Compare a lump-sum offer at pension commencement with monthly payments through a chosen planning age, or calculate an equivalent value using COLA and discount assumptions. This finite-horizon estimate does not price lifetime longevity insurance.
Pension Lump Sum vs Monthly Payment Formula
The monthly pension is converted to a value at pension commencement by discounting each future month-end payment. The first payment is one month after commencement; COLA first applies to payment 13 and then after each full year.
For the default monthly payment model, sum the discounted payments from month 1 through month N:
PV = sum of payment(m)/(1+r)^(m/12) payment(m) = M*(1+g)^floor((m-1)/12)
Nominal payments through the chosen planning age are:
Total = sum of payment(m), m = 1 to N
Variables:
- M is the initial monthly pension payment
- g is annual COLA expressed as a decimal
- r is the annual effective discount rate expressed as a decimal
- N is the whole number of months between the start and planning end ages
Comparison mode measures the pension’s present value against an offer payable at pension commencement. Equivalent-lump mode returns that present value. The optional annual approximation groups 12 payments at each year end and uses PV = 12M × [1 − ((1+g)/(1+r))^n] / (r−g), where n is whole years. When r=g, PV = 12M × n/(1+r).
A higher discount rate lowers the value assigned to distant payments.
Test several planning ages because longevity is a major driver of value.
Effect of Assumptions on Pension Value
Longer payment periods and larger COLAs increase value; higher discount rates reduce it.
| Monthly pension | Years | COLA | Discount rate | Monthly-model value |
|---|---|---|---|---|
| $3,500 | 25 | 0% | 3% | $741,354.63 |
| $3,500 | 25 | 0% | 5% | $605,391.60 |
| $3,500 | 25 | 2% | 5% | $738,128.35 |
| $3,500 | 30 | 2% | 5% | $831,721.26 |
Example Problems
Example 1: Compare an offer.
Compare a $650,000 offer at age 65 with $3,500 per month for the following 25 years, a 2 percent annual COLA, and a 5 percent annual effective discount rate. The month-end model gives $738,128.35 present value, $88,128.35 above the offer. Nominal payments total $1,345,272.59; the offer is reached at payment 164 (13 years 8 months), ignoring discounting.
Example 2: Find an equivalent lump sum.
Select Equivalent lump sum for a pension to calculate the present value of the same stream without entering an offer.
Frequently Asked Questions
What discount rate should I use?
Use a rate consistent with the risk and investment alternative, and test a range rather than one optimistic number.
Does higher present value settle the decision?
No. An actual lifetime pension can provide longevity protection beyond a chosen planning age, while a lump sum offers flexibility and possible inheritance. This estimate omits mortality probabilities and does not reproduce an actual plan quotation. Plan terms, prescribed valuation factors, taxes, guarantees, survivor benefits and investment risk matter.
How are survivor benefits handled?
This calculator models one payment stream. Use a survivor-benefit calculator for joint elections.
