# 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                                                  8.00%
Retirement age:                                                            65 years old
Draws retirement for:                                                      15 years
Age at adoption of pension plan:                                           55 years old
Length of prior service for employer                                       20 years
Years until retirement                                            _________ years
Salary at adoption of plan                                    \$     39,904
Expected rate of salary increases                                         5%
Expected salary at retirement                                 \$___________
Benefit formula (percentage of final salary)                            1.5%
Payment earned by one year of work                           \$___________ 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
8.00%                                                    8.00%
a            b          c          d           e            f               g               h        i           j           k       c+d-h+k
Employer
Projected                              Contribution            Amortization Net Pension
End of       Age of     Service   Interest   Payments      Benefit       Fair Value of Return on to Pension Payments        of Prior      Cost
Year       Employee     Cost       Cost     to Retiree   Obligation     Plan Assets Plan Assets    Plan      to Retiree Service Costs Recorded
0       55                                 -        77,312               -
1       56      4,175     6,185            -        87,671           17,283        -      17,283            -       7,731      18,091
2       57      4,509     7,014            -        99,193           35,948     1,383     17,283            -       7,731      17,871
3       58      4,869     7,935            -       111,998           56,106     2,876     17,283            -       7,731      17,660
4       59      5,259     8,960            -       126,217           77,877     4,488     17,283            -       7,731      17,461
5       60      5,679    10,097            -       141,993          101,390     6,230     17,283            -       7,731      17,278
6       61      6,134    11,359            -       159,487          126,784     8,111     17,283            -       7,731      17,113
7       62      6,625    12,759            -       178,870          154,209    10,143     17,283            -       7,731      16,972
8       63      7,154    14,310            -       200,334          183,828    12,337     17,283            -       7,731      16,859
9       64      7,727    16,027            -       224,088          215,817    14,706     17,283            -       7,731      16,778
10           65     8,345    17,927          -         250,360         250,365      17,265      17,283         -        7,731     16,738
11           66        -     20,029     (29,250)       241,139         241,144      20,029                 29,250
12           67        -     19,291     (29,250)       231,180         231,185      19,292                 29,250
13           68        -     18,494     (29,250)       220,424         220,430      18,495                 29,250
14           69        -     17,634     (29,250)       208,808         208,815      17,634                 29,250
15           70        -     16,705     (29,250)       196,263         196,270      16,705                 29,250
16           71        -     15,701     (29,250)       182,714         182,721      15,702                 29,250
17           72        -     14,617     (29,250)       168,081         168,089      14,618                 29,250
18           73        -     13,446     (29,250)       152,277         152,286      13,447                 29,250
19           74        -     12,182     (29,250)       135,209         135,219      12,183                 29,250
20           75        -     10,817     (29,250)       116,776         116,787      10,818                 29,250
21           76        -      9,342     (29,250)       96,868           96,880       9,343                 29,250
22           77        -      7,749     (29,250)       75,368           75,380       7,750                 29,250
23           78        -      6,029     (29,250)       52,147           52,160       6,030                 29,250
24           79        -      4,172     (29,250)       27,069           27,083       4,173                 29,250
25           80        -      2,166     (29,250)           (16)             (0)      2,167                 29,250

Document1                                                                             Page 2
Acct 414                                                                    Prof. Teresa Gordon

Notes on computations.

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

2.      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.

3.      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.

Document1                                                                                  Page 3
Acct 414                                                           Prof. Teresa Gordon

5                                    6                                                          8
5                                    5                                                          0
N=10
N=15

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)?

Document1                                                                       Page 4
Acct 414                                                             Prof. Teresa Gordon

5                                     6                                                           8
5                                     5                                                           0
N=10
N=15

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?

Document1                                                                          Page 5
Acct 414                                                                 Prof. Teresa Gordon

5                                       6                                                           8
5                                       5                                                           0
N=10
N=15

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)

Document1                                                                              Page 6
Acct 414                                                                Prof. Teresa Gordon

5                                      6                                                       8
5                                      5                                                       0
N=10
N=15

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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