Question

1 . An employee retiring from a firm after 36 years of service at age 68 has earned a pension of $63,000 per year paid in quarterly payments of $15,750. His expected life expectancy is 12 years further at age 80. The pension payments would end when he dies.

a. Given a 16% discount rate based on the investment risk of his employer, what is the lump sum value of the pension when he retires? Excerpts from the Present Value of an Annuity table will help you use the right present value factor. The discount rate is 4% (16% divided by 4) and the present value of an annuity factor at 4% for 48 periods is 21.195.

b. If the employer offered the employee a lump sum payment of $350,000 instead of the pension that he could put into an annuity with the same risk as receiving his employer’s pension paying 16% interest per year compounded quarterly, should he take it? What risk would the retiring employee have if he does not accept the lump sum?

PLEASE NOTE: The present value of an annuity factors at 2% (or 8% divided by 4) are:48 quarters or number of payments (from 12 years equaling 48 quarters): 30.67336 quarters or number of payments (from 9 years equaling 36 quarters): 25.499At what retirement age would the present value of the future payments be higher?

Answer 1

Solution :- Total Quarterly Pensions = 12 * 4 = 48

(A) Present Value of Pension when he retires = Quarterly Pension * PVAF ( 4% , 48 )

= $15,750 * 21.195

= $333,821.30

The lump sum value of the pension when he retires = $333,821.30

(B) If the employer offered the employee a lump sum payment of $350,000 instead of the pension that he could put into an annuity with the same risk as receiving his employer’s pension paying 16% interest per year compounded quarterly

Then he take $350,000 as the Present Value of Quarterly Payments of Pension is less than $333,821.30

The retiring employee that would have risk if he does not accept the lump sum is may be his early death and apart from this a risk of change in interest rate too .

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