Question

A​ BBB-rated corporate bond has a yield to maturity of 10.5%. A U.S. treasury security has a yield to maturity of 9.2%. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 9.4% 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

a.

For Treasury Bond,

YTM = 9.2%

Coupon rate = 9.4% semi-annually

Time to Maturity = 5 years

Let's take Bond Par Value = $100

Calculating Present Value of Bond,

PV = [FV = 100, T = 10, PMT = 4.7, I = 0.092/2]

PV = $100.79

So, Price = 100.79% of Par Value

b.

For BBB-rated corporate Bond,

YTM = 10.5%

Coupon rate = 9.4% semi-annually

Time to Maturity = 5 years

Let's take Bond Par Value = $100

Calculating Present Value of Bond,

PV = [FV = 100, T = 10, PMT = 4.7, I = 0.105/2]

PV = $95.8

So, Price = 95.80% of Par Value

c.

Credit Spread on BBB-rated Corporate Bond = (T-Bill Yield - BBB rated bond yield)

Credit Spread on BBB-rated Corporate Bond = 10.50 - 9.20

Credit Spread on BBB-rated Corporate Bond = 1.30%

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