Modified Internal Rate of Return (MIRR) Lab

Multi-Year Cash Flow & Compounding Schedule

Decomposition of project cash flows, present value discounting of funding outlays, and forward reinvestment compounding to terminal horizon.

Sensitivity Analysis 1: Financing Rate vs. Reinvestment Rate on MIRR (%)

Sensitivity of modified project return across shifts in debt borrowing costs and corporate reinvestment hurdle rates.

Sensitivity Analysis 2: Initial Outlay vs. Terminal Year Cash Flow on MIRR (%)

Capital efficiency matrix evaluating return resilience against initial CapEx overruns and final year cash realization.

Formulas and worked example

• Present Value of Outflows: $PV_{\text{outflows}} = \sum_{t=0}^{n} \frac{|C_t| \cdot \mathbb{I}(C_t < 0)}{(1 + r_{\text{finance}})^t}$
• Terminal Value of Inflows: $TV_{\text{inflows}} = \sum_{t=0}^{n} C_t \cdot \mathbb{I}(C_t > 0) \times (1 + r_{\text{reinvest}})^{n-t}$
• Modified Internal Rate of Return (MIRR): $\text{MIRR} = \left( \frac{TV_{\text{inflows}}}{PV_{\text{outflows}}} \right)^{1/n} - 1$
• Standard IRR: rate $r$ where $\sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} = 0$
• Reinvestment Spread: $\text{Spread} = \text{IRR} - \text{MIRR}$
• Net Present Value (NPV): $\text{NPV} = \sum_{t=0}^{n} \frac{C_t}{(1 + r_{\text{reinvest}})^t}$
• Profitability Index (PI): $PI = (\text{NPV} + PV_{\text{outflows}}) / PV_{\text{outflows}}$

A capital project requires an initial investment of $100,000 ($C_0 = -\$100\text{k}$) and yields cash inflows of $30,000, $45,000, $60,000, $80,000, and $120,000 across Years 1 through 5. The firm's financing rate is 8.0% and its reinvestment rate (WACC) is 10.0%. The present value of outflows is $100,000 ($PV_{\text{outflows}} = \$100\text{k}$). Compounding each inflow to Year 5 at 10.0% produces a terminal value of $384,171 ($30\text{k} \times 1.10^4 + 45\text{k} \times 1.10^3 + 60\text{k} \times 1.10^2 + 80\text{k} \times 1.10^1 + 120\text{k}$). The 5-year MIRR is $(\$384,171 / \$100,000)^{1/5} - 1 = 30.89\%$. By contrast, the standard IRR solver yields 55.77%, assuming unrealistic intermediate reinvestment at 55.77%. MIRR reveals a 24.88% reinvestment optimism spread, providing corporate treasurers with a realistic capital return.

Self-check quiz

1. What is the fundamental flaw of standard IRR that Modified IRR (MIRR) directly solves?

2. When a project has non-conventional cash flows (e.g. an initial outflow, intermediate inflows, and a final decommissioning cost), how does MIRR handle the late-stage negative cash flow?

3. If a capital project's standard IRR is 35.0% and the firm's cost of capital (reinvestment rate) is 10.0%, what will be true of its MIRR?

4. Under the MIRR capital budgeting decision rule, when should an independent project be accepted?

Check answers

Frequently asked questions

What is Modified Internal Rate of Return (MIRR) and how is it calculated?

Modified Internal Rate of Return (MIRR) is a capital budgeting metric that corrects the flaws of standard IRR. It discounts all negative cash flows to Year 0 using a financing cost, compounds all positive cash flows to the final terminal year using a realistic reinvestment rate (such as WACC), and computes the compound annual return: MIRR = (Terminal Value of Inflows / Present Value of Outflows)^(1/n) - 1.

Why is MIRR superior to standard Internal Rate of Return (IRR)?

Standard IRR assumes intermediate cash inflows are reinvested at the project's own internal rate of return, which can be unrealistically high (e.g. 40% to 60%). MIRR uses a realistic market reinvestment rate (the firm's cost of capital). Furthermore, MIRR avoids the multiple rate of return problem that occurs with non-conventional cash flows.

How does MIRR handle non-conventional cash flows with negative terminal outflows?

Non-conventional projects, such as mines or nuclear plants with late-stage decommissioning and restoration costs, have negative cash flows after Year 0. Standard IRR can produce multiple conflicting mathematical roots. MIRR solves this cleanly by discounting all negative cash flows back to Year 0 using the financing rate before computing the terminal return.

What is the relationship between MIRR, standard IRR, and the reinvestment rate?

When the reinvestment rate equals the standard IRR, MIRR equals IRR. When the reinvestment rate is lower than IRR (the common real-world case for high-return projects), MIRR is lower than IRR, eliminating reinvestment rate optimism. When the reinvestment rate is higher than IRR, MIRR is higher than IRR.

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