Definition
Internal rate of return is the discount rate at which the net present value of a stream of cash flows equals zero, expressed as an annualized rate.
Why it matters
Individuals and professionals often want to summarize a stream of cash flows as a single rate of return, both for internal reasoning and for comparison to alternative uses of capital. Internal rate of return provides that summary figure by solving for the rate that makes the discounted cash flows balance. It is the reciprocal question to net present value: rather than fixing a discount rate and computing the net present value, internal rate of return fixes a net present value of zero and solves for the discount rate.
How it works
Internal rate of return is found by iterating on the discount rate until the sum of discounted cash flows equals zero. Consider the same $500,000 premium and $30,000 annual income over 20 years as in the net present value example. At a 3 percent discount rate, the net present value is negative. At progressively lower rates, the discounted income stream grows in value; at approximately 2.7 percent, the discounted income stream just balances the premium, so the internal rate of return of the arrangement is approximately 2.7 percent under those assumptions. Interpretation requires the same caveats that apply to net present value: the figure reflects only the cash flows that have been included, and a lifetime income arrangement's actual receipt period varies with survival, which a fixed-period calculation does not represent. Actuarial internal rate of return, which weights each receipt by the probability of survival to that date, is the more faithful figure for lifetime income arrangements.
In practice
For an individual comparing a lifetime income arrangement to alternative uses of capital, internal rate of return provides a summary rate that can be set alongside expected returns from investment portfolios or debt paydown. The comparison is not directly interpretable, however, because a lifetime income arrangement provides longevity protection that a portfolio does not, and the internal rate of return figure does not price that protection. A professional working with the individual will typically produce the figure only with an accompanying note about what it does and does not capture, and often alongside an actuarial version that incorporates survival weighting. Individuals should be cautious about marketing that emphasizes an internal rate of return figure for a lifetime income arrangement without survival weighting; the resulting figure can be misleading in either direction depending on receipt-period assumptions.
Related terms
- Net present value
- Present value
- Actuarial present value
- Discount rate
- Break-even analysis (annuity context)
- Sharpe ratio
- Cost of income