MIRR, Explained: How the Modified Internal Rate of Return Fixes IRR's Reinvestment Fantasy

Your new packaging machine shows a 21.7% internal rate of return, comfortably above your 10% cost of capital. You approve the purchase feeling clever. But buried in that 21.7% is an assumption nobody told you about: it presumes you can reinvest every dollar the machine throws off, in years one and two, at 21.7% itself. Can you? If your spare cash actually earns 10% in the business — or 4% in a money market account while it waits — the project cannot deliver what its IRR promises. The modified internal rate of return, or MIRR, exists to strip that fantasy out and give you a rate built on reinvestment returns you can actually earn.

The Fantasy Inside Your IRR​

The internal rate of return is the discount rate that sets a project's net present value to zero. That is the textbook definition, and it hides a working assumption: discounting math behaves as if every interim cash inflow is reinvested inside the project, compounding at the IRR itself, for the rest of the project's life. Economists call the IRR the "economic yield" for exactly this reason — it is the rate the project supposedly earns on money it has not paid out yet.

For a project with a modest IRR near your cost of capital, the assumption is harmless. It turns dangerous precisely when a project looks most exciting. A project with a 30% IRR assumes you have somewhere to park its year-one proceeds at 30% until the project ends. Most small businesses do not. Surplus cash goes into working capital, a line-of-credit paydown, or a savings account — all earning far less than 30%. The IRR overstates what you will actually earn, and the overstatement grows with the IRR.

MIRR fixes this by splitting the single rate into two explicit inputs you choose: a finance rate for the money going out and a reinvestment rate for the money coming in.

What MIRR Actually Computes​

Think of MIRR as answering a plain question: if I discount what I spend at my cost of borrowing, compound what I receive at a realistic reinvestment return, and compare the two piles at the end, what single annual rate connects them?

The mechanics have three steps:

1. Discount every outflow to today at the finance rate. The finance rate is your cost of capital — what it costs you to fund the spending. Outflows in later years (a phase-two installation, a final cleanup bill) are pulled back to present value at this rate and added to the day-one outlay.
2. Compound every inflow forward to the final year at the reinvestment rate. The reinvestment rate is the return you realistically expect on cash the project releases early. Each inflow grows at this rate until the project's last period, and the results are summed into one terminal value.
3. Find the rate that grows the outflow pile into the inflow pile. That rate is the MIRR.

As a formula, with n periods:

MIRR = (terminal value of inflows / present value of outflows) ^ (1 / n) - 1

The terminal value uses the reinvestment rate; the present value of outflows uses the finance rate. When both rates equal your cost of capital — the standard textbook setup — MIRR is virtually always below the IRR, and the gap between them is the size of the reinvestment fantasy.

A Worked Example You Can Check​

Suppose you are weighing a $10,000 packaging machine with a three-year life. It saves you $4,000 in year one, $5,000 in year two, and $6,000 in year three. Your cost of capital is 10%, which you use as both the finance rate and the reinvestment rate.

Step 1: present value of outflows. The only outflow is the $10,000 day-one purchase, already at present value: $10,000.

Step 2: terminal value of inflows at 10%.

• Year-one $4,000 compounds for two years: $4,000 x 1.21 = $4,840
• Year-two $5,000 compounds for one year: $5,000 x 1.10 = $5,500
• Year-three $6,000 is already at the terminal date: $6,000
• Terminal value: $4,840 + $5,500 + $6,000 = $16,340

Step 3: connect the piles. ($16,340 / $10,000) ^ (1/3) - 1 = 1.634 ^ (1/3) - 1 = 17.8%.

So the MIRR is 17.8%. The same project's conventional IRR is about 21.7% — nearly four percentage points of that headline rate was the silent assumption that interim savings compound at 21.7%. The net present value at 10% is $2,276, positive, so the project still clears the bar. MIRR did not kill the project; it told you the truth about the rate.

Notice what happens if you raise the reinvestment rate to the IRR itself: the MIRR becomes the IRR. The two measures agree only in the fantasy world where you can reinvest at the project's own return. Everywhere else, MIRR sits below IRR — and the more aggressive the IRR, the wider the gap.

The Two Rates Are the Whole Game​

MIRR's honesty is only as good as the two rates you feed it, so choose them deliberately rather than accepting defaults.

The finance rate should reflect what funding the outflows actually costs you. For most small businesses that is the weighted cost of your funding mix: the interest on the equipment loan or line of credit, blended with the return your own equity could earn elsewhere. If the project is debt-funded at 8%, use 8%. If you are weighing projects of different risk, a higher finance rate for the riskier one is defensible — just document it, because the rate choice now drives the answer in a way IRR never showed you.

The reinvestment rate should reflect what interim cash will plausibly earn. Common honest choices:

• Your cost of capital, if freed-up cash flows back into the general business and earns the firm's average return.
• The rate on the debt you would pay down, if surplus cash retires a credit line — a 9% paydown is a risk-free 9% return.
• A conservative safe rate, if cash will sit in savings between projects.

Be wary of the lazy default of setting both rates to the cost of capital without thinking. For a business whose spare cash earns 4% in a sweep account, assuming 10% reinvestment just installs a smaller fantasy. Run the MIRR at two or three reinvestment rates — pessimistic, expected, optimistic — and see whether the project still beats your hurdle. If the decision flips on the reinvestment assumption, that sensitivity is itself the finding: the project is a bet on your ability to redeploy cash, not just on its own cash flows.

MIRR's Second Fix: One Answer Instead of Two​

The reinvestment assumption is not IRR's only quirk. When cash flows change sign more than once — an outflow, then inflows, then another outflow — the IRR equation can produce multiple answers or none at all. A leasehold improvement with a big restoration bill at the end of the lease is the classic small-business case: money goes out, comes in for years, then goes out again.

Take a stylized version: you spend $10,000 today, receive $23,000 in year one, and pay $13,200 in cleanup costs in year two. Solve for IRR and you get two mathematically valid answers, 10% and 20%. Which one is "the" return? The math refuses to say, and spreadsheet software will hand you one of them depending on its starting guess.

MIRR has no such ambiguity, because it collapses each side to a single pile before solving. Using an 8% finance rate and a 10% reinvestment rate:

• Terminal value of the inflow: $23,000 x 1.10 = $25,300
• Present value of outflows: $10,000 + $13,200 / 1.08^2 = $10,000 + $11,316.87 = $21,316.87
• MIRR: ($25,300 / $21,316.87) ^ (1/2) - 1 = 8.9%

One project, one answer: 8.9%. Whenever your project has a tail cost — decommissioning, lease restoration, a final balloon payment — compute the MIRR rather than trusting whichever IRR your spreadsheet happened to find.

Where MIRR Still Loses: The Scale Problem​

MIRR cures the reinvestment fantasy and the multiple-answer problem. It does not cure the oldest weakness of every rate-based measure: a percentage cannot tell you how many dollars you make.

Imagine two mutually exclusive uses of your year — you can only do one:

• Project A: invest $10,000, receive $15,000 in one year. MIRR: 50%.
• Project B: invest $100,000, receive $120,000 in one year. MIRR: 20%.

MIRR ranks A far ahead. But at a 10% cost of capital, A's net present value is $3,636 while B's is $9,091 — B creates two and a half times as much wealth. If your goal is to maximize the value of the business, B is the right choice and MIRR points the wrong way.

This is the scale problem, and no rate-based metric escapes it, because rates deliberately strip out size. The professional practice is a division of labor: use net present value to rank mutually exclusive projects and make the go/no-go decision, and use MIRR alongside it as the intuitive percentage — the "headroom" above your cost of capital — that NPV cannot express. When someone asks "how much cushion does this project have before it stops covering its cost of funds," a 17.8% MIRR against a 10% hurdle answers in a sentence. When someone asks "which project makes us richer," only NPV answers. Compute both, and let NPV break ties.

A related blind spot is project life. MIRR annualizes over each project's own horizon, so comparing a two-year project's MIRR with a ten-year project's MIRR is shakier than it looks — the terminal values assume very different reinvestment journeys. For unequal lives, either compare NPVs over a common horizon or annualize with an equivalent-annual-value computation before ranking.

Computing MIRR in a Spreadsheet​

Every major spreadsheet has MIRR built in. In Excel or Google Sheets:

=MIRR(values, finance_rate, reinvest_rate)

values is the full cash-flow series including the initial outflow as a negative number (at least one negative and one positive, or the function errors). For the packaging-machine example, with -10000, 4000, 5000, 6000 in cells A1:A4, =MIRR(A1:A4, 10%, 10%) returns 17.8%.

Two practical notes. First, the argument order — finance rate before reinvestment rate — is easy to transpose, and swapping them silently computes the wrong answer on projects with later-year outflows, so double-check. Second, MIRR assumes equally spaced periods; for irregular timing, build the terminal-value and present-value piles by hand with dated compounding rather than forcing dates into the function.

Tracking the Project in Your Books​

A capital-budgeting decision does not end at approval — the project's actual cash flows need somewhere to live so you can compare reality against the forecast that justified it. In a plain-text ledger, tag the machine and its savings to the project from day one:

2026-01-05 * "Acme Industrial" "Buy packaging machine -- Project Atlas"
  Assets:Equipment:Packaging-Machine   10,000.00 USD
  Assets:Checking
 
2026-12-31 * "Year-end" "Packaging labor savings -- Project Atlas"
  Assets:Checking    4,000.00 USD
  Income:Labor-Savings:Project-Atlas

With every project-tagged entry in one place, the year-three review writes itself: pull the actual inflows, recompute the realized MIRR with the same two rates, and see whether the machine earned its 17.8%. Most businesses never close this loop, which is why the same optimistic forecasts get approved year after year. The ledger makes the post-audit nearly free.

Common Mistakes to Avoid​

• Setting the reinvestment rate to the IRR by habit. Some analysts do this to "see the upside," but it just reproduces the IRR and defeats the purpose. Your reinvestment rate should describe your cash, not your hopes.
• Using MIRR alone to rank mutually exclusive projects. Scale and timing differences can flip rankings versus NPV. Always compute NPV as the decision rule.
• Ignoring later-year outflows in the finance-rate pile. Maintenance overhauls, balloon payments, and restoration costs belong in the present-value-of-outflows denominator, discounted at the finance rate — not netted against nearby inflows.
• Comparing MIRRs across different project lives. A 15% MIRR over two years and a 15% MIRR over ten years are not the same achievement. Normalize horizons before ranking.
• Quoting MIRR without naming the two rates. "The MIRR is 17.8%" is incomplete; "17.8% at a 10% finance rate and 10% reinvestment rate" lets anyone challenge your assumptions. Put both rates on the same slide as the answer.

Your Next Capital Decision, in Order​

The next time a project lands on your desk with an attractively high IRR, run this sequence before you approve it: compute the NPV at your cost of capital as the decision rule, compute the MIRR with an honest finance rate and a realistic reinvestment rate as the intuition check, stress the reinvestment rate up and down to find where the decision flips, and file the forecast next to project-tagged ledger entries so the post-audit happens. Four steps, one spreadsheet function, and no more 30% returns built on 30% reinvestment fantasies.