Question
An insurance company needs to make payments to a consumer of $10 million in 1 year (t=1) and $4 million in year 5 (t=5). The
An insurance company needs to make payments to a consumer of $10 million in 1 year (t=1) and $4 million in year 5 (t=5). The yield curve is considered to be flat at 10%.
a. | Time | Cash Flow | PV @ 10% | Weight | Duration |
1 | $ 10,000,000.00 | $9,090,909.09 | 0.7854 | 0.7854 | |
5 | $ 4,000,000.00 | $2,483,685.29 | 0.2146 | 1.0729 | |
Total | $11,574,594.38 | 1 | 1.8583 | ||
PV | $11,574,594.38 | ||||
Required maturity of zero | 1.8583 | ||||
Solution b. | |||||
The zero's market value | $11,574,594.38 | ||||
Face value | $13,817,413.73 | ||||
C. | |||||
Value of the zero | 12857733.14 | ||||
Given the information above answer D, E, and F. |
D. Utilizing the bond that was purchased in part (a) with the info that is in part (c), how can the insurance company make the payment of $10 million at t=1?
E. What is the value of the liability (after making the payment in (d)) that remains for the insurance company? Are they still close to being fully funded? explain why or why not?
F. With all of the steps that were taken at t=1, what must the insurance company do so that they continue to be immunized. Explain
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