Question

A​ BBB-rated corporate bond has a yield to maturity of 6.4%. A U.S. treasury security has a yield to maturity of 4.4%. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 4.7% 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

Assume Face Value of the Bond be $1000.

a). To find the price of Treasury Bond, we need to put the following values in the financial calculator:

N = 5*2 = 10;

I/Y = 4.4/2 = 2.2;

PMT = (4.7%/2) * 1000 = 23.5;

FV = 1000;

Press CPT, then PV, which gives us -1013.33

T-Bond's Price = $1013.33

%Price of the face value = T-Bond's Price / Face Value = $1013.33 / $1000 = 1.0133, or 101.33%

b). To find the price of BBB Bond, we need to put the following values in the financial calculator:

N = 5*2 = 10;

I/Y = 6.4/2 = 3.2;

PMT = (4.7%/2) * 1000 = 23.5;

FV = 1000;

Press CPT, then PV, which gives us -928.23

BBB-Bond's Price = $928.23

%Price of the face value = BBB-Bond's Price / Face Value = $928.23 / $1000 = 0.92823, or 92.82%

c). Credit Spread on BBB Bonds = Yield on BBB Bond - Yield on Treasury Bond

= 6.4% - 4.4% = 2.0%