The exact grid by holding period, the logarithm shortcut for doing it in your head, and why the same 2.20x can be 17.1 or 23.9 per cent.
For a single investment and a single exit, IRR = MOIC1/years − 1. A 2.0× over five years is 14.9 per cent, over three years 26.0 per cent and over seven only 10.4 per cent. The formula only holds for one cash flow in and one out: return 0.80× early through a recap and the same 2.20× jumps from 17.1 to 23.9 per cent.
Worked in full in The Buyout Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
MOIC says how much money was made; IRR says how fast. Buyout investors quote both because neither is enough alone, and the conversion between them is the most common piece of mental arithmetic in private equity, from interview tests to investment committee papers. Here is the exact grid, the shortcut, and the case where the shortcut breaks.
IRR = MOIC1/n − 1, and back again, MOIC = (1 + IRR)n
In Excel: =B2^(1/B3)-1 with the MOIC in B2 and the years in B3. For uneven
holding periods with real dates use =XIRR(flows, dates) instead.
It works because a single outflow and a single inflow have one compound growth rate joining them, and that rate is the IRR by definition.
| MOIC | 3 years | 4 years | 5 years | 6 years | 7 years |
|---|---|---|---|---|---|
| 1.5× | 14.5% | 10.7% | 8.4% | 7.0% | 6.0% |
| 2.0× | 26.0% | 18.9% | 14.9% | 12.2% | 10.4% |
| 2.5× | 35.7% | 25.7% | 20.1% | 16.5% | 14.0% |
| 3.0× | 44.2% | 31.6% | 24.6% | 20.1% | 17.0% |
| 4.0× | 58.7% | 41.4% | 32.0% | 26.0% | 21.9% |
Read along a row and the cost of time is plain. A 2.0× drops from 14.9 to 12.2 per cent if the exit slips from year five to year six; to stay at 14.9 per cent the sixth year would have to lift the multiple to 2.30×. Read down a column and notice the bands most people remember: in five years, 2.0× is about 15 per cent, 2.5× about 20, and 3.0× about 25.
The reverse question, what multiple a target return needs, comes up just as often:
| Target IRR | 3 years | 4 years | 5 years | 6 years | 7 years |
|---|---|---|---|---|---|
| 15% | 1.52× | 1.75× | 2.01× | 2.31× | 2.66× |
| 20% | 1.73× | 2.07× | 2.49× | 2.99× | 3.58× |
A fund underwriting 20 per cent on a seven-year hold needs 3.58×. That is why long holds are so hard to underwrite to the same IRR, and why sponsors under IRR pressure sell early.
Use natural logarithms. Divide ln(MOIC) by the years to get a continuously compounded rate, then nudge it up. For 2.0× over five years: ln 2 = 0.693, divided by five is 13.9 per cent, and converting to an annual rate gives 14.9. The rule of 72 is the same idea for doubling only: 72 / 5 = 14.4 per cent, close enough in an interview. Five logarithms cover nearly every case: ln 1.5 = 0.41, ln 2 = 0.69, ln 2.5 = 0.92, ln 3 = 1.10, ln 4 = 1.39. For 3.0× over five years, 1.10 / 5 is 22.0 per cent, and the exact answer is 24.6: the higher the rate, the bigger the nudge.
The grid assumes the money comes back in one piece. Real deals pay dividends, recapitalise and sell in tranches. The MOIC ignores timing entirely; the IRR is dominated by it. Five deals with the same 2.20×:
| Cash flow shape | MOIC | IRR |
|---|---|---|
| Single exit in year 6 | 2.20× | 14.0% |
| Single exit in year 5 | 2.20× | 17.1% |
| Single exit in year 4 | 2.20× | 21.8% |
| Recap of 0.80× in year 2, then 1.40× in year 5 | 2.20× | 23.9% |
| 0.40× a year in years 1 to 3, then 1.00× in year 5 | 2.20× | 29.8% |
A recap that hands back 0.80× in year two adds 6.8 points of IRR without adding a cent of profit. Early distributions shorten the effective holding period, and IRR rewards that steeply. The flip side is that a recapitalised deal compounds less money for the rest of the hold, which is why limited partners read the MOIC beside the IRR rather than either one alone.
The worked case in The Buyout Investor returns 2.20× and 17.05 per cent over five years. The single-exit formula gives 17.08 per cent: close, because the case's cash essentially goes in once and comes out once. Add a dividend recap and the formula would no longer describe it.
Dividing the profit by the years. A 2.0× over five years is a gain of 100 per cent, and 100 / 5 = 20.0 per cent "a year" sounds right but is a simple average that ignores compounding: the true figure is 14.9. On a 3.0× over seven years the error widens to 28.6 against 17.0 per cent. The opposite mistake is quoting a deal's IRR without its holding period or its cash flow shape: a 29.8 per cent IRR built on early distributions and a 21.8 per cent IRR from a clean four-year exit are the same multiple of money.
To see how a deal-level IRR shrinks before it reaches the fund's investors, read why net IRR is lower than gross IRR. The deal behind the 2.20×, year by year, with returns by annual and by dated flows, is in the free workbook for this case on the companion page of The Buyout Investor.
About 24.6 per cent, assuming the money goes in once and comes back once: 3.0 to the power one fifth is 1.246. Over seven years the same 3.0x falls to 17.0 per cent, and over three years it rises to 44.2. Any dividends or partial exits along the way would push the IRR higher at the same multiple.
It depends entirely on the holding period: 1.73x over three years, 2.49x over five and 3.58x over seven, for a single exit. The required multiple roughly doubles between a three-year and a seven-year hold, which is why longer holds are hard to underwrite to the same IRR target.
Because IRR depends on when the cash comes back and MOIC does not. Two illustrative deals both returning 2.20x show 17.1 per cent if everything arrives at year five, and 23.9 per cent if 0.80x is returned through a recapitalisation in year two. The profit is identical; the second simply returns money sooner.
This article is one calculation from The Buyout Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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