Question

A​ BBB-rated corporate bond has a yield to maturity of 10.1%. A U.S. treasury security has a yield to maturity of 8.3%. 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

Bond Price Formula-

Where n is the number of periods

i = Yield

C = Coupon value

M - Face Value

As the bond pays semi annually, n = 10 (2 periods in a year, total 5 years)

Answer a: As the price has to be percentage of face value, we assume face value to be 100.

Coupon Rate = 9 % (Bond pays $ 9 coupons per year - or $ 4.5 in 6 months)

i = 8.3% /2 = 4.15%

C = 4.5

M = 100

Bond Price has been calculated through excel as shown below through the above formula. The price comes out to be $ 102.88 (Treasury Bond) which is 102.8% of the face value.

The formulae in the excel are as shown below :

Answer b: Similarly, for convenience, we assume face value as 100 for a BBB Rated bond. Using the same formula as above, we will have-

Coupon Rate = 9 % (Bond pays $ 9 coupons per year - or $ 4.5 in 6 months)

i = 10.1% /2 = 5.05%

C = 4.5

M = 100

The bond price in this case comes out to be $ 95.76 which is 95.76% of the face value. This is shown in the excel below.

Formulae will remain the same as part a, just the interest rate will change as shown here.

Answer c:

Credit spread is the difference in yields of two bonds with same maturity due to difference in their risk ratings.

Credit Spread = Difference in rate of return between BBB Bond and Treasury Bond

= 10.1% - 8.3%

= 1.8%

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