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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