A company must pay liabilities of 5000 in 6 months and 7000 in one year. The only investments available to the company are
(a) A 6 month bond with face amount 1,000 and a nominal 5% annual coupon rate convertible semiannually, and a 4% nominal annual yield rate convertible semiannually
(b) A one-year bond with face amount 1000, a 6% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually.
Find the amount of each bond to purchase to exactly match these liabilities (you can buy fractional bonds). Number of 6 month bonds?number of one year bonds?
What is the total cost of purchasing these bonds?
Answer:
the semiannual yield on 6 month bond is 4%/2 = 2% and the semiannual yield on 1 year bond is 7%/2 = 3.5%.
Amount of bond to purchase = PV of the amounts required
= 5000/ (1+0.02) + 7000/ (1+0.035)^2
= $4901.96 + $6535.57
= $ 11,437.53
Therefore, an investment of $11,437.53 is required to pay $5,000 after 6 months and 7,000 after 1 year.
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