49. A company is obligated to pay a four year immediate annuity to a customer wi
ID: 2643003 • Letter: 4
Question
49. A company is obligated to pay a four year immediate annuity to a customer with annual payments of 1000. There are only four assets available for investment: one and two year zero coupon bonds, a three year 5% annual coupon bond and a four year 6% annual coupon bond. The company wants to exactly match its liabilities by purchasing these assets. The bonds can be bought in any quantity including fractional units. Determine the combined price of the 2 zero coupon bonds given the following spot rates:Explanation / Answer
Solution :
The price of a bond is equal to the present value of all of its cash flows. The spot rate is the current yield for a given term.
The price of one year zero coupon bond = 1000 / ( 1+0.05)1
The price of one year zero coupon bond = $ 952.38
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The price of two year zero coupon bond = 1000 / ( 1+0.05)1 + 1000 / (1+0.0575)2
The price of two year zero coupon bond = $ 952.38 + $ 894.20
The price of two year zero coupon bond = $ 1846.58
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The combined price of one and two year zero coupon bond = $ 952.38 + $ 1846.58
The combined price of one and two year zero coupon bond = $ 2798.96
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