How to Calculate Modified Internal Rate of Return (MIRR) on the BA II Plus Calculator

The Modified Internal Rate of Return (MIRR) is a sophisticated capital budgeting tool that addresses some of the limitations of the traditional Internal Rate of Return (IRR). While the BA II Plus calculator is a powerful financial tool, it does not have a direct MIRR function on its standard model. However, you can still calculate MIRR by leveraging its cash flow and time value of money (TVM) functions. This guide will walk you through the concept of MIRR, why it's important, and how to compute it using your BA II Plus.

Understanding MIRR: Why It Matters

The Internal Rate of Return (IRR) is a popular metric for evaluating investment projects, representing the discount rate at which the Net Present Value (NPV) of all cash flows from a particular project equals zero. However, IRR has two main drawbacks:

• Reinvestment Rate Assumption: IRR assumes that all positive cash flows generated by a project are reinvested at the IRR itself. This is often an unrealistic assumption, as companies usually reinvest funds at their cost of capital or a more conservative rate.
• Multiple IRRs: For projects with non-conventional cash flow patterns (e.g., alternating positive and negative cash flows after the initial investment), the IRR calculation can yield multiple IRRs, making interpretation difficult.

MIRR solves these problems by explicitly allowing you to specify different rates for reinvesting positive cash flows (reinvestment rate) and discounting negative cash flows (financing rate, often the cost of capital). This provides a more realistic and reliable measure of a project's profitability.

The MIRR Formula

At its core, MIRR is calculated using the following formula:

MIRR = (Future Value of Positive Cash Flows / Present Value of Negative Cash Flows)^(1/n) - 1

Where:

• Future Value of Positive Cash Flows (FVPCF): This is the future value of all cash inflows, compounded to the end of the project's life at the specified reinvestment rate.
• Present Value of Negative Cash Flows (PVNCF): This is the present value of all cash outflows (including the initial investment), discounted to time zero at the specified financing rate.
• n: The number of periods (years) over which the project runs.

Step-by-Step Calculation on the BA II Plus

Since the standard BA II Plus does not have a dedicated MIRR button, we will calculate its components manually using the calculator's features and then combine them.

Example Scenario:

An investment project requires an initial outlay of $10,000 (CF0). It is expected to generate subsequent cash flows over 4 years: $2,000 (Year 1), -$3,000 (Year 2), $5,000 (Year 3), and $8,000 (Year 4).

The company's reinvestment rate is 10%, and its financing rate (cost of capital) is 8%.

Steps:

1. Clear Previous Work:
   • Press 2ND then CLR WORK (above CE/C key).
   • Press 2ND then CLR TVM (above FV key).
2. Identify and Separate Cash Flows:
   • Negative Cash Flows (Outflows): CF0 = -$10,000, CF2 = -$3,000
   • Positive Cash Flows (Inflows): CF1 = $2,000, CF3 = $5,000, CF4 = $8,000
   • Total Periods (n): 4 years (from year 0 to year 4)
3. Calculate Present Value of Negative Cash Flows (PVNCF):

   We need to discount all negative cash flows to time zero using the financing rate (8%).

   • For CF0 = -$10,000: This is already at time zero, so its PV is -$10,000.
   • For CF2 = -$3,000: This occurs in Year 2.
     • Enter 3000 then +/- (to make it negative) then FV.
     • Enter 2 then N.
     • Enter 8 then I/Y.
     • Press CPT then PV. You should get approximately -2,572.01.
   • Sum PVNCF: -10,000 + (-2,572.01) = -12,572.01. We will use the absolute value: 12,572.01.
4. Calculate Future Value of Positive Cash Flows (FVPCF):

   We need to compound all positive cash flows to the end of the project (Year 4) using the reinvestment rate (10%).

   • For CF1 = $2,000 (at Year 1): This needs to be compounded for 3 more years (4 - 1).
     • Enter 2000 then PV.
     • Enter 3 then N.
     • Enter 10 then I/Y.
     • Press CPT then FV. You should get approximately -2,662.00. (Note: Calculator displays PV/FV with opposite signs, so use 2662.00).
   • For CF3 = $5,000 (at Year 3): This needs to be compounded for 1 more year (4 - 3).
     • Enter 5000 then PV.
     • Enter 1 then N.
     • Enter 10 then I/Y.
     • Press CPT then FV. You should get approximately -5,500.00.
   • For CF4 = $8,000 (at Year 4): This is already at the end of the project, so its FV is $8,000.
   • Sum FVPCF: 2,662.00 + 5,500.00 + 8,000 = 16,162.00.
5. Calculate MIRR:

   Now, substitute the calculated values into the MIRR formula:

   MIRR = (FVPCF / PVNCF)^(1/n) - 1

   MIRR = (16,162.00 / 12,572.01)^(1/4) - 1

   On your calculator:

   1. 16162.00 / 12572.01 = 1.285527
   2. 1 / 4 = 0.25
   3. Raise the result from step 1 to the power of the result from step 2: 1.285527 y^x 0.25 = 1.0648 (approximately)
   4. Subtract 1: 1.0648 - 1 = 0.0648
   5. Multiply by 100 to get percentage: 0.0648 * 100 = 6.48%

   So, the MIRR for this project is approximately 6.48%.

Interpreting the MIRR Result

The MIRR indicates the compound annual growth rate that an investment is expected to earn, assuming that interim cash flows are reinvested at a specified rate (the reinvestment rate) and financed at a specified cost (the financing rate). A project is generally considered acceptable if its MIRR is greater than the company's cost of capital or required rate of return.

In our example, an MIRR of 6.48% would need to be compared against the hurdle rate to determine if the project should be undertaken. If the company's cost of capital is, say, 7%, then this project might not be acceptable as its MIRR is lower.

Conclusion

While the BA II Plus calculator requires a manual, multi-step process for MIRR, understanding these steps deepens your comprehension of capital budgeting principles. By carefully calculating the present value of outflows and the future value of inflows, you can arrive at a more robust and realistic measure of a project's potential profitability, avoiding the pitfalls of traditional IRR assumptions.