond = pv(0.05/2,2*2,20,1000) = 981.19
a. The price of the bond expressed as a percentage of face value = 981.19/1000 = 98.119%
b. The yield to matuiry of the bond = 4.995% = 5%
c. The price of the bond = 981.19
f. If the YTM increases by 20 basis points, new rate= 5.20% and the new price is =pv(0.052/2,2*2,40/2,1000) = 977.48
The % chnage = (981.19- 977.48) /981.19 = 0.378% = 0.38% decrease in the bond price.
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