Modified Internal Rate of Return
The Modified Internal Rate of Return (MIRR) is a capital budgeting metric that corrects for the fundamental flaw of the traditional Internal Rate of Return (IRR) by explicitly specifying the reinvestment rate for positive cash flows and a financing rate for negative cash flows, producing a single, consistent rate of return that more accurately reflects a project's or investment's true profitability.
Key takeaways
- Traditional IRR implicitly assumes that all interim cash flows are reinvested at the IRR itself — an often unrealistic assumption that leads to overstatement of returns for highly profitable projects.
- MIRR uses two explicit rates: a finance rate for negative cash flows (typically the cost of capital) and a reinvestment rate for positive cash flows (typically the firm's expected return on reinvestment).
- Unlike IRR, MIRR always produces a single unique answer, avoiding the multiple-IRR problem that arises when cash flows change sign more than once.
- MIRR is calculated by: (1) computing the future value of all positive cash flows at the reinvestment rate, (2) computing the present value of all negative cash flows at the finance rate, and (3) solving for the rate that equates these two values over the project's life.
- MIRR is more conservative than IRR for most investment projects, as the reinvestment rate is typically lower than the project's IRR.
Explanation
The Modified Internal Rate of Return was developed to address the most significant theoretical weakness of the traditional IRR metric: its implicit assumption that cash flows generated during a project's life can be reinvested at the project's own IRR. For a highly profitable project with an IRR of 30%, the traditional IRR implicitly assumes that every dollar returned during the project's life can immediately be redeployed into another opportunity earning 30% — an assumption that is rarely achievable in practice, particularly for exceptional projects that represent once-in-a-lifetime opportunities.
The reinvestment rate assumption in IRR leads to a systematic upward bias in return estimates for high-IRR projects. Consider a private equity investment with an IRR of 35% — the IRR calculation assumes that distributions received in year three can be reinvested at 35% for the remaining years of the fund. In reality, the general partner may only be able to reinvest those distributions at 12–15% in new deals. MIRR corrects this by using a more realistic reinvestment rate (typically the cost of capital or the expected portfolio return) when compounding interim cash flows forward to the terminal date.
The MIRR calculation proceeds in three steps. First, all negative cash flows (initial investment and any subsequent negative cash flows representing additional investment) are discounted back to time zero at the finance rate (usually the firm's weighted average cost of capital), producing the present value of the total investment cost. Second, all positive cash flows (project revenues and proceeds) are compounded forward to the terminal date at the reinvestment rate, producing the terminal value of all positive cash flows. Third, MIRR is defined as the rate r that satisfies: Terminal Value of Positive Cash Flows = PV of Negative Cash Flows × (1+r)^n, where n is the project life in periods.
In the context of alternative investments and private equity, MIRR provides a more nuanced and defensible return metric than IRR, especially for funds with irregular cash flows and long durations. However, it requires explicit specification of the reinvestment and finance rates, introducing a degree of subjectivity that can make comparison across managers or vintages more complex. Despite its theoretical superiority, IRR remains dominant in practice due to historical convention and the computational simplicity of its single-input requirement.
Formula
MIRR = (FV of Positive Cash Flows at Reinvestment Rate / PV of Negative Cash Flows at Finance Rate)^(1/n) − 1
Example
A private equity fund makes an initial investment of $10 million (cash outflow at t=0), receives $3 million at t=1, $4 million at t=2, and $8 million at t=3. Using a finance rate of 10% (WACC) and reinvestment rate of 12% (expected portfolio return): Terminal value of positive cash flows (compounded to t=3 at 12%): $3M × 1.12² + $4M × 1.12¹ + $8M × 1.12⁰ = $3.763M + $4.480M + $8M = $16.243M. PV of negative cash flows at 10%: $10M (already at t=0). MIRR = ($16.243M / $10M)^(1/3) − 1 = 17.5%. The traditional IRR for this project is approximately 21.5% — the MIRR's lower figure reflects the more conservative reinvestment assumption.
Related terms
Annuity Cholesky Decomposition Equity General Partner Internal Rate Of Return Jensens Inequality Law Of Large Numbers Present Value Private Equity Stable Distribution Terminal Value