Question

You work for a pension fund company. One account starts its pension payments at the end of two years from now. The duration of pension payment is 10.5 years when the pension starts. The present value of the pension payment is $123,456. Currently, the pension’s yield is 5%. To neutralize the interest rate risk, you would like to use a zero coupon bond (ZCB). What should be the maturity of ZCB? What is the face value (future value) of ZCB?

Answer 1

A pension fund company:

Zero coupon bond value (ZCBV) = $ 123,456

Rate of yield (r) = 5%

Time (t) = 10.5%

Face value (FV) = ?

ZCBV = FV / (1+r) ^t

$ 123,456 = FV / (1+0.05)^10.5

$ 123,456 = FV / (1.05)^10.5

$ 123,456 = FV / 1.669 ( Here 1.05^10.5 is 1.669)

FV = $ 123,456 × 1.669

Face value is $ 206,050 (approximately)

The bondholder will get at maturity is $ 206,050.