Pension Lump Sum Vs Annuity Calculator

Purpose and model boundary

Use this calculator to compare a pension income stream with a lump-sum offer. It converts the pension, any annual increase and any survivor payments to a present value, then shows which option is worth more under your assumptions and the discount rate at which they are equal.

This is a present-value comparison, not a recommendation. It does not model mortality, pension-plan funding or credit risk, insurance protection, taxes, or the investments you would choose after taking a lump sum.

Inputs and units

Governing relationships

For annual pension amount A, escalation g, discount rate r and term n, present value is A (1 - ((1 + g)/(1 + r))^n) / (r - g). When r equals g, the calculator uses the limiting value A n / (1 + r) instead of dividing by zero. A survivor benefit is valued with the same relationship and discounted back across the main pension term. The break-even discount rate is found by repeatedly narrowing the rate interval until pension present value equals the lump sum.

Calculation sequence

1. Read the monthly pension, the number of years of payments, any escalation, the survivor share and survivor years, the lump sum offered and the discount rate.
2. Annualise the monthly pension and discount the main payment stream at the discount rate, using the escalating form when an escalation is given and the limiting form when the escalation equals the discount rate.
3. Value the survivor leg on the survivor share over the survivor years, then discount it back across the main payment period.
4. Add the two legs to get the present value of the pension.
5. Subtract the lump sum to get the advantage, and report which option is worth more.
6. Solve for the discount rate at which the present value equals the lump sum, by bisection between zero and one hundred percent.
7. Evaluate the status in the order given below.

Outputs and interpretation

The headline figures are Advantage Of Lump Sum, Better Option and Break Even Discount Rate. Everything else is supporting detail for those.

Validation and status logic

The workbook evaluates status in this order, and the first condition that is true wins. The status text below is the exact wording the workbook returns; angle brackets mark a value substituted into the message at calculation time.

Assumptions and limitations

• The discount rate is the return you believe you could earn on the lump sum. The comparison is only as good as that assumption.
• Payments are certain for the stated number of years. Mortality is not modelled, so a pension is neither shortened by death nor lengthened by longevity.
• Scheme solvency, any insurance guarantee, and the tax treatment of either option are outside the model.
• The survivor benefit is a fixed share paid for a fixed number of years after the main payment period ends.

Restrictions and non-computing states

The monthly pension and the lump sum must both be greater than zero, because the comparison needs two sides. The years of payments must be at least one. The discount rate, escalation, survivor share and survivor years are held within their published ranges. Where the pension is worth less than the lump sum at every non-negative rate there is no break-even rate to report, and the workbook says so rather than returning a misleading number.

Errors and warnings

A rejected entry means a value fell outside the published input rules, and no calculation was attempted. Workbook NOT VALID means the model ran and could not produce a meaningful answer, so the results are withheld. Workbook CHECK means the numbers stand but a condition is worth reading before you rely on them. A connection or calculation-service failure is an availability problem, not a finding of any kind, and never means zero.

The present-value and break-even relationships are standard financial mathematics and are documented with a worked derivation in the delivered audit. General context on the tax treatment of pension and annuity income is available from the Internal Revenue Service in Publication 575, Pension and Annuity Income. The workbook does not reproduce a statutory table, a mortality table, or any scheme's terms.

This model is arithmetic. It is not financial, tax, investment or retirement advice, and it is not a recommendation to save, invest, withdraw, claim or accept any amount. Decisions about retirement funding should be taken with a qualified professional who knows your circumstances.