Understanding the Difference Between IRR and MIRR

When evaluating potential investments, businesses need to carefully analyze the projected cash flows to determine if the investment will be profitable. Two popular methods for this analysis are the internal rate of return (IRR) and modified internal rate of return (MIRR). While both can provide useful information, there are some key differences between IRR and MIRR that investors should understand.

What is IRR?

The internal rate of return is a metric used to estimate the profitability of a potential investment. It is the discount rate that results in a net present value of zero for the investment’s cash flows. In other words, it is the expected compound annual growth rate that the investment would need to generate in order to “break even.”

To calculate IRR, the present value of each cash flow associated with the investment is calculated using the same discount rate. This discount rate is adjusted until the net present value equals zero. A higher IRR indicates a more desirable investment, since it suggests higher growth potential.

IRR has some advantages as an investment analysis tool

• It provides a percentage return that is easy to interpret. A project with a 10% IRR seems better than one with a 5% IRR.

• It accounts for the time value of money by discounting future cash flows.

• It summarizes multiple cash flows over time into a single metric.

However IRR also has some limitations to be aware of

• It assumes reinvestment of interim cash flows at the IRR. This may not be realistic.

• It can produce multiple solutions for certain cash flow patterns, creating ambiguity.

• It does not indicate the absolute size of the investment, only the percent return.

What is MIRR?

The modified internal rate of return (MIRR) aims to address some of the shortcomings of the regular IRR formula. It is similar to IRR in that it expresses investment profitability as a percentage return, but it makes different assumptions regarding the reinvestment of interim cash flows.

Rather than assuming reinvestment at the IRR, MIRR allows you to specify a separate reinvestment rate for the inflows and a finance rate for the outflows. The reinvestment rate is often the company’s cost of capital, while the finance rate is its borrowing cost.

To calculate MIRR, the future value of the investment’s inflows is determined using the reinvestment rate. The present value of the outflows is then calculated using the financing rate. The MIRR is the rate that equates those two values.

Compared to regular IRR, MIRR has some advantages:

• It allows for more realistic reinvestment assumptions.

• It will always produce a single result, even for irregular cash flows.

• It better accounts for the cost of financing.

However, MIRR also requires more inputs and assumptions than IRR. The reinvestment and financing rates must be estimated appropriately.

Key Differences Between IRR and MIRR

Let’s summarize some of the main differences between the two measures:

• Reinvestment rate – IRR assumes reinvestment at the IRR, while MIRR allows a separate reinvestment rate to be specified, often the cost of capital.

• Number of solutions – IRR can produce multiple solutions for certain cash flow patterns. MIRR will always produce a single result.

• Cost of capital – IRR does not explicitly account for financing costs. MIRR uses specified financing and reinvestment rates.

• Calculation method – IRR equates inflows and outflows using the same discount rate. MIRR keeps them separate.

• Accuracy – MIRR is considered a more realistic estimate in many cases due to its flexibility with rates.

• Complexity – MIRR requires more inputs and assumptions than IRR. However, it avoids potential multiple solution issues.

In general, MIRR is often preferred for investment analysis due to its more realistic assumptions and flexibility. However, both measures have their place depending on the specifics of the investment and analysis objectives.

When to Use IRR vs. MIRR

So when should you use each metric? Here are some guidelines:

IRR tends to be better when:

• Simple “back of the envelope” estimate is needed

• Cash flows are conventional and reinvestment at IRR is reasonable

• Easy interpretation of a single metric is preferred

MIRR tends to have advantages when:

• Cash flow patterns are complex or unconventional

• Specific reinvestment and financing rates are known

• More precision is needed in the estimate

• Cost of capital considerations are important

For many investments, calculating both IRR and MIRR can provide helpful insight into profitability from different perspectives. Comparing the two can indicate if reinvestment assumptions significantly impact the numbers. Large differences between IRR and MIRR would suggest more care should be taken in selecting appropriate rates.

An Example Comparing IRR and MIRR

Let’s look at a simple example to illustrate the differences between IRR and MIRR.

A piece of equipment costs $20,000 upfront and is expected to produce cash flows of $8,000 per year for 5 years. After 5 years, it can be sold for an estimated $2,000.

• The company’s cost of capital is 10%
• Its borrowing rate is 8%

Using these inputs, here are the IRR and MIRR values:

• IRR = 18.1%
• MIRR = 14.8%

(Calculated using Excel or financial calculator)

In this case, the IRR overstates the expected return because it assumes reinvestment of interim cash flows at 18.1%. More realistically, those funds would earn the firm’s 10% cost of capital. MIRR accounts for this through its separate reinvestment rate input.

The lower MIRR provides a more conservative estimate of the investment return given the expected financing and reinvestment scenarios. However, IRR still provides a quick approximation that may be useful for initial screening.

This example demonstrates how the two measures can produce different results for the same cash flows based on their underlying assumptions. Depending on the specifics of the investment, one metric may be more appropriate to evaluate projected profitability.

Key Takeaways on IRR vs. MIRR

• IRR calculates the expected return by equating inflows and outflows at the same rate. MIRR keeps them separate using specified reinvestment and financing rates.

• IRR can produce multiple solutions for certain cash flow patterns. MIRR will always result in one solution.

• MIRR allows for more customized assumptions around reinvestment and financing rates.

• For conventional cash flows, IRR provides a quick estimate of profitability as a percentage return.

• For complex projects or when more precision is needed, MIRR often provides better results.

• Comparing IRR and MIRR for an investment can provide insights into the impact of reinvestment assumptions.