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How do you avoid the reinvestment rate assumption problem in IRR?

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The internal rate of return (IRR) is a popular method of evaluating the profitability of an investment project. It is the discount rate that makes the net present value (NPV) of the project's cash flows equal to zero. However, the IRR has a major drawback: it assumes that the cash flows generated by the project are reinvested at the same rate as the IRR. This is often unrealistic, as the actual reinvestment rate may be higher or lower than the IRR. In this article, you will learn how to avoid the reinvestment rate assumption problem in IRR and use alternative methods that account for different reinvestment rates.

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Meng Hock Tan ????

External Audit | Financial Reporting | Know Your Client Compliance | Big Four | Associate Member of the Institute of…

1 What is the reinvestment rate assumption problem in IRR?

The reinvestment rate assumption problem in IRR is the issue that the IRR calculation implicitly assumes that the cash flows generated by the project are reinvested at the same rate as the IRR. This means that the IRR overestimates the true return of the project if the reinvestment rate is lower than the IRR, and underestimates it if the reinvestment rate is higher than the IRR. For example, suppose a project has an initial cost of $100,000 and generates $50,000 in cash flows for four years. The IRR of this project is 21.6%, which means that the project breaks even if the discount rate is 21.6%. However, this also means that the project assumes that the $50,000 cash flows are reinvested at 21.6% each year, which may not be feasible or realistic.

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Meng Hock Tan ????

External Audit | Financial Reporting | Know Your Client Compliance | Big Four | Associate Member of the Institute of Singapore Chartered Accountants (ISCA)
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Internal Rate of Return (IRR) always assumes that all interim cash flows can be reinvested at using the same rate, which can be unrealistic if the IRR of the project is much higher than the cost of capital of the company. Furthermore, multiple rates can be computed when a project has uneven stream of cash flows. Hence, this can lead to sub-optimal decisions compared with decisions made using the Net Present Value (NPV) method.

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2 How to calculate the reinvestment rate of a project?

The reinvestment rate of a project is the rate at which the cash flows generated by the project are actually reinvested. It depends on the availability and cost of capital, the risk and return of alternative investments, and the market conditions. One way to calculate the reinvestment rate of a project is to use the modified internal rate of return (MIRR) formula, which is:

MIRR = (FV of cash inflows / PV of cash outflows)^(1/n) - 1

where FV is the future value, PV is the present value, n is the number of periods, and cash inflows and outflows are separated. The MIRR formula uses two different discount rates: one for the cash outflows (the cost of capital) and one for the cash inflows (the reinvestment rate). The MIRR reflects the true return of the project by accounting for different reinvestment rates.

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3 How to compare projects with different reinvestment rates?

If you have multiple projects with different reinvestment rates, you can use the MIRR to compare them and choose the one with the highest MIRR. The MIRR is a better indicator of the profitability of a project than the IRR, as it avoids the reinvestment rate assumption problem and ensures that the projects have a common basis for comparison. However, the MIRR also has some limitations, such as requiring an estimate of the reinvestment rate and ignoring the timing of cash flows. Therefore, you should also use other methods of capital budgeting, such as the NPV, the profitability index, or the payback period, to complement the MIRR analysis.

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Meng Hock Tan ????

External Audit | Financial Reporting | Know Your Client Compliance | Big Four | Associate Member of the Institute of Singapore Chartered Accountants (ISCA)
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At times, there are projects with different Internal Rate of Return (IRR) and Net Present Value (NPV) for comparison purposes. For instance, if a project has a higher IRR also has the lowest NPV. One of the causes could be due to the project may require a higher required rate of return due to reasons such as the location and uncertainty of cash flows, hence it leads to a lower NPV. Certainly, the Modified Internal Rate of Return (MIRR) is used to get rid the problems of multiple rates generated if the stream of cash flows is uneven.

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4 How to use Excel to calculate the MIRR?

Excel has a built-in function to calculate the MIRR of a project, which is:

=MIRR(values, finance_rate, reinvest_rate)

where values is a range of cells that contain the cash flows of the project, finance_rate is the discount rate for the cash outflows, and reinvest_rate is the discount rate for the cash inflows. For example, using the same project as before, with a cost of capital of 10% and a reinvestment rate of 15%, you can enter the following formula in Excel:

=MIRR(-100000,50000,50000,50000,50000,0.1,0.15)

The result is 18.1%, which is the MIRR of the project.

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Meng Hock Tan ????

External Audit | Financial Reporting | Know Your Client Compliance | Big Four | Associate Member of the Institute of Singapore Chartered Accountants (ISCA)
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Using the Excel to calculate the MIRR is pretty simple by punching in the values into the MIRR formula function that has already embedded in the Excel "=MIRR(values, finance_rate, reinvest_rate)". Alternatively, we can also calculate the MIRR manually by hand and calculator. Let us assume the project has the following cash flows and discount rate is 15%: Year 0: -$1,000 Year 1: $600 Year 2: $800 Year 3: $400 Then, we would have to compound the Year 1 $600 and Year 2 $800 to Year 3 to see how much it is worth (i.e., their Future Value (FV)). FV for Year 1 = $793.50 FV for Year 2 = $920 Total Amount for Year 3 = $793.50 + $920 + $400 = $2,113.50 MIRR = Cube Root (2,113.50 / 1,000) - 1 = 28.33%

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5 How to interpret the MIRR?

The MIRR is the annualized return of the project that accounts for different reinvestment rates. It tells you how much your investment will grow over time if you reinvest the cash flows at a specified rate. The higher the MIRR, the more profitable the project is. However, the MIRR does not tell you how long it will take to recover your initial investment or how sensitive the project is to changes in assumptions. Therefore, you should use the MIRR along with other criteria, such as the NPV, the profitability index, or the payback period, to make a comprehensive decision about a project.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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Capital Budgeting

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How do you avoid the reinvestment rate assumption problem in IRR?

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1 What is the reinvestment rate assumption problem in IRR?

2 How to calculate the reinvestment rate of a project?

3 How to compare projects with different reinvestment rates?

4 How to use Excel to calculate the MIRR?

5 How to interpret the MIRR?

6 Here’s what else to consider

Capital Budgeting

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