What MIRR fixes about the internal rate of return
Plain IRR carries a hidden assumption. The rate that discounts your cash flows to zero is arithmetically the same as the rate at which each interim inflow must be reinvested for the project to deliver that return over its whole life. A project showing a 25.75% IRR has quietly assumed that every dollar it hands back can be put straight to work at 25.75% until the final period.
That assumption is almost never available. If you could reliably earn 25.75% on spare cash, your cost of capital would be 25.75% and the project would not clear it. MIRR removes the circularity by making the reinvestment rate an input you have to defend — typically your cost of capital, which is what a firm actually earns on marginal cash.
MIRR also removes a second defect. Because the modified calculation collapses the whole stream into one outflow at period zero and one inflow at period n, there is only ever one sign change left. A stream with two IRRs has exactly one MIRR. This makes MIRR the right measure for projects with mid-life capital calls, environmental remediation costs, or staged construction — the cases where plain IRR stops being a number you can compare to a hurdle rate.
What MIRR does not do is replace net present value. It is still a rate, still scale-free, and still cannot rank projects of different size. Use it as a better-behaved version of the headline percentage, not as the decision.
The formula, one leg at a time
MIRR is built from two separate present-value calculations that meet at a single ratio.
The inflow leg (numerator). Take every period with a positive net cash flow and compound it forward to the final period at the reinvestment rate k. A flow in period t has n − t periods left to grow, so it is multiplied by (1 + k)n−t. The last period's flow is multiplied by (1 + k)0 = 1 because it arrives at the finish line. The sum is the terminal value: the single lump the project is worth at period n if you actually reinvest as stated.
The outflow leg (denominator). Take the initial investment plus every later period with a negative net cash flow, and discount them back to period zero at the finance rate f. A negative flow in period t is divided by (1 + f)t. The outlay itself sits at period 0 and is not discounted. The sum is the total capital the project requires, stated in today's money.
The ratio and the root. Dividing the terminal value by the present value of the outflows gives the total multiple your money grows by over n periods. Taking the n-th root converts that multiple into a rate per period, and subtracting one turns the growth factor into a return. This is the same operation as a compound annual growth rate — MIRR is a CAGR between two synthetic end points that you built out of the messy stream in between.
Two rates, two directions, two jobs. The reinvestment rate answers "what do I earn on money the project gives me?" The finance rate answers "what do I pay for money the project asks me for?" When every period after the outlay is positive, the finance rate has nothing to act on and changing it does not move the answer at all.
Worked example: a $100,000 project reinvesting at 10%
Take the same packaging line used across these capital-budgeting tools: $100,000 up front, then $30,000, $35,000, $40,000, $45,000 and $50,000 over five years. Reinvest spare cash at 10%; the finance rate is 8%.
- Compound year 1 forward four periods. 1.104 = 1.4641. $30,000 × 1.4641 = $43,923.
- Year 2, three periods. 1.103 = 1.331. $35,000 × 1.331 = $46,585.
- Year 3, two periods. 1.102 = 1.21. $40,000 × 1.21 = $48,400.
- Year 4, one period. $45,000 × 1.10 = $49,500.
- Year 5, no compounding. $50,000 × 1 = $50,000.
- Add them. 43,923 + 46,585 + 48,400 + 49,500 + 50,000 = $238,408 terminal value.
- Value the outflow leg. The only outflow is the $100,000 at period zero, so its present value is $100,000 and the 8% finance rate is inert.
- Form the ratio. $238,408 ÷ $100,000 = 2.38408. The money multiplies 2.384 times over five years.
- Take the fifth root. 2.384080.2 = 1.189773.
- Subtract one. MIRR = 18.9773% per year.
Compare that to the plain IRR of the same stream, 25.7516%. The 6.77-percentage-point gap is the entire cost of IRR's reinvestment assumption on this project. Nothing about the cash flows changed; only the honesty of the assumption about what happens to cash after it arrives.
Now check the identity. Set the reinvestment rate to 25.7516% and recompute: the terminal value becomes $100,000 × 1.2575165 = $314,462, and 3.144620.2 − 1 = 25.7516%. MIRR collapses onto IRR exactly when you assume reinvestment at the IRR — which is the proof that IRR was making that assumption all along.
How to read the MIRR you get
Compare MIRR to the same hurdle rate you would use for IRR: the risk-adjusted return you require on capital of this type. The accept test is unchanged — beat the hurdle and the project adds value — but the number you are testing no longer contains an assumption you cannot honour.
The gap to IRR tells you how forecast-dependent the headline rate was. A small gap means the project returns most of its cash late, so there is little to reinvest and the assumption barely matters. A large gap means the project front-loads its cash and the IRR was leaning heavily on reinvestment. Two things widen it: cash arriving early, which leaves more of it sitting in the reinvestment assumption for longer, and an IRR far above the rate you entered. A project whose entire return arrives in the final period has a gap of exactly zero, because there is nothing to reinvest.
Compare MIRR against the reinvestment rate you entered, not just against your hurdle. MIRR is not bounded below by that rate — a project that loses money returns a MIRR well under it, and can be negative. But when a MIRR lands only just above the reinvestment rate, you are being paid almost nothing for taking project risk instead of simply earning that rate on the cash. That comparison is the one worth making out loud in an investment committee.
Do not compare MIRRs computed with different reinvestment rates. The rate is an input, and raising it raises every MIRR. Fix one reinvestment rate across your whole project set — normally the firm's cost of capital — and only then rank.
Length still matters. Like IRR, MIRR is a rate per period, so a five-year 19% and a two-year 19% are only comparable if you can redeploy the two-year project's capital at 19% for the remaining three years. If you cannot, extend both to a common horizon or fall back on NPV.
Read MIRR next to the discounted payback period for exposure and the profitability index for value per dollar committed. Together those three cover rate, time and scale.
MIRR of the worked example at different reinvestment rates
| Reinvestment rate | Terminal value at year 5 | Multiple | MIRR |
|---|---|---|---|
| 0% | $200,000 | 2.0000 | 14.8698% |
| 5% | $218,332 | 2.1833 | 16.9024% |
| 10% | $238,408 | 2.3841 | 18.9773% |
| 15% | $260,351 | 2.6035 | 21.0910% |
| 20% | $284,288 | 2.8429 | 23.2400% |
| 25.7516% | $314,462 | 3.1446 | 25.7516% |
The last row is the plain IRR of the same stream. MIRR equals IRR precisely when the reinvestment rate is set to the IRR, and every row above it shows what the honest rate looks like at a reinvestment assumption you could actually achieve.
Which reinvestment rate to use
Use your after-tax weighted average cost of capital. That is the rate at which the firm's marginal dollar of cash actually earns — pay down debt, buy back stock, or fund the next project at the margin, and the return converges on the cost of capital. Build it with the WACC calculator.
Two variants appear in practice. Some analysts set the reinvestment rate to the cost of capital and the finance rate to the firm's actual borrowing rate, which is the arrangement this calculator defaults to. Others set both to the cost of capital, which makes MIRR a pure restatement of NPV in rate form. Both are defensible; state which you used. Setting the reinvestment rate to a project-specific target return is not defensible — it reintroduces exactly the circularity MIRR exists to remove.
Mistakes that make MIRR misleading
- Setting the reinvestment rate to the IRR. This reproduces the IRR exactly and tells you nothing. The whole point is to substitute a rate you can actually earn.
- Comparing projects computed at different reinvestment rates. The rate is an assumption, not a property of the project. Fix it firm-wide before ranking anything.
- Putting the outlay in the cash flow list. Enter it in the Initial investment field. A negative first entry in the list is treated as a period-1 outflow and discounted one period at the finance rate, which changes the denominator.
- Expecting the finance rate to matter when it cannot. With no negative periods after t = 0 the outflow leg is just the outlay, so the finance rate is inert. If moving it does nothing, that is correct behaviour, not a bug.
- Reading MIRR as a value measure. It is scale-free. A 40% MIRR on $5,000 loses to a 14% MIRR on $5m. Rank by NPV, or by profitability index under a budget constraint.
- Mixing period lengths. Every entry must cover the same span, because the exponent n − t counts periods, not calendar time. Convert quarterly and annual flows to a common period first.
- Using pre-tax cash flows. MIRR needs incremental after-tax free cash flow, and the reinvestment and finance rates must be stated after tax to match.
MIRR against the other rate measures
There are three ways to turn a cash flow stream into a single rate, and they differ only in what they assume about the cash in between.
IRR assumes reinvestment at the IRR itself. It needs no extra inputs, which is why it is popular, and it can produce several answers or none. It is safe for conventional streams evaluated against a fixed hurdle.
MIRR assumes reinvestment at a rate you supply and financing at another rate you supply. It always produces exactly one answer, it is generally closer to the return an investor actually experiences, and it requires you to state two assumptions in the open.
Money-weighted and time-weighted returns answer the portfolio version of the same question. A money-weighted return is mathematically an IRR of the investor's own contributions and withdrawals; a time-weighted return strips out the effect of cash flow timing entirely to measure the manager rather than the investor.
For a project decision, the working protocol is unchanged: NPV decides, MIRR is the rate you quote, payback screens for liquidity, and profitability index ranks under a budget. When the cash flow dates are irregular rather than periodic, none of these apply directly — move to a date-aware method such as XIRR. And when you are comparing a lease against an outright purchase, put both through the same discounting machinery with a lease versus buy NPV model rather than comparing rates on incompatible streams.
Key terms
- Terminal value (in MIRR)
- The sum of all positive cash flows compounded forward to the final period at the reinvestment rate. It is the single lump the project is worth at period n under your stated reinvestment assumption.
- Reinvestment rate
- The return you assume on cash the project releases before it ends. Usually the cost of capital. This is the assumption MIRR exists to make explicit.
- Finance rate
- The rate at which you discount negative cash flows back to period zero — your cost of the money that funds outflows. It only affects the answer when a period after the outlay is negative.
- Reinvestment assumption
- The implicit claim inside any discounted rate measure about what happens to interim cash. IRR assumes the IRR; MIRR assumes whatever you enter; NPV makes no such claim because it never converts to a rate.
- Geometric mean return
- The constant per-period rate that connects a starting value to an ending value, equal to (end ÷ start)^(1/n) − 1. MIRR is exactly this, computed between two synthetic end points.