Question

A​ BBB-rated corporate bond has a yield to maturity of 12.2 %. A U.S. treasury security has a yield to maturity of 10.5 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 11.0 % and have five years to maturity.     a. What is the price​ (expressed as a percentage of the face​ value) of the treasury​ bond? b. What is the price​ (expressed as a percentage of the face​ value) of the​ BBB-rated corporate​ bond? c. What is the credit spread on the BBB​ bonds?

dont round show me the whole decimal

Answer 1

a) YTM of treasury bond = 10.50%
Rate half yearly = 10.50%/2 = 5.25%
Coupon = 11%*1000/2 = 55
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value = 55*(1-(1+5.25%)^-10)/5.25% + 1000/(1+5.25%)¹⁰ = 1019.07
Price as percentage of face value = 101.91%

b) YTM of BBB-rated corporate bond = 12.2%
Rate half yearly = 12.20%/2 = 6.10%
Coupon = 11%*1000/2 = 55
Par Value = 1000
Number of Periods = 5*2 = 10
Price of Bond = PV of Coupons + PV of Par Value = 55*(1-(1+6.10%)^-10)/6.10% + 1000/(1+6.10%)¹⁰ = 956.05
Price as percentage of face value = 95.60%

c) Credit spread of Treasury bill and BBB bond = 12.2%-10.5% = 1.7%

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