To calculate the Modified Internal Rate of Return (MIRR) on a BA II Plus, you first need to understand that this financial calculator does not have a dedicated MIRR key. Unlike higher-end models, the BA II Plus requires you to perform the calculation using the built-in time value of money (TVM) functions and manual steps. The process involves determining the future value of positive cash flows and the present value of negative cash flows, then using those results to solve for the MIRR.
Understanding the MIRR Calculation Methodology
The MIRR is a refined version of the traditional Internal Rate of Return (IRR) that assumes positive cash flows are reinvested at the firm's cost of capital, and that the initial outlays are financed at the firm's financing cost. This provides a more realistic rate of return compared to the standard IRR, which assumes cash flows are reinvested at the IRR itself. The calculation follows a specific three-step sequence that aligns perfectly with the BA II Plus's functionality.
Step 1: Calculating the Future Value of Inflows
The first step requires you to take all positive cash flows (inflows) and compound them forward to the end of the project's life. You will use the BA II Plus TVM solver to input each cash flow's value and its respective number of periods, calculating the future value at the specified reinvestment rate. This step effectively answers the question: "What is the total value of all cash inflows at the end of the project if they are invested at the cost of capital?"
Handling Multiple Cash Flows
If your project has multiple positive cash flows at different points in time, you must calculate the future value of each one individually. For example, if you have a $1,000 inflow in year 1 and a $2,000 inflow in year 2, you would calculate the future value of the $1,000 for two years and add it to the $2,000. It is often efficient to calculate these sequentially, using the "FV" register to accumulate the total future value of all inflows.
Step 2: Calculating the Present Value of Outflows
Next, you determine the present value of all negative cash flows (outflows). These are typically the initial investment or subsequent costs. You will discount these amounts back to the present (time zero) using the financing rate. On the BA II Plus, you input these cash flows as negative numbers and solve for the present value. This step answers the question: "What is the total cost of the project today, accounting for the time value of money?"
Step 3: Solving for the MIRR
With the future value of inflows (FV) and the present value of outflows (PV) calculated, you can now determine the MIRR. The formula requires you to take the Nth root of the ratio of FV to PV, where N is the total number of periods. On the BA II Plus, you input the FV as a positive number and PV as a negative number into the TVM solver, set N to the project duration, and then press the "CPT" and "I/Y" keys to solve for the interest rate, which is your MIRR.
