Question

A​ BBB-rated corporate bond has a yield to maturity of 9.5 %. A U.S. treasury security has a yield to maturity of 7.8 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 8.8 % 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

Let face value of the bond be $100

a). For treasury bond,

Yield to maturity = 7.8% compounded semiannually,

Coupon rate = 8.8% paid semiannually

So, semiannual coupon payment = (8.8%/2) of 100 = $4.4

years to maturity = 5 years

So, price of the bond can be calculated on financial calculator using following values:

FV = 100

PMT = 4.4

N = 2*5 = 10

I/Y = 7.8/2 = 3.9

compute for PV, we get PV = -104.08

So, price of BBB-rate corporate bond = $104.08 or 104.08/100 = 104.08% of face value

b). For BBB-rated corporate bond,

Yield to maturity = 9.5% compounded semiannually,

Coupon rate = 8.8% paid semiannually

So, semiannual coupon payment = (8.8%/2) of 100 = $4.4

years to maturity = 5 years

So, price of the bond can be calculated on financial calculator using following values:

FV = 100

PMT = 4.4

N = 2*5 = 10

I/Y = 9.5/2 = 4.75

compute for PV, we get PV = -97.26

So, price of BBB-rate corporate bond = $97.26 or 97.26/100 = 97.26% of face value

c). credit spread on the BBB bond = YTM of BBB bond - YTM on T-bond = 9.5% - 7.8% = 1.7% or 170 basis points