In: Finance
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?
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 | ||||||||