Question

A company is obligated to make payments of $120,000 at end of year 2 and $180,000 at the end of year 4. To fund these liabilities, the company intends to purchase appropriate amounts of the following two bonds with annual payments as shown in the table below: End of year payments Bond A Year 1 Year 2 30 Year 3 Year 4 1030 Bond B 40 40 1040 0 30 Table 05 Assume that the year one, year two, year three and year four spot rates are 4.9 %, 5.3%, 5.8 % and 6.5% respectively. (a) Calculate the price for each of the two bonds. (4 marks) (b) Calculate the quasi-modified duration for each of the two bonds. (6 marks) (c) Calculate the present value and the quasi-modified duration of the obligation. (6 marks) (d) Describe and illustrate how much dollar value of each of the two bonds the company has to purchase in order to form a bond portfolio which immunizes against the risk of interest change (4 marks)

Answer 1

From the table mentioned, we observe that
coupon payment on Bond A = 3%
coupon payment on Bond B = 4%
Face value of both bonds is $1000

Spot rate in year 1 = 4.9%
Assuming the interest rate spread due to credit risk of the bonds is zero, the bonds will trade at a price so that the yield on the bonds equals 4.9%

Price of Bond = Coupon Rate/ Spot Rate X Face Value of Bond

Price of Bond A = 3%/4.9% X 1000 = 612.25
Price of Bond A = 4%/4.9% X 1000 = 816.32