Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero coupon bond held? c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still approximately fund the future payments by showing that the present values of the two after the drop in market interest rates are still roughly the same
Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual payments). The first payment will come in exactly 5 years (at the end of year 5) and the last payment in 9 years (at the end of year 9). a. What is the duration of the pension obligation? The current interest rate is 9% per year for all maturities. b. To generate the scheduled pension payments, the pension fund wants to invest the present value of the future payouts in bonds and match the duration of its obligation in part a). If the fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how much money (dollar amount) ought to be placed in each bond now? What should be the total face value (not current market value) of each zero coupon bond held? c. Right after the fund made its investment outlined in part b), market interest rates for all maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in part b) can still approximately fund the future payments by showing that the present values of the two after the drop in market interest rates are still roughly the same
Chapter5: The Time Value Of Money
Section: Chapter Questions
Problem 44P
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Transcribed Image Text:Consider a pension plan that will pay $10,000 once a year for a 5-year period (5 annual
payments). The first payment will come in exactly 5 years (at the end of year 5) and the last
payment in 9 years (at the end of year 9).
a. What is the duration of the pension obligation? The current interest rate is 9% per year for all
maturities.
b. To generate the scheduled pension payments, the pension fund wants to invest the present
value of the future payouts in bonds and match the duration of its obligation in part a). If the
fund uses 5-year and 10-year zero-coupon bonds to construct its investment position, how
much money (dollar amount) ought to be placed in each bond now? What should be the total
face value (not current market value) of each zero coupon bond held?
c. Right after the fund made its investment outlined in part b), market interest rates for all
maturities dropped from 9% p.a.to 8% p.a. Show that the investment position constructed in
part b) can still approximately fund the future payments by showing that the present values of
the two after the drop in market interest rates are still roughly the same
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