MACH96
Internal Rate of Return
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MACH96 · Wealth Planning Series
MACH96
Wealth Planning Series · Vol. II

Internal Rate of Return

Annuity Income Valued Against Longevity
Prepared by MACH96
Understanding the Metric

The internal rate of return is the single annual rate that makes an income annuity's future payments worth exactly the premium paid for them today — the true yield of the income stream. Unlike a bond's fixed yield, an income annuity's IRR builds with longevity: the longer income is received, the higher the realized return. This report measures that return across three life-expectancy benchmarks — a median lifetime, an extended one, and the long-lived tail.

I · Client & Contract Inputs
Establish the Parameters
Enter the annuitant's age, the proposed contract, and the income design. The IRR is then evaluated at three longevity benchmarks — because the return an income annuity delivers is governed by how long the income is received.
A
Primary Client
B
Joint Annuitant
C
The Annuity Contract
Value the payout % is applied to. Defaults to premium if equal.
Annual income = payout × income base at start.
Equal to current age = immediate income.
Set to Yes to model base roll-up during deferral and an annual step-up to income.
Annual growth of the base before income begins. Use 0 if the base above is already the value at the start age.
Annual step-up applied to each year's income.
D
Advisor & Report
Contract Parameters
First-Year Income
—
—
IRR at Median Longevity
—
—
Break-Even Age
—
—
II · Longevity Projection
Life Expectancy & Survival
Per the SSA Period Life Table — Social Security Administration, 2022 mortality data (2025 Trustees Report). These survival benchmarks define how long the annuity's income is expected to be received.
Survival Probability Curve
Longevity Milestones
III · Income Structure
How the Contract Pays
The premium is committed today; income begins at the elected start age and continues for life. The roll-up grows the base during deferral; the payout factor converts it into guaranteed annual income.
Contract Mechanics
Recovery & Hurdle
IV · Internal Rate of Return
Return Built by Longevity
The IRR equates the present value of lifetime income to the premium paid. It is deeply negative at an early death, crosses zero once cumulative income recovers the premium, and climbs the longer income is received — which is precisely the longevity risk an income annuity is designed to hedge.
IRR by Age at Death · The Longevity Build Curve
Cumulative Income vs. Premium · Premium Recovery
Plan Interpretation
V · Year-by-Year Detail
Income, Cumulative Income & IRR
For each contract year: the income paid, the cumulative income received, and the IRR realized if income were to stop that year. The IRR is negative until cumulative income recovers the premium — the break-even year, highlighted below.
Math Behind the Number
Valuation Methodology
Income Base at Start
—
After roll-up during deferral
First-Year Income
—
Payout factor × income base
Premium Recovery Age
—
Cumulative income recovers premium
Longevity-Tail IRR
—
If among the longest-lived 5%
The internal rate of return is the discount rate at which the present value of the income stream equals the initial premium. Income is modeled as an annual payment beginning at the income-start age and continuing for life; the income base grows at the roll-up rate during any deferral, and each year's payment is stepped up by the increasing-income factor. As with the standard industry calculation, the IRR carries no death benefit — it stays negative until cumulative income recovers the premium (the break-even age), then climbs the longer income is received. Returns are shown at three survival horizons drawn from the SSA Period Life Table: the median lifetime, an extended (25th-percentile) life, and the longevity-tail (longest-lived 5%). Joint contracts assume income continues to the last surviving annuitant. This illustration excludes contract fees, rider charges, surrender penalties, and taxes, and is not a guarantee of future results.
Sources & Methodology
Life expectancy and survival probabilities derive from the Social Security Administration Period Life Table (2022 mortality experience, as published in the 2025 OASDI Trustees Report). The internal rate of return is computed by solving for the discount rate that sets the net present value of the income stream, net of the initial premium, to zero, with income credited in arrears (at year-end) following the standard convention. No death benefit is assumed, so the IRR is negative until cumulative income recovers the premium. Returns are evaluated at the 50th-, 25th-, and 5th-percentile survival horizons drawn from that table. Joint-and-survivor contracts assume income continues to the last surviving annuitant, the standard actuarial convention.
Disclosure
This tool produces illustrative estimates based on published actuarial data and the contract assumptions entered. It is not a guarantee of future results and does not reflect contract fees, rider charges, surrender periods, or taxation. IRR is one of several measures used to evaluate an income annuity and does not capture liquidity, guarantees, or other product features. For implementation, consult a MACH96 advisor.