Question

6. Bond Valuation A BBB-rated corporate bond has a yield to maturity of 9%. AU.S. Treasury security has a yield to maturity of 7.5% These yields are quoted as APRS with semiannual compounding. Both bonds pay semiannual coupons at an annual rate of 8.4% 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? 7. Bond Valuation Consider two bonds, each pays semi-annual coupons and 5 years left until maturity. One has a coupon rate of 5% and the other has a coupon rate of 10%, but both currently have a yield to maturity of 8% How much will the price of each bond change if its yield to maturity decreases from 8% to 7%?

Answer 1

Question 6:

For both the bonds assuming Face value = 1K, PMT i.e. coupon = 48 @ 8.4% semiannually(8.4% / 2) , Number of payments = 10 (5 yrs semiannual, 5*2)

For BBB rated corporate bond I/Y = 9 / 2 (semiannual) therefore price 976.261

For Treasury bond I/Y = 7.5 / 2 (semiannual) therefore price 1036.95

Question 7:

For both the bonds assuming Face value = 1K, Number of payments = 10 (5 yrs semiannual, 5*2)

Bond with coupon rate 5%

PMT = 25 (5% of 1000 = 50 / 2 aince coupon is semiannual)

When,

I/Y = 8 / 2 (Semiannual) , price = 878.33

I/Y = 7 / 2 (Semiannual), price = 916.83

Price difference = 916.83-878.33 = 38.50

Bond with coupon rate 10%

PMT = 50(10% of 1000 = 100 / 2 since coupon is semiannual)

When,

I/Y = 8 / 2 (Semiannual) , price = 1081.10

I/Y = 7 / 2 (Semiannual), price = 1124.74

Price difference = 1124.74 - 1081.10 = 43.63