How to Calculate Modified Internal Rate of Return (MIRR)

The Modified Internal Rate of Return (MIRR) serves as a capital budgeting tool designed to evaluate the profitability of potential investment projects. It offers a financial metric for decision-makers to assess whether a project is likely to generate sufficient returns. The fundamental purpose of MIRR is to determine an investment’s attractiveness by considering the time value of money and the reinvestment of cash flows.

MIRR addresses certain limitations found in the traditional Internal Rate of Return by making more realistic assumptions about how intermediate cash flows are reinvested. This method aims to provide a more accurate reflection of a project’s actual rate of return. By adjusting for these assumptions, MIRR offers a refined perspective on an investment’s potential to create value.

Understanding the Components of MIRR

Calculating the Modified Internal Rate of Return requires several distinct inputs. The initial investment, or outflow at time zero, represents the total cost incurred at the project’s inception. This amount forms the baseline against which future returns are measured, capturing all upfront expenses necessary to begin the project.

Positive cash flows are the financial inflows generated by the project over its operational life, representing revenues or savings. Negative cash flows, if occurring after the initial investment, are additional outflows required during the project’s duration, such as significant maintenance costs or further capital injections.

The reinvestment rate is the assumed rate at which positive cash flows can be reinvested. This rate typically reflects the firm’s weighted average cost of capital or a conservative estimate of achievable returns. It dictates how the project’s generated funds grow over time, aligning with the company’s actual investment opportunities.

The financing rate, or cost of capital for negative cash flows, is the rate at which the company can borrow funds. This rate discounts any outflows occurring after the initial investment back to the present value, reflecting the true cost of those funds. The project life signifies the total duration over which cash flows are expected to occur, determining the number of periods for calculations.

Step-by-Step MIRR Calculation

The calculation of the Modified Internal Rate of Return involves a systematic process that consolidates cash flows. The first step requires calculating the present value (PV) of all negative cash flows, including the initial investment. Each future outflow is discounted back to time zero using the specified financing rate, effectively converting all costs into a single equivalent value at the project’s start. This ensures all capital outlays are accounted for at their true cost of financing.

The next step involves computing the future value (FV) of all positive cash flows, compounding them forward to the end of the project’s life. Each positive cash inflow is grown at the reinvestment rate until the project’s conclusion. The sum of these compounded inflows is the terminal value, representing the total accumulated wealth generated by the project’s positive cash flows. This reflects the assumption that cash generated can be reinvested at a rate consistent with the firm’s opportunities.

Once the present value of negative cash flows and the future value of positive cash flows are determined, the MIRR formula can be applied. The formula is: MIRR = (FV of Positive Cash Flows / PV of Negative Cash Flows)^(1/n) – 1. Here, ‘n’ represents the number of periods or the total project life. This mathematical relationship connects the initial outlay, adjusted for financing costs, to the project’s terminal value, adjusted for reinvestment opportunities.

Solving for MIRR involves performing the division, raising the result to the power of one divided by the number of periods, and then subtracting one. This calculation yields a percentage representing the modified internal rate of return for the project. The result offers a single, comprehensive rate that accounts for different borrowing and reinvestment rates, providing a more refined profitability metric.

Practical Example of MIRR Calculation

Consider a hypothetical project requiring an initial investment of $100,000 at time zero. This project is projected to generate positive cash flows of $30,000 in year 1, $40,000 in year 2, and $50,000 in year 3. Assume no additional negative cash flows after the initial outlay. The project has a life of three years.

For this example, let’s set the financing rate, which is the rate used to discount negative cash flows, at 8%. The reinvestment rate, used to compound positive cash flows, will be 10%. The initial investment of $100,000 is at time zero, so its present value is $100,000. Since there are no other negative cash flows, the present value of all negative cash flows remains $100,000.

Next, we calculate the future value of the positive cash flows at the end of year 3, using the 10% reinvestment rate. The $30,000 from year 1 will compound for two years: $30,000 (1 + 0.10)^2 = $36,300. The $40,000 from year 2 will compound for one year: $40,000 (1 + 0.10)^1 = $44,000. The $50,000 from year 3 is already at the end of the project life, so its future value is $50,000.

Summing these future values provides the terminal value of positive cash flows: $36,300 + $44,000 + $50,000 = $130,300. This terminal value represents the total accumulated amount if all positive cash flows are reinvested at the specified rate until the project’s conclusion.

Finally, we apply the MIRR formula with the calculated present value of negative cash flows ($100,000) and the future value of positive cash flows ($130,300) over the three-year project life. The calculation is: MIRR = ($130,300 / $100,000)^(1/3) – 1. Performing the division gives 1.303. Raising this to the power of (1/3) yields approximately 1.0923. Subtracting 1 gives 0.0923. Therefore, the Modified Internal Rate of Return for this project is approximately 9.23%.