Why Re-Employment Requires Careful Rule Reading
When a former employee returns to work, it is tempting to add all prior and new service and apply the current pension formula. That may be correct under one plan and wrong under another. The outcome depends on the plan’s rules for a break in service, prior vesting, refunds, and benefits already in payment. Re-employment does not, by itself, erase an earlier entitlement or restore earlier service.
The analysis should separate three questions: does the returning employee re-enter active membership; does the plan restore earlier service; and what happens to any benefit or refund from the earlier period? A plan may answer these differently. For example, it could permit new accrual without restoring old service, or restore service only after repayment of a prior refund.
A useful rule-reading sequence is to identify the prior status first. The former employee might have a vested deferred pension, an unvested benefit, a refund of contributions, or a pension already in payment. Next, determine the return conditions: a time limit, an application deadline, repayment of a refund with interest, or a minimum period of renewed employment. Finally, identify the precise benefit treatment, including whether prior service is restored, the earlier benefit is preserved separately, or payments are suspended during renewed employment.
Record whether the employee left with a deferred pension, received a refund, or had already commenced a pension. Do not treat these as interchangeable.
Apply the plan’s time limit, membership rules, repayment terms, and any required election or application.
Determine whether past service is restored, remains separate, or is excluded, and whether earlier payments continue or are suspended.
Use the correct service and salary basis for each benefit, then value payments using an explicitly stated actuarial basis.
What Can Happen to Earlier Service and Benefits?
A plan may restore prior service in full, restore it only after a condition is satisfied, or leave it as a separate deferred entitlement. These treatments produce different benefit calculations. If service is restored under a final-average salary formula, for instance, the plan might use total restored and new service with the salary defined by its rules. If service is not restored, the earlier pension may remain based on the salary and service applicable when the employee left, while the new period earns a separate benefit.
A contribution refund also needs explicit treatment. If the plan conditions restoration on repayment, the relevant repayment may be the refund accumulated at a specified rate from its payment date. Repaying the refund is not the same as repaying pension benefits that were properly paid. Conversely, if a pension was already in payment, the plan may suspend it during renewed active employment, continue it, or apply another stated rule. Do not infer an offset or repayment requirement unless the plan says so.
| Earlier position | Possible plan treatment on return | Key calculation question |
|---|---|---|
| Vested deferred pension | Preserve separately, or cancel and recalculate if service is restored | Which salary and service basis applies to each entitlement? |
| Refund of contributions | Require repayment, possibly with specified interest, before restoration | What amount is due on the return date? |
| Pension already in payment | Continue, suspend, or otherwise adjust payments under the plan | Are payments due during renewed employment, and does new service accrue? |
| No vested entitlement | Allow new membership, with earlier service excluded unless restoration rules apply | Does the earlier period count toward any stated eligibility condition? |
The benefit formula does not determine the re-employment rule. It is applied only after the plan’s service and benefit treatment has been established. The examples use hypothetical plan provisions and a simplified valuation basis to keep that distinction visible. For every valuation below, assume an effective annual interest rate \(i=4\%\), annual pension payments in arrears, and an independent annual survival probability \(p=0.96\) after pension commencement. Thus annual mortality is \(q=0.04\), and the future lifetime in whole years has a geometric distribution with survival probabilities \({}_kp_x=0.96^k\). Assume the pension is paid only if the member is alive on each payment date, with no escalation or spouse’s benefit.
Why the Simplified Pension Value Is \(12B\)
Let \(v=1/(1+i)=1/1.04\). The payment at the end of year \(k\) is made with probability \({}_kp_x=0.96^k\), so its expected present value is \(Bv^k0.96^k\). Summing over all possible payment years gives a geometric series. Since \(v(0.96)=12/13\), the series converges and its value is \(12B\).
This derivation also shows why payment timing matters. An annual payment in arrears starts after one year, so the sum begins at \(k=1\). If a payment were made immediately at commencement, there would be an additional certain payment at time zero; the factor would be different.
Worked Example: Restoring Service After a Contribution Refund
A hypothetical plan provides an annual pension of 1.5% of final-average salary for each credited year of service. A former employee left with six years of service and received an $8,000 contribution refund. The employee returns two years later. Under the plan, prior service is restored if the employee repays the refund accumulated at 3% per year and meets the return deadline. The employee satisfies the deadline, repays the required amount, and earns four further years of service. At retirement, final-average salary is $72,000. Find the restored annual pension and its expected present value at commencement.
Assumptions. The refund accumulates annually at an effective 3% for two years. The pension valuation uses effective annual interest \(i=4\%\), annual-arrears payments, independent annual survival probability \(p=0.96\) (annual mortality \(q=0.04\)), and the geometric lifetime distribution stated above. Salary and pension are level after commencement.
Method: test the restoration condition, then calculate the benefit. The required refund repayment is
The employee repays this amount, so the six earlier years are restored under the stated hypothetical rule. Total credited service is
The annual pension is therefore
Using the factor derived above, the expected present value at commencement is \(12(\$10{,}800)=\$129{,}600\). The check is that each of the ten years contributes \(1.5\%\) of $72,000, or $1,080, for a total of $10,800 annually. The common mistake is to restore service while ignoring the repayment condition: without repayment, this plan’s stated rule would not permit restoration.
Worked Example: Returning After Pension Commencement
A hypothetical plan pays an annual pension of $9,600 to a retired member. The member returns to work after receiving two annual payments. The plan suspends the pension during active re-employment but does not require repayment of prior payments. It permits renewed membership, with a new annual pension accrual of 1.25% of final-average salary per year. The member works three years, retires again, and has final-average salary of $80,000. Find the annual pension after the second retirement and its expected present value at that date.
Assumptions. The two prior payments were made while the member was alive and are not recoverable under the stated rule. The original $9,600 pension resumes after the second retirement. New accrual uses only the three years of renewed service. For the value at the second retirement, use effective annual \(i=4\%\), annual-arrears payments, independent annual survival probability \(p=0.96\), annual mortality \(q=0.04\), and a geometric lifetime distribution. Assume no escalation.
Method: keep past payments, suspended payments, and new accrual separate. The new annual pension is
At the second retirement, the original pension resumes and the new benefit is added. Thus the annual amount is
The expected present value at the second retirement is \(12(\$12{,}600)=\$151{,}200\). The earlier two payments total \(2(\$9{,}600)=\$19{,}200\), but those payments occurred before the second retirement and are not subtracted from the pension under the stated rule. The pension was suspended during the three re-employment years, so no $9,600 payments are included for those years. The check is that the value includes only the $12,600 annual pension payable after the second retirement. A common error is to deduct the prior $19,200 from the resumed pension despite the plan expressly requiring no repayment or offset.
Worked Example: Return Outside the Restoration Window
A hypothetical plan credits 1.4% of salary for each year of service. A member leaves with a vested deferred pension after seven years, when the applicable final-average salary is $55,000. The plan permits restoration only if the member returns within five years. The member instead returns after six years and earns five new years of service. The plan preserves the earlier deferred pension separately and calculates the new benefit using the new period’s final-average salary of $82,000. Both benefits commence together at retirement. Find the combined annual pension and its expected present value.
Assumptions. The six-year absence makes the employee ineligible for restoration under this rule. The earlier benefit remains based on the stated $55,000 salary; the new benefit uses $82,000. At their common commencement date, value level annual-arrears payments using effective annual \(i=4\%\), independent annual survival probability \(p=0.96\), annual mortality \(q=0.04\), and the geometric lifetime distribution. Assume no escalation.
Method: calculate each preserved benefit on its own basis. The earlier deferred annual pension is
The new-period annual pension is
The combined annual pension is \(\$5{,}390+\$5{,}740=\$11{,}130\), and its expected present value is \(12(\$11{,}130)=\$133{,}560\). As a check, the two separate amounts sum to the combined annual benefit before valuation. Restoring all twelve years at the new salary would instead give \(0.014(12)(\$82{,}000)=\$13{,}776\), an annual overstatement of $2,646 and an expected present-value overstatement of \(12(\$2{,}646)=\$31{,}752\). The common mistake is to use total career service and current salary even though the employee returned outside the restoration window.
Common Mistakes and Exam-Relevant Checks
The difficult part is often not the multiplication in the pension formula; it is translating the plan rule into the correct service and payment history. A concise check before calculating is to write down the status at departure, the condition for restoration, the status on return, and the benefit treatment at the later retirement date.
- Assuming return restores service automatically. Check whether the plan sets a return deadline, repayment condition, election, or other requirement.
- Combining separate salary bases. If prior service is preserved as a deferred benefit, it may use its own salary basis rather than the salary at the later departure.
- Treating a refund like a pension payment. A refund may need repayment to restore service; pension installments already paid may instead be retained, suspended, or adjusted as specified.
- Counting payments during suspension. If the plan suspends a pension during active re-employment, those years are not payment years under that rule.
- Subtracting past benefits without authority. Prior payments are not automatically an offset against new accrual or a resumed pension.
- Using a valuation factor outside its assumptions. The factor \(12\) depends on the stated interest, survival, payment timing, and level-benefit assumptions.
A disciplined answer states the applicable hypothetical plan rule before applying a formula. It then identifies which service counts, whether an earlier benefit survives separately, and when each payment is due. This approach is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus, where benefit valuation depends on correctly translating plan provisions into cash flows.
Check Your Understanding
Use the plan rule and assumptions stated in each question; do not assume that service is restored unless the rule permits it.
- A hypothetical plan requires a contribution refund to be repaid with 2% annual compound interest before service can be restored. An employee received $5,000 three years ago and now meets the return deadline. What repayment is due, to the nearest cent? (Answer: $5,306.04)
- A plan restores prior service only within four years. A member returns after three years, satisfies all other conditions, and has five prior service years plus two new years. Under a formula of 1.6% of final-average salary per service year and a $70,000 final-average salary, what is the annual pension if all service is restored? (Answer: $7,840)
- A pensioner receives $7,500 annually. The plan suspends payments during re-employment, does not require repayment of earlier installments, and allows three new service years at 1% of an $80,000 salary per year. What is the annual pension when the original pension resumes after re-retirement? (Answer: $9,900)
- A plan preserves a deferred pension separately when the employee returns outside its restoration window. The earlier benefit is 1.2% times six years times a $50,000 salary; the new benefit is 1.2% times four years times a $75,000 salary. If both commence together, what is their combined annual amount? (Answer: $7,200)
- For a level annual pension payable in arrears while alive, assume effective annual interest \(i=4\%\), independent annual survival probability \(p=0.96\), and geometric future lifetime in whole years. What is the expected present value at commencement of a $5,250 annual pension? (Answer: $63,000)