Question

An insurance company must make payments to a customer of $11 million in one year and $7 million in five years. The yield curve is flat at 6%.

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?

b. What must be the face value and market value of that zero-coupon bond?

Answer 1

a) PV of first payment (P1)= 11/1.06 = 10.38

PV of the sencond payment P2 = 7 / (1.06^5) = 5.23

Total PV = 10.38 + 5.23 = 15.61

Weight of 1st payment W1 = 10.38 / 15.51 = 0.6649

Wight of 2nd payment W2 = 5.23/15.61 = 0.3351

Duration = T1*W1 + T2*W2 = 1*0.6649 + 5*0.3351 = 2.34 years

So, a single issue of a zero-coupon bond, with maturity of 2.34 years must be purchased.

b) Face value of that zero coupon bond = 11 + 7 = 18 million

Market value =18 / (1.05^2.34) = 15.71 Million