Company abc has liabilities of 20,000, 50,000 and 70,000 due at the end of years 1, 2 and 3 respectively. the company would like to exactly (absolutely) match these liabilities using the following assets: a one-year zero coupon bond with a yield of 4%a two-year zero coupon bond with a yield of 5%a three-year coupon bond with annual coupons of 6% and a yield of 5.5%what is the total cost of the asset portfolio that will exactly match the liabilities?

Ans. Bond A =$20,800; Bond B =$55,125; Bond C =$69,068.29

Explanation:

Hello, First, we have to find the price of the bond, or in other words what is the percentage of its nominal rate that will match its face value, that is , for bond A (zero coupon, yield=4%, 1 year) $20,000, for bond B (zero coupon, yield=5%, 2 years) $50,000, and bond C (coupon=6%, yield=5.5%, 3 year) $70,000. The equation is as follows.

For the first 2 bonds, the math is as follows

For Bond C, remember that this is a coupon bond so we have to find the present value of this instrument by using the following equation.

So, the amount in Bond value for each one that will match each debt is:

Bond A = 20000/0.961538462=$20,800

Bond B = 50000/0.907029478=$55,125

Bond C = 70000/1.013489667=$69,068.29

Best of luck.

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