Question

BBB -rated corporate bond has a yield to, maturity of 8.5%.US treasury security has a yield to maturity of 7.0%. These yields are quoted as APR with semiannual compounding, Both pay semiannual coupons of 7.3% and hhave 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 of the BBB bonds?

a. What is the price (expressed as a percentage of the face value) of the treasury bonds?

Answer 1

Given that,

YTM on BBB rate corporate bond = 8.5%

YTM on treasury bond = 7%

Let face value be $100 for bond the bonds,

Coupon rate = 7.3% paid semiannually,

So, semiannual coupon payment = (7.3%/2) of 100 = $3.65

years to maturity for both bonds = 5 years

a). price of the bonds can be calculated on financial calculator.

For treasury bond use following values:

FV = 100

N = 2*5 = 10

PMT = 3.65

I/Y = 7/2 = 3.5

compute for PV, we get PV = -101.25

So, price of Treasury bond = 101.25% of its face value

b). For treasury bond use following values:

FV = 100

N = 2*5 = 10

PMT = 3.65

I/Y = 8.5/2 = 4.25

compute for PV, we get PV = -95.19

So, price of corporate bond is 95.19% of face value

c). Credit spread of BBB bond = YTM of BBB bond - YTM of Treasury bond = 8.5 - 7 = 1.5%