The Formula
IRR is the discount rate that sets the net present value of every cash flow in the hold to zero.
0 = CF₀ + CF₁/(1 + IRR)¹ + CF₂/(1 + IRR)² + ... + CFₙ/(1 + IRR)ⁿ
CF₀ is the cash invested at purchase, entered as a negative number. CF₁ through CFₙ are the cash flows in each year after the mortgage, and the final year also carries the net sale proceeds. There is no closed-form solution. A spreadsheet or calculator tries rates until the discounted inflows exactly offset the money that went in.
The Duplex, Worked
I run the same $425,000 duplex across this site so the numbers agree wherever a reader lands. It earns $26,220 of NOI. With 20% down, the buyer puts in $85,000 and borrows $340,000 at 7% over 30 years, which costs $27,144 a year in principal and interest.
Annual cash flow = $26,220 − $27,144 = −$924
The owner feeds the property $924 a year. Now assume a 7-year hold, 3% annual appreciation, and 7% selling costs for commission and transfer taxes.
Sale price = $425,000 × 1.03⁷ = $522,700
Net of costs = $522,700 × (1 − 7%) = $486,111
Loan payoff = balance after 84 payments = $309,900
Net proceeds = $486,111 − $309,900 = $176,211
The cash flow row, year 0 through year 7:
Year 0 −85,000
Years 1 to 6 −924 each
Year 7 175,287 (−924 + 176,211)
Solve for the rate that zeroes that row and IRR comes out at 10.17%, which rounds to 10.2%. Total cash returned is $176,211 − (7 × $924) = $169,743, against $85,000 invested.
The Trap: The Sale Is the Whole Return
Look at where the $169,743 comes from. Seven years of operations lose $6,468. The sale produces $176,211. More than all of the return arrives in a single year, and that year's number is a forecast of a price nobody will set until year seven.
That makes the 10.2% very sensitive to the one input nobody can measure today. Hold everything else constant and change only appreciation:
| Appreciation | Sale price | Net proceeds | IRR |
|---|---|---|---|
| 3% a year | $522,700 | $176,211 | 10.2% |
| 2% a year | $488,200 | $144,126 | 7.0% |
| 0% | $425,000 | $85,350 | −1.0% |
A one-point change in the growth assumption moves IRR by more than three points. At flat prices the deal returns $78,882 on $85,000 invested and IRR goes negative. On this duplex, IRR is less a measurement of the property than a forecast of the exit price, restated as a rate.
Why Timing Changes the Answer
The same total dollars produce very different IRRs depending on when they arrive. Take the duplex's $169,743 of total return on $85,000 invested and move it around:
| When the $169,743 arrives | Equity multiple | IRR |
|---|---|---|
| All in year 7 | 2.00x | 10.4% |
| All in year 5 | 2.00x | 14.8% |
| $24,249 a year, years 1 to 7 | 2.00x | 21.0% |
The profit is identical in all three rows. Only the timing changes, and IRR roughly doubles between the first row and the third, because money received earlier is discounted less. That is the whole reason to run IRR instead of a simple total return: a deal that pays along the way and a deal that pays at the end can show the same profit and still be very different investments.
The duplex sits close to the first row, which is the least favorable shape for IRR. Its cash flows are slightly negative until the sale, so almost nothing arrives early.
How to Calculate It in a Spreadsheet
Put the cash flow row in consecutive cells, year 0 first, with the investment as a negative number. For the duplex, cells A1 through H1 hold:
−85000 −924 −924 −924 −924 −924 −924 175287
Then:
=IRR(A1:H1) → 10.17%
=IRR assumes the cash flows are evenly spaced, one period apart. When they aren't, =XIRR takes a second range of actual dates and returns an annualized rate. That matters for a purchase that closes mid-year, a capital call in month 14, or a refinance that lands between annual periods.
Rents actually arrive monthly, not in one lump at year-end. Running the duplex monthly ($77 a month of negative cash flow for 84 months, sale at month 84) gives an annualized IRR of 10.13% against 10.17% on annual periods. On a deal with small interim cash flows the difference is noise. On a deal with large monthly distributions it is worth modeling at the monthly level.
Levered vs Unlevered IRR
Everything above is levered IRR: the return on the buyer's $85,000 after the mortgage. Unlevered IRR runs the same property as an all-cash purchase, so it describes the building rather than the financing.
Year 0 −425,000
Years 1 to 6 26,220 each (NOI, no debt service)
Year 7 512,331 (26,220 + 486,111 net sale)
Unlevered IRR on the duplex is 7.8%, with an equity multiple of 1.58x. Leverage lifts that to 10.2% levered, because the property's return beats the 7% cost of the loan once appreciation is counted. The same leverage is why the levered version is so exposed to the sale: at 0% appreciation the unlevered deal still earns its NOI every year, while the levered deal loses money.
Comparing two properties on levered IRR mixes the buildings with the loans. Unlevered IRR separates them, and the gap between the two numbers shows how much of the return the debt is producing.
Equity Multiple Belongs Next to IRR
Equity multiple is total cash returned divided by cash invested, with no time weighting.
Equity Multiple = $169,743 ÷ $85,000 = 2.00x
IRR gives the rate. Multiple gives the size. They answer different questions, and the duplex shows why both are needed. Run the same assumptions over three hold periods:
| Hold | Sale price | Loan payoff | Equity multiple | IRR |
|---|---|---|---|---|
| 5 years | $492,700 | $320,000 | 1.57x | 9.3% |
| 7 years | $522,700 | $309,900 | 2.00x | 10.2% |
| 10 years | $571,200 | $291,800 | 2.71x | 10.2% |
Going from 7 to 10 years barely moves IRR, while the multiple rises from 2.00x to 2.71x. On IRR alone the two holds look the same. On dollars, the 10-year hold returns $230,176 against $169,743. The reverse case is also common: a fast flip can post a high IRR on a small multiple, earning a high rate on money that was only at work briefly.
The Reinvestment Assumption and MIRR
IRR carries a hidden assumption: every interim cash flow is treated as if it could be reinvested at the IRR itself. On a deal that pays out early, that assumption does a lot of work.
MIRR replaces it with rates I choose. Negative cash flows are discounted at a finance rate, positive ones are compounded forward at a reinvestment rate, and the result is solved as a single rate. In a spreadsheet:
=MIRR(values, finance_rate, reinvest_rate)
On the duplex, the assumption barely matters. There is almost nothing to reinvest until the sale, and MIRR at a 7% finance rate and 7% reinvestment rate comes out at 10.1%, next to the 10.2% IRR.
On the even-payout row from the timing table, it matters a great deal. That stream shows a 21.0% IRR, which implies each $24,249 payment earns 21.0% after it arrives. If the realistic place to park those payments earns 4%, MIRR at a 7% finance rate and 4% reinvestment rate is 12.3%. The 4% is my assumption for the example, not a market figure. The point is the gap: the higher the IRR and the earlier the cash arrives, the more of the stated rate depends on reinvestment the investor may not actually get.
Common Mistakes
Leaving out transaction costs. Selling costs come straight out of the one cash flow that drives the result. Drop the 7% selling costs from the duplex and IRR rises from 10.2% to 13.3%. The purchase side counts too. If the buyer also pays $8,500 in closing costs at purchase, cash invested becomes $93,500 and IRR falls to 8.7%. Loan fees, title, inspections, and any capital spent before the first rent check all belong in year 0.
An exit price the rent doesn't support. The $522,700 sale price assumes 3% annual growth. If NOI stays at $26,220, that price is a 5.0% cap rate ($26,220 ÷ $522,700), against the 6.2% the buyer paid. Holding the cap rate at 6.2% supports that price only if NOI also grows about 3% a year, to roughly $32,250 by year 7. If rent stalls and the next buyer prices the duplex at the same 6.2% cap on $26,220, the sale comes in near $422,900 and IRR falls to −1.4%. Every IRR projection contains an exit cap rate, whether or not the model writes it down. Checking what cap rate the assumed sale price implies is the quickest test of whether the forecast holds together.
Mistiming the cash flows. Putting the sale in the wrong year, spreading a year-0 renovation across year 1, or using =IRR on flows that aren't evenly spaced all change the answer. The timing table above shows how much. A two-year shift in the same dollars moved IRR from 10.4% to 14.8%.
Ranking deals on IRR alone. Two deals with the same IRR can return very different dollars, as the hold-period table shows. IRR also breaks down when cash flows change sign more than once, such as a deal with a large capital call midway through the hold. That stream can have more than one mathematically valid IRR, and the single number stops meaning what it appears to mean.
FAQ
What does IRR measure in real estate?
The annual rate at which the present value of every cash flow, including the purchase and the sale, nets to zero. On the duplex, $85,000 in, $924 a year out for seven years, and $176,211 of net sale proceeds in year 7 produce an IRR of 10.2%.
What is the difference between IRR and cash-on-cash return?
Cash-on-cash is one year of cash flow divided by cash invested, and it ignores the sale. IRR covers the whole hold including the sale and weights each cash flow by when it arrives. The duplex has a negative cash-on-cash return and a positive IRR, because the entire return is in the sale.
What is a good IRR for a rental property?
The number only means something alongside the hold period, the leverage, and how much of it depends on the exit price. A 10.2% IRR built from a forecast sale and a 10.2% IRR built from years of collected rent carry very different risk, even though they read the same.
Why is IRR higher than the property's cap rate?
Two things push it up on the duplex: appreciation in the sale price, and leverage. Unlevered, the deal earns 7.8%. With 80% financing at 7%, it earns 10.2%. The same leverage turns the 0% appreciation case negative.
Can IRR be negative?
Yes, whenever total cash returned is less than cash invested. The duplex at flat prices returns $78,882 on $85,000 and shows an IRR of −1.0%.
Related Reading
- Cash-on-Cash Return Guide: the one-year cash metric IRR extends across the full hold
- Cap Rate Explained: the unlevered yield, and the exit cap rate hiding inside every sale-price assumption
- Cap Rate vs Cash-on-Cash Return: how the property's return and the investor's return diverge once debt enters
A 10.2% IRR on this duplex says the deal works if the price grows 3% a year. The same spreadsheet at 2% says 7.0%. Below about 0.2% a year, a sale near $431,600, the deal returns less than the $85,000 that went in. IRR is precise about timing and silent about whether the forecast is right, which makes the break-even growth rate a more honest number to carry into the decision than the IRR itself.
Keep reading
- 1031 Exchange Rules: Timelines, Like-Kind Property and What Gets DeferredHow a 1031 exchange defers capital gains on a property sale: the like-kind and equal-value rules, the 45 and 180 day deadlines, and where exchanges fail.
- Break-Even Occupancy: How Empty a Rental Can Get Before It Loses MoneyThe break-even occupancy and break-even rent formulas for a rental property, worked with real numbers, and what the result says about risk and financing.
- The BRRRR Method: Buy, Rehab, Rent, Refinance, Repeat, With the MathHow the BRRRR method works step by step, how much cash the refinance actually returns, and where the numbers break when the appraisal comes in low.
