Evaluate a pension service-credit buyback by calculating present value, net value, nominal benefits, and discounted break-even period using your assumptions.
Pension Buyback Formula
A service-credit purchase is evaluated by comparing its cost with the present value of the added pension.
Value at retirement:
PV_{retirement}=P*(1-((1+g)/(1+r))^n)/(r-g)
When r=g: PV_{retirement}=n*P/(1+r)
Discount through the waiting period:
PV_{today}=PV_{retirement}/(1+r)^w
Net present value:
NPV=PV_{today}-BuybackCost
Variables:
- P is first annual added pension
- g is the assumed annual compound COLA rate as a decimal; actual plan indexing may differ
- r is discount or alternative return
- n is a whole number of modeled annual payment periods (1–100)
- w is the deferral to the retirement valuation date (0–100 years); annual payments are modeled at w+1 through w+n
Value mode calculates present value and NPV from annual year-end payments, with P equal to 12 times the entered monthly increase at retirement. It is an annual approximation rather than actual monthly payment timing. Break-even is the first whole annual payment period whose discounted sum reaches the cost; zero cost is already recovered today.
The discount rate represents the alternative use of the money committed to the purchase.
Eligibility dates, retiree health benefits, and survivor effects are excluded unless reflected in the entered pension increase.
Simple Added Pension Needed
Ignoring COLA and discounting, monthly benefit needed to recover selected costs.
| Cost | 20 years | 25 years | 30 years |
|---|---|---|---|
| $25,000 | $104/month | $83/month | $69/month |
| $50,000 | $208/month | $167/month | $139/month |
| $75,000 | $313/month | $250/month | $208/month |
| $100,000 | $417/month | $333/month | $278/month |
Example Problems
Example 1: Calculate value.
A $50,000 purchase adds $400 per month at a retirement valuation date five years from today, for 25 modeled annual periods with an assumed 2% compound COLA and 5% discount rate. Under the annual year-end convention, payments occur at years 6 through 30; present value is about $64,628.31 and NPV is $14,628.31.
Example 2: Find break-even.
Discount each annual payment and identify the first period cumulative value reaches $50,000. In this example, it is the 18th annual payment period after retirement, or year 23 from today.
Frequently Asked Questions
What discount rate should I use?
The rate is an assumption about time value and opportunity cost, not a recommended investment return. Compare scenarios on a consistent nominal and tax basis. Use the plan’s actual cost and added-benefit quote; eligibility, caps, indexation and survivor rules can change the result.
How does longevity matter?
Longer receipt increases value; an earlier death reduces realized payments unless survivor benefits continue.
Should taxes be included?
The calculator compares pre-tax cash flows, so a tax-adjusted analysis may be appropriate.
