Modified Internal Rate of Return (IRRM)

Purpose

This calculator finds the Modified Internal Rate of Return for a series of cash flows, an alternative to the standard Internal Rate of Return (IRR) that lets you separately control the cost of financing outgoing cash flows and the return earned by reinvesting incoming cash flows. It is useful when the plain IRR's assumption — that all positive cash flows are reinvested at the project's own IRR — does not match reality.

It supports cash flows at irregular periods, so Period values do not need to be consecutive.

Background

Why "modified"

The standard IRR implicitly assumes that any positive cash flow a project produces is reinvested at that same project's IRR until the end of the series, which can be an unrealistic (often overly optimistic) assumption, especially for high-IRR projects. MIRR instead lets you specify two separate rates: a Finance Rate, used to discount the negative cash flows (money you need to finance), and a Reinvestment Rate, used to grow the positive cash flows (money you receive and reinvest) to the end of the series. It then finds the single rate that reconciles these two discounted/compounded totals, giving a typically more conservative and realistic measure of return than the plain IRR.

Inputs

Cashflow Interval

The time period between entries in the Cashflows series (for example, yr for one entry per year).

Cashflows

A table with exactly two columns in this order:

• Period (first column), for example 1, 10, 15, 25, 26.
• Cashflow (second column), the corresponding cash flow amount.

Any renamed, reordered, missing, or extra column is rejected.

Finance Rate

The rate used to discount the series' negative cash flows back to the present — representing the cost of financing those outflows (for example, your borrowing rate).

Reinvestment Rate

The rate used to grow the series' positive cash flows forward to the end of the series — representing the return you expect to earn by reinvesting those proceeds elsewhere.

Results

Periodic Interest Rate

The Modified Internal Rate of Return per Cashflow Interval, reconciling the Finance Rate-discounted outflows with the Reinvestment Rate-compounded inflows of the Cashflows series.

Annual Interest Rate

The same rate restated as an equivalent effective annual rate, regardless of the Cashflow Interval used, so it can be compared with annual rates quoted elsewhere.

Understanding the Calculation

All negative cash flows in the series are discounted back to the present using the Finance Rate; all positive cash flows are compounded forward to the final period using the Reinvestment Rate. The Modified Internal Rate of Return is then the single periodic rate that would grow the present value of the financed outflows into the future value of the reinvested inflows over the same number of periods.

Using explicit numeric period timestamps t_k (measured in the same unit as Cashflow Interval) and final period T, negative cash flows are discounted by the Finance Rate using their absolute timestamps and positive cash flows are compounded by the Reinvestment Rate to the final period:

$$PV_{neg} = \sum_{k \in neg} \dfrac{Cashflow_k}{(1+f)^{t_k}}$$

$$FV_{pos} = \sum_{k \in pos} Cashflow_k \times (1+r_f)^{T - t_k}$$

The Modified IRR is then the single periodic rate that equates these two quantities over the horizon T:

$$IRRM = \left(\dfrac{-FV_{pos}}{PV_{neg}}\right)^{1/T} - 1$$

Notes: - Period values are treated as absolute numeric timestamps (for example years when Cashflow Interval is yr); they need not be consecutive and may be irregular. - If your data uses 1,2,3... but you meant the first entry to be time 0, supply 0,1,2,... in the Period column to reflect that origin.

Example

Using the default cash flow series -40000, 5000, 8000, 12000, 30000 (one entry per year), a Finance Rate of 10% per year, and a Reinvestment Rate of 12% per year, the calculator finds a Periodic Interest Rate and Annual Interest Rate of approximately 10.90% per year — close to, but distinct from, the plain IRR of about 10.58% for the same series, because of the differing assumed reinvestment rate.

Raising the Reinvestment Rate to 20% per year (leaving everything else unchanged) raises the result to approximately 12.71% per year, showing that a more optimistic assumption about reinvesting the project's positive cash flows increases its measured rate of return.

Important Assumptions and Interpretation

• Unlike the plain IRR, MIRR always produces a single, well-defined result for a normal cash flow series, since it no longer depends on solving a polynomial that can have multiple roots.
• Choosing realistic Finance Rate and Reinvestment Rate values matters — MIRR is only as reliable as these two assumptions. Overly optimistic reinvestment rates will produce an overly optimistic MIRR.
• The result describes the rate implied by the cash flows and the two rates you provide; it is not a forecast of future project performance.