Question

Today’s business headlines frequently cite pensions being underfunded, thus costing companies more in contributions to their pension fund as well as pensioners risking not receiving what they had planned for retirement. This has been caused by underperformance of the pension fund itself and the over promising of benefits to retirees.

Take the following example:

Assume $20m was invested today to provide for pension payments for a group of employees. Assume also that the average return on these funds was 8.5%

1. How big will the fund be in 25 years?
2. Suppose at year 12 the fund decreased in value by 30%. What returns would be required for the next 13 years to achieve the 25 year amount?
3. Advisor's counseled the company that a conservative investment return of 6% annually for the next 13 years would be advisable and that the company would have to contribute annually to make up the shortfall.How much would have to be contributed annually beginning year 13 if the fund earned 6% in order to achieve the 25 year goal?

Answer each of the question above. Be sure to show your work and explain your methods.

Answer 1

SOLUTION:

AN AMOUNT OF $ 20M IN PENSION FUND IN 25 YEARS AT 8.5% INTEREST IS

FV= PV(1+r)t = 20000000 (1+ 0.085)²⁵

= $ 153,735,247.12

AT 12 YEARS THE AMOUNT WOULD BE

FV= PV(1+r)t = 20000000 (1+ 0.085)¹²

=$53,233,724.40

AND IT IS DECREASED BY 30% = $53,233,724.40 - 30%

= $15970,117.40

AT 12 TH YEAR THE BALANCE IN THE PENSION FUND = $53,233,724.65 - $15,970,117.40

=$ 32263,607.25

THE PENSION FUND AFTER 25 YEARS WOULD BE

= $ 153,735,247.12

BUT THE AMOUNT AT THE END OF 12 YEARS IS $32,263,607.25  

SO THE REMAINING BALANCE AMOUNT i.e.,

=$153,735,247.12 - $32263,607.25

= $121,471,639.87 HAS REQUIRED TO BE SAVED DURING 13TH YEAR PERIOD.

TO ACHIEVE 25 YEAR GOAL,

PV = FV(PVIF 8.5% , 13)

= $121,471,639.87(PVIF 8.5%, 13)

= $42061,843.01

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