A BBB-rated corporate bond has a yield to maturity of 6.8 %6.8%. A U.S. treasury

Question

A BBB-rated corporate bond has a yield to maturity of 6.8 %6.8%. A U.S. treasury security has a yield to maturity of 4.9 %4.9%. These yields are quoted as APRs with semiannual compounding. Both bonds pay semi-annual coupons at a rate of 5.3 %5.3% 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?

Explanation / Answer

BBB bonds (YTM) = 6.8%

US Treasury security = 4.9%

Coupon rate for both bonds are 5.3%

Time to Maturity for both bonds = 5 years

Price of BBB bonds = Coupon rate* Face Value of the bond PVIFA (YTM%, n years) +Face Value of the bond * PVIF (YTM%, n Years)

Let us suppose that the face value of the BBB bond is $1000

So, coupon interest for full year will be = $1000*0.053 = $53

Again coupon interest for half year will be = $53/2 = $26.50

So, Price of BBB bonds = 26.50*PVIFA (6.8%/2, 5*2years) + 1000* PVIF (6.8%/2, 5*2years) {since coupon payments are semiannual in nature so time has been doubled and YTM has been halved}

Or, Price of BBB bonds = 26.50*(8.36) + 1000* (0.7158) = $937.34

Price as a % of Face Value of BBB bonds = $937.34/$1000*100= 93.73%

Price of US Treasury Security = Coupon rate* Face Value of the Treasury security PVIFA (YTM%, n years) +Face Value of the Treasury Security * PVIF (YTM%, n Years)

Let us suppose that the face value of the Treasury security is $1000

So, coupon interest for full year will be = $1000*0.053 = $53

Again coupon interest for half year will be = $53/2 = $26.50

So, Price of Treasury Security = 26.50*PVIFA (4.9%/2, 5*2years) + 1000* PVIF (4.9%/2, 5*2years) {since coupon payments are semiannual in nature so time has been doubled and YTM has been halved}

Or, Price of Treasury Security = 26.50*(8.77) + 1000* (0.7850) = $1017.405

Price as a % of Face Value of Treasury Security = $1017.405/$1000*100= 101.74%

Type of Bonds/Securities

Coupon Interest%

Price % of Face Value

BBB bonds

5 Years

Treasury Security

5 Years

Credit spread is the difference in the yield to maturity of 2 bonds with the same time to maturity. Hence in this case the spread would be (6.8% - 4.9%) = 1.9%

Type of Bonds/Securities

Coupon Interest%

Price % of Face Value

BBB bonds

5 Years

Treasury Security

5 Years

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