The Modified Internal Rate of Return (MIRR) calculator is a financial tool designed to evaluate the profitability of investments. Unlike the traditional Internal Rate of Return (IRR), which might give multiple rates for projects with alternating cash flows, MIRR provides a single, more accurate measure by accounting for the cost of investment and the profit from reinvestment. This article explains the workings, definition, and formula of the MIRR calculator, making it simple for anyone to understand and apply.
Purpose and Functionality
MIRR is used to assess the attractiveness of investments by calculating a single annual percentage rate that equates the present value of cash outflows with the future value of cash inflows, adjusted for both the cost of investment (finance rate) and the returns on reinvestment (reinvestment rate). It helps investors make informed decisions by providing a clearer picture of an investment’s expected profitability over time.
The MIRR calculator requires the following inputs:
- A list of cash flows (including the initial investment as a negative number and subsequent cash flows, which could be negative or positive).
- The finance rate (fr) – the cost of capital or the interest rate paid on the money used for the investments.
- The reinvestment rate (rr) – the rate at which cash flows received from the investment can be reinvested.
- The total number of periods (n).
The MIRR Formula
The MIRR is calculated using the formula:
MIRR=(FV of Positive Cash FlowsPV of Negative Cash Flows)1−1MIRR=(PV of Negative Cash FlowsFV of Positive Cash Flows)n1−1
Where:
- FV of Positive Cash Flows is the future value of positive cash flows, calculated using the reinvestment rate.
- PV of Negative Cash Flows is the present value of negative cash flows, calculated using the finance rate.
- n is the total number of periods.
Calculations involved:
- PV of Negative Cash Flows is calculated by discounting all negative cash flows back to the present value using the finance rate.
- FV of Positive Cash Flows is calculated by compounding all positive cash flows to the end of the investment period using the reinvestment rate.
Step-by-Step Example
Let’s say an investor has an initial investment of $10,000 (negative cash flow) and expects to receive $3,000, $4,000, and $5,000 in the next three years (positive cash flows). The finance rate is 5%, and the reinvestment rate is 10%.
- Calculate PV of Negative Cash Flows: -$10,000 (since there’s only one negative cash flow at time 0, it remains the same).
- Calculate FV of Positive Cash Flows using the reinvestment rate of 10% for each of the cash inflows at their respective periods.
- Apply the MIRR formula with the calculated PV of Negative Cash Flows and FV of Positive Cash Flows.
Relevant Information Table
| Year | Cash Flow | Type | Calculation Using Rate |
|---|---|---|---|
| 0 | -10,000 | Negative (PV) | -10,000 |
| 1 | 3,000 | Positive (FV) | Compounded at 10% |
| 2 | 4,000 | Positive (FV) | Compounded at 10% |
| 3 | 5,000 | Positive (FV) | Compounded at 10% |
Conclusion
The MIRR calculator stands out as a robust tool for assessing the true profitability of investments, especially when compared to the traditional IRR method. It takes into account the cost of investment and the potential gains from reinvestment, offering a more comprehensive understanding of an investment’s value over time. By incorporating both the finance and reinvestment rates, MIRR helps investors make more informed decisions, ensuring that their investments are aligned with their financial goals and risk tolerance. Whether you’re a seasoned investor or new to finance, understanding and utilizing the MIRR calculator can significantly enhance your investment analysis process.