Question
In: Finance
An insurance company must make payments to a customer of $9 million in one year and...
An insurance company must make payments to a customer of $9 million in one year and $4 million in six years. The yield curve is flat at 7%.
a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? (Do not round intermediate calculations. Round your answer to 4 decimal places.)
b. What must be the face value and market value of that zero-coupon bond?
Solutions
Expert Solution
| a. | |||||||||
| Calculation of maturity of bond | |||||||||
| Year | Cash outflow | Discount factor @ 7% | Present value | Weight of present value | Year*Weight | ||||
| 1 | 9000000 | 0.93458 | $8,411,214.95 | 0.7594 | 0.7594 | ||||
| 6 | 4000000 | 0.66634 | $2,665,368.90 | 0.2406 | 1.4438 | ||||
| $11,076,583.85 | 2.2032 | ||||||||
| Therefore the maturity of the zero coupon bond should be 2.2032 | |||||||||
| b. | |||||||||
| The market value of the bond would be equal to present value of payment to be made by the insurance company and so the market value should be $11,076,583.85 | |||||||||
| c. | |||||||||
| Face value of bond = Market value*(1+r)^n | |||||||||
| where r is the interest rate | |||||||||
| n is the time period | |||||||||
| Face value of bond = 11076583.85*(1.07^2.2032) | |||||||||
| Face value of bond | $12,857,094.88 | ||||||||
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