Question

A​ BBB-rated corporate bond has a yield to maturity of 10.0 %. A U.S. treasury security has a yield to maturity of 8.4 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 9.0 % 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?

Answer 1

Step-by-step explanation:

b)

BBB-rated corporate bond:

Face value = 1000

semiannual coupon = 9%/2 = 4.5%

semiannual yield = 10%/2 = 5%

number of payments = 5*2 = 10

PV of bond = PV of maturity + PV of interest

PV of maturity = Face value * PVF(5%;10) = 1000*0.614=614

PV of interest = interest *PVIFA(5%;10) = 45*7.7217= 347.4765

Price of bond = 961.4765

a)

semiannual yield = 8.4%/2 = 4.2%

US treasury security:

PV of maturity = Face value * PVF(4.2%;10) = 1000*0.66271=662.71

PV of coupon = 45*8.03074 = 361.3833

Price of bond = 1024

c) credit spread = BBB yield - risk-free yield = 10% - 8.4% = 1.6%