Newsletter #8: Enhancing IRR - the case for Modified Internal Rate of Return

When assessing the feasibility of a potential investment or project, management typically employs a variety of evaluation techniques which help determine the potential profitability and risks associated with the investment. Some of the commonly applied techniques are:

• Net Present Value

• Internal Rate of Return

• Profitability Index

• Payback period

• Book value return on investment

Studies suggest that management generally favors using the Internal Rate of Return (IRR) as a benchmark against the company's current cost of capital. The IRR is often used in conjunction with the Net Present Value (NPV) technique.

Source: Reprinted from J. R. Graham and C. R. Harvey, “The Theory and Practice of Finance: Evidence from the Field,” Journal of Financial Economics 61 (2001), pp. 187–243, © 2001 with permission from Elsevier Science.

Essentially IRR answers to question "at what rate of return will the initial investment equal to net present value of project's cash flows?". IRR formula is explained in formula below.

The litmus test for project acceptance is this: a project should be accepted if the IRR exceeds the cost of capital, which typically serves as the hurdle rate.

This newsletter uses 4 scenarios to illustrate the limitations of IRR in project evaluation—a topic familiar to many. The newsletter also seeks to explore scenarios where the Modified Internal Rate of Return (MIRR) provides a more accurate assessment of the profitability of potential projects.

Consider the Scenario#1: Company A plans to raise capital at $100 to invest in either R&D Project A or Project B. Assuming the cost of fund is 10% per annum and management has prepared two sets of cash flows as follows.

At a glance, Project A stands out due to its higher rate of return and superior NPV. However, it is essential to recognize that a higher IRR typically indicates a higher level of risk, which generally corresponds with a lower NPV. Therefore, it seems counterintuitive that Project A not only yields a higher IRR but also a greater NPV of $35, compared to Project B’s NPV of $23, especially when taking into account the higher discount rate applied to Project A. This apparent contradiction requires a more thorough review. Although the inconsistency can be explained by the variations in the timing and patterns of cash flows between the two projects, it would be difficult for management to convincingly present or justify these cash flow projections to shareholders and investors, given the anomaly.

Scenario #2 below illustrates that both R&D Projects C and D while having NPV at $10, are derived from different discount rates, and varying cash flow patterns.

A higher IRR for Project C suggests a potentially higher return, but implies greater risk compared to Project D. Considering the increased risk, one might prefer Project D, as it generates the same NPV at a lower cost of capital. Moreover, this makes Project D less expensive to finance and significantly less risky to manage, with an IRR of 9.4%.

In Scenario #3 below, the IRR for Project E is calculated to be 0%, suggesting that the project is not profitable and therefore not a viable investment. However, this assessment seems flawed as the NPV of $11 (at cost of capital of 10%). Positive NPV indicates that Project E is expected to be profitable and will add value to the company.

Furthermore, there can be situations where a project exhibits multiple IRRs or none at all, especially when net cash outflows and inflows are expected throughout the project's life cycle. These fluctuations affect the IRR calculation, presenting an inaccurate assessment of the project profitability. Scenario #4 below exemplifies this with Project F, which has two IRRs. The presence of multiple IRRs can complicate management's evaluation process, making it more challenging to determine the true profitability and viability of the project.

Denote: At NPV = 0, IRR rests at 2.087% and 8.887%.

The inconsistent outcomes across all four scenarios suggest that the IRR technique may lack the rigor required to accurately handle cash flow series that fluctuate between negative and positive amounts throughout a project's lifespan. This limitation arises from the IRR's inherent sensitivity to irregular cash flows, which can lead to misleading conclusions about a project's profitability.

Now, let's examine how the Modified Internal Rate of Return (MIRR) overcomes the limitations of the traditional IRR, making it a reliable tool for evaluating potential projects -- what has been adjusted to make this enhancement?

MIRR can be interpreted as follows:

Revisiting Project E" (Scenario #3 where an IRR of 0% was originally calculated) and apply MIRR technique in following steps:

Step 1:	Present value back all "negative" incremental cash flow back to t=0, at cost of capital, 10%.
Step 2:	Projecting all "positive" incremental cash flows to the end of project period at t=5 at cost of capital 10%.
Step 3:	Apply formula to compute MIRR.

Denote: MIRR of 10.463% was derived at cost of capital of 10% and investment rate is 10%., as opposed to previous IRR at 0%. Using this approach, the MIRR for Project E at 10.463%, is slightly higher than the cost of capital of 10%. suggesting that Project E should be accepted.

Let's compute MIRR for Project F in Scenorio #4 (initially has more than one IRR).

Assuming at cost of capital of 8%, NPV for Project F" is estimated to be +$6,300. The MIRR is therefore calculated at 9.063% which is greater than cost of capital at 8%, indicating that Project is to be accepted by management.

Based on the above, the MIRR effectively addresses the issue of multiple IRR, providing a more reliable and consistent measure of a project's viability. This refinement is one of the key advantages of using MIRR over the standard IRR. The MIRR accounts for variations in cash flows by considering the reinvestment rate - the rate at which interim cash flows are reinvested into the project to foster revenue growth. This crucial aspect of reinvested capital has a direct impact on the project's financial health and growth, thereby offering a more realistic assessment of an investment's potential returns.

IRR, on the other hand, assumes that all positive cash flows are reinvested at the project's own rate of return, which is not always practical or achievable. Consequently, this assumption can lead to inaccurate and misleading assessments. As illustrated above, the MIRR effectively highlights the merits of a potential project compared to the conventional IRR technique. When used alongside other evaluation methods such as NPV method, MIRR produces a more accurate assessment of the project's financial viability, ultimately aiding management and investors in the financial decision-making process.

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