In: Finance
Tower Insurance must make payments to a customer of $10 million in one year and $4 million in five years. The yield curve is flat at 10%. 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? What must be the face value and market value of that zero-coupon bond?
Year |
Payment |
PV Factor @10% (1/(1+10%)^Year |
PV (Payment * PV Factor |
Weight (PV/Sum of PV) |
Duration (Weight *Year) |
1 |
16 |
0.909 |
14.545 |
0.8541 |
0.8541 |
5 |
4 |
0.62 |
2.484 |
0.1459 |
0.7293 |
17.029 |
1.5835 |
Maturity of Zero coupon bond= 1.5835 Years
Face Value of zero coupon bond =17.209*(1+10%)^1.5835
= $ 19.803 Million
Market value of zero coupon bond =Present Value of payment= $17.029 Million