MathIsimple
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intermediate

IRR: The Investment Metric Everyone Cites and Few Understand

Why internal rate of return is useful, when it lies, and why a 40% IRR can be worth less than a 15% IRR.

March 24, 2026
Finance
Investing
Real Estate
Business Math

Everyone Nods When Someone Says "22% IRR"

Sit in a real estate pitch. Private equity deck. Any investment meeting. Someone will say the IRR is 22%, or 18%, or 31%. Everyone writes it down.

Ask five of those people afterward what IRR actually measures. You'll get five different answers — and at least two of them will be confidently wrong.

IRR is the most cited metric in finance and one of the least understood. Including by the people citing it.

What It Actually Is

IRR is the discount rate that makes the Net Present Value of all your cash flows equal zero.

That definition is useless until you understand NPV. So: money today is worth more than money later. If you can earn 8% elsewhere, then $1 arriving one year from now is only worth \\frac{\\$1}{1.08} \\approx \\$0.926 in today's terms. NPV applies that logic to every cash flow across the entire investment.

NPV Formula

NPV=t=0nCt(1+r)tNPV = \sum_{t=0}^{n} \frac{C_t}{(1+r)^t}

where CtC_t = cash flow at time t, rr = discount rate

IRR asks: what value of r makes NPV = 0? That rate is your internal rate of return. It's the breakeven discount rate — the return the investment is implicitly earning.

A Concrete Example

You invest $200,000 today. The deal pays you $12,000/year for 4 years, then $252,000 in year 5 (cash flow + principal returned).

YearCash FlowPV at 13.1%
0−$200,000−$200,000
1$12,000$10,609
2$12,000$9,380
3$12,000$8,293
4$12,000$7,332
5$252,000$136,386 (approx)

At a discount rate of ~13.1%, the present values sum to roughly $200,000 — NPV ≈ 0. So IRR = 13.1%.

You can't solve this algebraically. There's no formula that spits out the answer. Every calculator and spreadsheet solves it by iteration — guessing and refining until NPV gets close enough to zero.

Three Ways IRR Can Mislead You

IRR has a few genuine blind spots. Not hypothetical edge cases — things that come up in real deals.

1. It ignores deal size

A 40% IRR on a $10,000 investment makes you $4,000. A 15% IRR on a $10,000,000 investment makes you $1,500,000. IRR says the first deal is better. Your bank account disagrees.

This is why serious investors look at both IRR (efficiency) and NPV (dollars). IRR ranks deals. NPV measures wealth created.

2. Multiple IRRs can exist

If your cash flows change sign more than once — you invest, get some back, invest more, then get paid out — the math can produce two valid IRR solutions. Most spreadsheets just show you one. Which one depends on the starting guess.

Real example: a mining project that requires a large cleanup cost at the end. Cash flows go negative → positive → negative. Can produce two valid IRRs. Neither one is "the" answer.

3. It assumes reinvestment at the same rate

IRR implicitly assumes that every cash flow you receive gets reinvested at the IRR itself. A deal with 25% IRR assumes you can redeploy those interim distributions at 25% too. Usually unrealistic.

MIRR (Modified IRR) fixes this by letting you specify a separate reinvestment rate. Less commonly used, but more honest.

How IRR Compares to the Other Metrics

MetricWhat it measuresWhat it misses
IRRAnnualized return rate, time-weightedDeal size, reinvestment rate
NPVTotal dollars created above your hurdle rateReturn efficiency (a huge NPV could come from a mediocre rate on a giant deal)
ROITotal return as % of costTime — 5% ROI over 1 year is completely different from 5% over 10 years
Cash-on-CashAnnual cash income ÷ cash investedAppreciation, loan paydown — anything that isn't cash in hand

Smart investors use all four. IRR for ranking. NPV for sizing the prize. Cash-on-cash for "does this thing pay my bills while I hold it." ROI for back-of-napkin comparisons.

Common Questions

What's a "good" IRR?

Depends entirely on the asset class and risk. Real estate private equity typically targets 15–25%. Venture capital expects 25%+ because most deals fail. S&P 500 historically returns ~10% annualized. A "good" IRR is one that exceeds your hurdle rate — the minimum return that justifies the risk and illiquidity of not putting money in the index fund instead.

Why can't you calculate IRR by hand?

The IRR equation is a polynomial. For a 5-year investment, it's a 5th-degree polynomial. The Abel-Ruffini theorem proves there's no general algebraic solution for polynomials of degree 5 or higher. So every tool — Excel, calculators, Python — uses numerical methods (Newton-Raphson iteration) to converge on an answer.

IRR vs. CAGR — what's the difference?

CAGR works for a single investment with one entry and one exit — no intermediate cash flows. IRR handles multiple cash flows at different times. For a buy-and-hold with no dividends, they give the same answer. For anything with distributions along the way, use IRR.

Calculate IRR on Your Investment

Enter your initial investment and cash flows by year. The calculator handles the iteration.

*IRR assumes reinvestment at the same rate. Use MIRR for more conservative projections.

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