# Pension Present Value Example

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Acct 414

Prof. Teresa Gordon

In Class Example Present Value Computations for Pension Plan
Consider a defined benefit, noncontributory plan. Assume that retirement benefits are paid at end of each year and employees are given credit for years of service prior to the adoption of the plan. The plan pays each employee an annual benefit equal to the number of years of qualifying service multiplied by a specified percentage of the final year’s salary. We will consider the pension computations for a single employee: Assumed discount rate Retirement age: Draws retirement for: Age at adoption of pension plan: Length of prior service for employer Years until retirement Salary at adoption of plan Expected rate of salary increases Expected salary at retirement Benefit formula (percentage of final salary) Payment earned by one year of work \$ 8.00% 65 years old 15 years 55 years old 20 years _________ years 39,904 5% \$___________ 1.5% \$___________ Per year until death

1. With these assumptions, how much will the company need to have set aside in a pension plan when the employee retires (so the promised benefit can be paid)?

2. If the company wants to set aside the necessary funds in 10 equal payments starting one year from now, how much will they need to contribute to the pension plan?

3. What is the liability related to the pension plan at adoption? (Hint: related to prior service period – but more than one possible way to measure – ABO vs PBO)

4. Compute service cost for the first year of the plan (Hint: this is the cost of ONE year’s benefit).

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Acct 414

Prof. Teresa Gordon

In Class Example – Accumulation and Distribution Schedules for PBO and Plan Assets
a b c 8.00% d e f Projected Benefit Obligation 77,312 87,671 99,193 111,998 126,217 141,993 159,487 178,870 200,334 224,088 250,360 241,139 231,180 220,424 208,808 196,263 182,714 168,081 152,277 135,209 116,776 96,868 75,368 52,147 27,069 (16) g 8.00% h i j
k

c+d-h+k

End of Year

Age of Employee 0 55 1 56 2 57 3 58 4 59 5 60 6 61 7 62 8 63 9 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Service Cost 4,175 4,509 4,869 5,259 5,679 6,134 6,625 7,154 7,727 8,345 -

Interest Cost 6,185 7,014 7,935 8,960 10,097 11,359 12,759 14,310 16,027 17,927 20,029 19,291 18,494 17,634 16,705 15,701 14,617 13,446 12,182 10,817 9,342 7,749 6,029 4,172 2,166

Payments to Retiree (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250) (29,250)

Employer Contribution Amortization Net Pension Fair Value of Return on to Pension Payments Cost of Prior Plan Assets Plan Assets Plan to Retiree Service Costs Recorded 17,283 17,283 7,731 18,091 35,948 1,383 17,283 7,731 17,871 56,106 2,876 17,283 7,731 17,660 77,877 4,488 17,283 7,731 17,461 101,390 6,230 17,283 7,731 17,278 126,784 8,111 17,283 7,731 17,113 154,209 10,143 17,283 7,731 16,972 183,828 12,337 17,283 7,731 16,859 215,817 14,706 17,283 7,731 16,778 250,365 241,144 231,185 220,430 208,815 196,270 182,721 168,089 152,286 135,219 116,787 96,880 75,380 52,160 27,083 (0) 17,265 20,029 19,292 18,495 17,634 16,705 15,702 14,618 13,447 12,183 10,818 9,343 7,750 6,030 4,173 2,167 17,283 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 29,250 7,731 16,738

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

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Acct 414 Notes on computations.

Prof. Teresa Gordon

The number in the BOX under PBO and FV of plan assets is the answer to the first question. It is the amount that will be needed at the date of retirement to make the promised payment to the employee assuming he works until retirement and all our assumptions are true. The first number in the PBO (projected benefit obligation) column is the answer to the third question. It is what we owe immediately because the employee has already worked for us and is getting credit for past services. So we have an immediate obligation to give him at least (\$65,000 * .015 * 20 years of prior service) per year from retirement age until he dies. The subsequent PBO figures are computed as the balance forward + service cost + interest cost – payments to retiree. Interest cost is the discount rate times the PBO at end of previous year. The first number in the Service cost column is the answer to the fourth question. It is the amount we would need to invest at the end of the first year of the pension plan to pay an additional year’s benefit (\$65,000 * .015) to the employee from retirement age until he dies. We have only 9 years left to earn interest before he retires. Notice that the next year’s service cost is higher because we only have 8 more years to earn the necessary interest. 1. Annual payment = 29,250 (65,000 * .015 * 30) n= 15 years life expectancy i = 8% discount rate, FV = 0, PVA = 250,365 To determine the annual amount to fund the plan (\$17,283 in this example), we take the amount we will need at retirement as the FV of an annuity, use n=number of years until retirement, and solve for the payment. If the plan will earn MORE or LESS than the discount rate, we have to figure what we’ll need in the plan assets at age 65 using the rate of return expected for the plan assets. Accordingly, the amount in PBO and the amount in the Plan Assets at retirement will NOT be equal unless the discount rate = the expected rate of return on investments in the pension plan. However, we should still run out of plan assets and PBO should be zero at the expected date of death. Plan assets are increased by contributions, decreased by payments to retirees, increased by “returns” (interest/dividends) earned on pension assets. First need to determine FUTURE salary level: PV=41,900, i=5% salary increase rate, n=9 (number of years during which raises could be received), Pmt=0, solve for FV=\$65,000 Next, determine payments during retirement (based on prior service only) = 19,500 or (\$65,000 * .015 * 20) n=15 years life expectancy, i=8%, FV=0, ordinary annuity PVA at age 65 = 166,910, discounted to age 55 (i.e., deferred 10 years) = 77,312 (To compute the ABO at plan adoption, we would use current salary instead of \$65,000 – however, GAAP assumes salaries will increase) 4. Service cost is based on working one more year: pmt = 975, i=8%, n=15 years (life expectancy), FV =0, the compute PVA at age 65 = \$8,345. We have only 9 years before retirement (he had to work a year to earn this benefit), so the value at age 56 is \$4,175. (\$8,345 = FV, pmt=0, n=9, i=8%, PV=?) The service cost increases as we approach retirement because we have less time to "earn" money to pay the benefit.

2.

3.

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Acct 414

Prof. Teresa Gordon

55 N=10

65 N=15

80

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