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?
Please show the method used to solve this problem.

Answer 1

Answer:

1) in 25 years, the pension fund should equal:

future value = present value x (1 + interest rate)ⁿ

FV = $20,000,000 x (1 + 8.5%)²⁵ = $153,735,247

2) the value in 12 years = $20,000,000 x (1 - 30%) = $14,000,000

future value = present value x (1 + interest rate)ⁿ

$153,735,247 = $14,000,000 x (1 + interest rate)¹³

(1 + interest rate)¹³ = $153,735,247 / $14,000,000 = 10.981

¹³√(1 + interest rate)¹³ = ¹³√10.981

1 + interest rate = 1.2024

interest rate = 1.2024 - 1 = 20.24%

3) if the fund only earns 6%, in 13 years it will be worth:

FV = $14,000,000 (1 + 6%)¹³ = $29,860,996

so you need $153,735,247 - $29,860,996 = $123,874,251 more

we need to use the future value of an annuity formula:

FV of an annuity = annuity payment x annuity factor

• FV of an annuity = $123,874,251
• annuity payment = ?
• annuity factor (6%, 13 periods) = 18.882

annuity payment = $123,874,251 / 18.882 = $6,560,441