Question

A​ BBB-rated corporate bond has a yield to maturity of

11.8 %11.8%.

A U.S. treasury security has a yield to maturity of

9.8 %9.8%.

These yields are quoted as

APRs

with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of

10.8 %10.8%

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

Part a)

The price of of the treasury​ bond can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 9.8%/2 = 4.9%, Nper = 5*2 = 10, PMT = 1,000*10.8%*1/2 = $54 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Price of Treasury Bond = PV(4.9%,10,54,1000) = $1,038.80

Price (Expressed as a Percentage of the Face Value) of Treasury Bond = Price of Treasury Bond/Face Value*100 = 1,038.80/1,000*100 = 103.88% (answer for Part a)

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Part b)

The price of of the corporate​ bond can also be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate, Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

Here, Rate = 11.8%/2 = 5.9%, Nper = 5*2 = 10, PMT = 1,000*10.8%*1/2 = $54 and FV = $1,000

Using these values in the above function/formula for PV, we get,

Price of BBB-Rated Corporate Bond = PV(5.9%,10,54,1000) = $963.02

Price (Expressed as a Percentage of the Face Value) of BBB-Rated Corporate Bond = Price of Corporate Bond/Face Value*100 = 963.02/1,000*100 = 96.30% (answer for Part b)

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Part c)

The credit spread on BBB bonds is determined as below:

Credit Spread on BBB Bonds = Yield to Maturity of BBB-Rated Corporate Bonds - Yield to to Maturity of Treasury Bonds

Substituting values in the above formula, we get,

Credit Spread on BBB Bonds = 11.8% - 9.8% = 2% (answer for Part c)