A company is attempting to immunize a schedule of liability cash flows via cash flow matching. The cash flows are as follows:

Year	Liability (000s)
1	250
2	330
3	455

Starting from the end and working backward, the company decides to match the year 3 cash flow by investing in a 3 year 6.79% annual coupon bond, currently priced at 98.52 per $100 of par value, then a 2 year 6.42% coupon bond priced at 98.44 per $100 of par value, and finally a 1 year 5.19% coupon bond priced at 98.86 per $100 of par value.

What is the market value of the 2 year bond that the company must buy to match the year 2 liability?

Correct Answer

278,494

Work backwards and first find the amount of 3 year bond the company will buy, then figure out the amount of annual coupon from the 3 year bond. Then find the amount of 2 year bond the company must buy to match the remaining year 2 liability (given that some of it will be matched by the coupon from the 3 year bond).

Finally note that this problem asks for the market value of the 2 year bond, not just the face value.