Apple Numbers MIRR: Financing and Reinvestment Rates
Model modified internal rate of return in Numbers, preserve zero periods and verify financing and reinvestment calculations with a complete cash-flow example.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: For cash flows -10000, 3000, 4000, 5000 at equal annual intervals, =MIRR(B2:B5,8%,5%) gives approximately 7.74327454% per year when those values occupy B2:B5. The first rate finances negative flows; the second reinvests positive flows.
Availability and version history
- Introduced: The first supported release and introduction date are not established by the checked sources.
- Availability: Currently documented in Apple’s Formulas and Functions Help 15.4 documentation edition; no final support endpoint is established.
- Scope: Shared iWork function reference. This edition number does not establish a Numbers app version or identical behavior across older Mac, iPad, iPhone and iCloud clients.
- Checked: October 14, 2026, against the official MIRR reference. Documentation and independent numerical models; no native Numbers test.
Syntax and required inputs
=MIRR(flows-range, finance-rate, reinvest-rate)
All three arguments are required. The cash-flow collection must contain numeric values, including at least one positive amount and one negative amount. Arrange them chronologically at equal intervals. Apple explicitly instructs using 0 for a period without a cash flow.
The finance rate applies to outflows and the reinvestment rate to inflows. Enter rates as decimals or percentages. Keep their period consistent with the timeline: annual flows use annual rates; monthly flows need monthly rates.
MIRR incorporates two stated rate assumptions. IRR instead solves for a rate that makes a cash-flow series balance. Neither function determines whether the forecasts or rate assumptions are realistic.
Build an annual project table
Create a table named Project, with at least seven columns A:G and eight rows. Enter Period, Cash flow and Reinvested positive flow in A1:C1. Enter the following values in A2:B5:
| Row | A: Period | B: Cash flow |
|---|---|---|
| 2 | 0 | -10000 |
| 3 | 1 | 3000 |
| 4 | 2 | 4000 |
| 5 | 3 | 5000 |
Put Finance rate and Reinvest rate in E1:F1, then 8% in E2 and 5% in F2. Enter =MIRR(B2:B5,E2,F2) in G2. Format it as a percentage with eight decimal places: expect 7.74327454%.
Four cash-flow entries span three intervals, from period 0 to period 3. Do not use four as the number of compounding periods when checking this result.
Independently reconstruct the calculation
The initial outflow already occurs at time zero, so its present cost is 10000. Reinvest each later positive flow to the end of period 3. Enter =B3*(1+$F$2)^(3-A3) in C3 and fill through C5:
| Cell | Calculation | Expected value |
|---|---|---|
| C3 | 3000 × 1.05² | 3307.50 |
| C4 | 4000 × 1.05 | 4200.00 |
| C5 | 5000 × 1 | 5000.00 |
In G3 enter =C3+C4+C5; expect 12507.50. In G4 enter =(G3/(-B2))^(1/3)-1; it reproduces the 7.74327454% modified return.
As a reverse check, enter =(-B2)*(1+G2)^3 in G5. Its expected value is 12507.50. This connects the initial present cost to the reinvested ending value using the returned compound rate.
The finance rate does not affect this particular dataset’s result because its only negative flow occurs at time zero. That does not make the argument generally irrelevant; the next example adds a later outflow.
Advanced: a second funding payment
Create a separate table named Staged, with seven columns A:G and six rows. Use Period and Cash flow in A1:B1. Enter periods 0, 1, 2, 3 in A2:A5 and cash flows -10000, -2000, 5000, 8000 in B2:B5. Put 8% in E2 and 5% in F2.
In G2 enter =MIRR(B2:B5,E2,F2). Expect approximately 3.78706277%.
For a transparent check, enter these formulas separately:
| Cell | Formula | Expected value |
|---|---|---|
| D2 | =-B2-B3/(1+E2) |
11851.851851852 |
| D3 | =B4*(1+F2)+B5 |
13250.00 |
| D4 | =(D3/D2)^(1/3)-1 |
3.78706277% |
D2 discounts the later funding requirement back one period; D3 reinvests the period-2 receipt for one period. These helper formulas are tailored to this exact sign pattern. If the timing or signs change, rebuild the negative-flow and positive-flow sums rather than copying them blindly.
Why a zero period matters
On a new table named Timing, with three columns and four rows, enter -1000, 0, 1210 in A2:A4. In B2 enter =MIRR(A2:A4,5%,5%); expect 10% across two intervals.
Put -1000 in C2 and 1210 in C3. In B3 enter =MIRR(C2:C3,5%,5%); expect 21% across one interval. The total received is unchanged, but its timing is different. Removing the zero is not merely tidying the data.
Compare reinvestment assumptions
Back on Project, leave the cash-flow cells unchanged. Put =MIRR(B2:B5,E2,0%) in G7 and =MIRR(B2:B5,E2,10%) in G8. Expected results are 6.26585692% and 9.22317711%, respectively. The 5% reinvestment case remains in G2 between them.
These are controlled assumptions, not guaranteed future returns. A monthly MIRR would be a monthly compound rate; annualizing it with (1+monthly_MIRR)^12-1 additionally assumes that repeating-rate interpretation is appropriate.
Apple’s example and practical limits
Apple’s separate example uses seven entries -50000, -25000, -10000, 0, 10000, 30000, 100000. With 9% financing and 4.25% reinvestment, its published result is 9.74693238643805%. Independent present-cost and ending-value calculations reproduce that result over six intervals.
The reference does not enumerate every invalid-rate domain or error code. Keep a valid mixed-sign numeric collection, explicit zero periods and required rates rather than importing another editor’s blank/error rules. Use XIRR for a rate based on dated uneven cash flows; it does not add separate financing and reinvestment arguments. Use NPV when you want a discounted amount at one chosen rate.