Question

A​ BBB-rated corporate bond has a yield to maturity of 12.7 %. A U.S. treasury security has a yield to maturity of 10.7 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay​ semi-annual coupons at a rate of 11.5 % 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

Solution

Price of a Bond = Present Value of Interest Payments or Coupon Amount + Present value of Redemption proceeds

a) Price of Treasury Bond

If its a Semi Annual Compounding, The coupon and Yield is cut in half and Maturity is Doubled.

Coupon Payment = ($1000 * 11.5%) / 2 = $57.5

Redemption Value = $1,000

Yield = 10.7% / 2 = 5.35%

Maturity = 5 * 2 = 10 Years.

Price = ($57.5 * PVIFA ^{5.35, 10} ) + ($1,000 * PVIF ^{5.35, 10} )

= ($57.5 *7.5922) + ($1,000 * .5939)

= $436.55 + $593.9

= $1030.45

Percentage of Face Value =($1030.45 / $1000 ) * 100

= 103.045 %

b) Price of BBB Rated Corporate Bond

If its a Semi Annual Compounding, The coupon and Yield is cut in half and Maturity is Doubled.

Coupon Payment = ($1000 * 11.5%) / 2 = $57.5

Redemption Value = $1,000

Yield = 12.7% / 2 = 6.35%

Maturity = 5 * 2 = 10 Years.

Price = ($57.5 * PVIFA ^6.35,10 ) + ($1,000 * PVIF ^{6.35, 10} )

= ($57.5 *7.2396) + ($1,000 * .5403)

= $416.28 +$540.3

= $956.58

Percentage of Face Value =($956.58 / $1000 ) * 100

= 95.658 %

c) Credit Spread

It is the difference in yield between 2 bonds of similar maturity but different trade quality.

= 12.7 % - 10.7 %

  = 2 % or 200 basis point of spread.