Question

A BBB-rated corporate bond has a yield to maturity of 9.5%. A U.S. Treasury security has a yield to maturity of 7.6 %. These yields are quoted as APRs with semiannual compounding. Both bonds pay semi-annual coupons at a rate of 8.5%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?

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

The price of the Treasury bond as a percentage of face value is ____ % (Round to three decimal places.)

Answer 1

Price of a bond is mathematically represented as:

where P is price of bond with periodic coupon C, M face value, n periods to maturity and periodic YTM i.

a) Priceof treasury bond

Assume M = $100, n = 2 * 5 = 10 semi-annual periods, C = 8.5% * $100/2 $4.25 (semi-annually), i = 7.6%/2 = 3.8% (semi-annually)

P = 34.817 + 68.869

P = $103.687

So as % of face value, value of Treasury bond is 103.69%

b) Priceof BBB rated corporate bond

Assume M = $100, n = 2 * 5 = 10 semi-annual periods, C = 8.5% * $100/2 $4.25 (semi-annually), i = 9.5%/2 = 4.75% (semi-annually)

P = 33.219 + 62.872

P = $96.092

So as % of face value, value of Corporate bond is 96.09%

c) Credit spread on BBB bonds = YTM on Corporate bond - YTM on Treasury Bond = 9.5% - 7.6% = 1.90%