# Internal Rate of Return(IRR)

Before undertaking any new project or investment, it is natural to do a cost-profit analysis of the same. That way, the concerned investor, be it an individual or a company, can understand how it compares with other projects. The Internal Rate of Return is one such measure in the broad realm of profitability ratios.

## What is the IRR?

The IRR also referred to as a discounted cash flow rate of return, is a discount rate that is supposed to equate the Net Present Value of all the cash flows – inflows and outflows – from a specific outlay to zero.

Alternatively, it can also be understood as the estimated compounded annual growth rate of a particular cost.

Analysts primarily use this metric in capital budgeting to estimate the profitability of investments or projects into consideration.

Typically, every company has a margin or a required rate of return (RRR) from a particular outlay or project that makes it worth the consideration.

Therefore, by virtue of being a profitability measure, the IRR of such a project must be equal to or more than that of RRR to be eligible for consideration.

However, it must be noted that IRR of a cost merely equalling it is RRR is not often the sole ground on which the cost-bearing entity takes a decision.

Instead, there are other quantitative and qualitative yardsticks to such costs that are also considered.

## What is the Formula for Internal Rate of Return?

The IRR formula is inherently the same as that of the Net Present Value (NPV) of cash flows. However, since the underlying principle of usage of NPV and IRR differs, the Internal Rate of Return is derived through trial and error and not analytically. That is because the precondition of NPV is equal to zero in the determination of IRR.

The Internal Rate of Return formula is as follows:

0 = CF0 + (CF1 / 1 + IRR) + (CF2 / 1 + IRR)^2 + … (CFn / 1 + IRR)^n

In this formula, CF0 stands for initial outlay/investment, CF1, CF2 … CFn denotes the future cash flows, n represents each period, and IRR is the acronym for Internal Rate of Return.

Or,

In this formula, NPV is the abbreviation for Net Present Value, t represents the total number of periods, Ct stands for cash flows for t period, and C0 is the initial cash outflow.

In all cases, the initial outlay, i.e. the C0 or the CF0 is always negative as it is an outflow. The subsequent cash flows can either be positive or negative.

Analysts often use financial calculators or software applications like Microsoft Excel to compute the IRR for a given array of cash flows. This can be owed to the fact that the formula is complex and might merit miscalculations.

### IRR Example

The Internal Rate of Return is predominantly used to evenly rank the profitability of varying projects or investments, assuming the investments are similar for all of them. Since IRR is a product of trial and error, its determination for a single venture might take multiple attempts.

Nevertheless, a simple example is provided below to exemplify the usage of IRR as a metric in capital budgeting.

Example: LLC Limited is considering whether to undertake Project A – opening a new warehouse – or Project B – renovating and expanding its existing warehouse. Both are expected to add value to the organization, but the management is torn between the options.

Project A would require an investment of Rs.20 lakh (CF0) and future cash flows from it for the next 3 years are estimated to be Rs.7 lakh (CF1), 8 lakh (CF2), and 9 lakh (CF3) respectively. LLC Limited tries out a discount rate of 5% (IRR).

So, as per the formula –

Since, NPV ≠ 0, therefore, a higher discount rate must be considered. Let’s consider a discount rate of 9%. Ergo,

Therefore, the IRR for Project A is 9%

Project B would require an outlay of Rs.15 lakh (CF0) and estimated cash flows from it for the next 3 years stand at Rs.5 lakh, Rs.6.5 lakh, and Rs.7 lakh respectively. LLC Limited considers an IRR of 9% at first.

Since the NPV is positive, let’s consider a higher IRR of 11%.

Therefore, IRR for Project B is 11%. Since, Project B, i.e. renovation and expansion of an existing warehouse, yields a better Internal Rate of Return, LLC Limited can go forward with this.

## How is IRR Interpreted?

The Internal Rate of Return is primarily an indicator of the profitability of prospective investments or projects. However, since it is based on speculative figures, it might differ from the actual profitability.

Nevertheless, analysts can still draw particular inferences from the metric, which are –

• Higher IRR is better

As perhaps substantiated in the example above, a higher IRR indicates better profitability of an outlay. Therefore, analysts use this metric to compare varying projects to determine which one would be worth the while and money.

• IRR vis-á-vis NPV

Analysts most commonly use IRR as a profitability metric, vis-á-vis the Net Present Value. It provides a clearer understanding of the same.

For instance, a high Internal Rate of Return but a low NPV is indicative that while the returns might witness substantial annual growth, it will not add much value to the cost-bearing entity. It is typical for projects of short duration.

Conversely, a low IRR but a high NPV suggests that even though the returns might be slow, it would reward significant value to an organization. It is usual for projects of a long duration.

### Limitations of IRR as a Metric?

Even though the Internal Rate of Return is a significant metric to reckon the expected compounded annual growth of prospective outlays, it falls short in some areas. These are –

• Overly optimistic

The IRR is overly positive in its inference. Although the IRR discounts the growth rate from the initial outlay as well as future reinvestments in a project, it does not account for the inherent nature of such reinvestment.

Typically, reinvestment takes place at the cost of capital and not in the rate of return, as inferences drawn solely from IRR wrongly posit. It leads the Internal Rate of Return to posit an overestimation of future cash flow.

• Multiple IRR for a single investment

A critical shortcoming of IRR as a metric is that a single project might have multiple IRR. It mainly holds when a specific project is expected to generate both positive and negative periodical cash flows across its tenure. It inevitably confuses analysts and negates the IRR’s utility as a metric for profitability.

Therefore, analysts use another metric to counter the shortcomings of IRR, called the Modified Internal Rate of Return (MIRR).

## MIRR vs IRR

The Modified Internal Rate of Return considers the cost of capital when accounting for reinvestment of positive cash flows – an issue that IRR overlooks. Furthermore, irrespective of whether a project is expected to generate both positive and negative cash flows, MIRR shows a single value for it, unlike IRR that might have multiple values for the same.

Since the Modified Rate of Return rights the issues persistent with IRR and its inference, it is lower than the Internal Rate of Return. MIRR thus portrays a much more realistic growth rate estimation, over IRR.

## Application of IRR

This is a very important concept in corporate finance as business firms are ultimately concerned with earning a rate of return on every investment that is higher than the cost of capital.

This can also be effectively applied in portfolio management whereby only those investment avenues that yield a high IRR can be accepted.

Consider an investment of Rs 10,000 that grows to Rs.11,000 at the end of the year. The yield is 10%. This would not be able to compute the impact of varying cash inflows or outflows during the year.

## Investing Based on IRR

The internal rate of return can be considered as a guideline for assessing whether one must go ahead with the project and investment or not. According to the general rule of IRR, if the IRR on an investment is higher than the cost of capital, then the investment can be taken ahead.

On the other end, if the IRR on an investment is lower than the cost of capital, then it is better to avoid the investment or the project.

## Conclusion

In conclusion, IRR is becoming a popular method of computing returns especially in portfolio management and mutual funds where there are several annuities involved with different time periods.

Disclaimer: The views expressed in this post are that of the author and not those of Groww

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