INTERNAL RATE OF RETURN: WHAT IT IS FOR, CALCULATION AND EXAMPLES - DUDAS - 2025

The internal rate of return (IRR) is an indicator used in capital budgeting to estimate the return on likely investments. It is the deduction rate that causes the net present value (NPV) of the total cash flows of a specific project to be equal to zero.

The term “internal” refers to the fact that the calculation of this rate excludes external factors, such as inflation, the cost of capital or various financial risks.

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For a fixed income investment in which the money is deposited only once, the interest on this deposit is paid to the investor at a specific interest rate each period of time. If the original deposit does not increase or decrease, it would have an IRR equal to the specified interest rate.

IRR assessment

Receiving a certain return on investment at one point is worth more than receiving the same return at a later time. Therefore, the latter would produce a lower IRR than the former, if all other factors are equal.

An investment that has the same total returns as a previous investment, but lags returns for one or more periods of time, would have a lower IRR.

Although the actual rate of return that a given project ends up generating will often be different from its estimated internal rate of return, a project with a substantially higher IRR amount will have a much greater chance of strong growth than other alternatives. available.

What is the internal rate of return for?

You can think of the internal rate of return as the expected growth rate that a project will generate.

Return on an investment

Corporations use the IRR in capital budgeting to compare the profitability of capital projects in terms of the rate of return.

For example, a corporation will compare an investment in a new plant versus an extension of an existing plant based on the IRR of each project. To maximize returns, the higher the IRR of a project, the more desirable it is to undertake the project.

To maximize return, the project with the highest IRR would be considered the best, and will be done first.

Maximize net present value

The IRR is an indicator of the profitability, efficiency or performance of an investment. This contrasts with the net present value. This is an indicator of the net worth or magnitude added when making an investment.

Applying the IRR method to maximize the value of the company, any investment would be accepted if its profitability, measured by the internal rate of return, is greater than the minimum acceptable rate of return.

The minimum rate appropriate to maximize value added for the business is the cost of capital. That is, the internal rate of return on a new project must be greater than the company's cost of capital.

This is because only an investment with an internal rate of return that exceeds the cost of equity has a positive net present value.

However, the selection of investments may be subject to budgetary restrictions. There may also be mutually exclusive competing projects, or the ability to manage more projects may be virtually limited.

In the example of the corporation comparing an investment in a new plant to expanding an existing plant, there could be reasons why the company would not participate in both projects.

Fixed rent

The IRR is also used to calculate the yield to maturity and the yield on amortization.

passive

The internal rate of return and the net present value can be applied to both liabilities and investments. For a liability, a lower internal rate of return is preferable to a higher one.

Capital management

Corporations use the internal rate of return to evaluate share issues and share buyback programs.

The benefit of a share buyback occurs if the return of equity to shareholders has a higher internal rate of return than candidate equity investment projects or acquisition projects at current market prices.

Financing new projects by obtaining new debt may also involve measuring the cost of new debt in terms of yield to maturity (internal rate of return).

Private capital

The IRR is also used for private equity, from the perspective of limited partners. It is used as an indicator of the performance of the general partner as an investment manager.

This is because the general partner is the one who controls the cash flows, including the reduction of the committed capital of the limited partners.

How is it calculated?

Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return is derived from the net present value as a function of the rate of return. The internal rate of return will be a rate of return for which this function is zero.

Given the pairs (period, cash flow) (n, Cn) where n is a non-negative integer, N is the total number of periods, and NPV is the net present value. The IRR is given by r, according to the formula:

Formula considerations

The C0 value, which is less than or equal to 0, corresponds to the initial investment at the beginning of the project.

Period n is generally given in years. However, the calculation can be made simpler by calculating r using the period in which most of the problem is defined. For example, months are used if the majority of cash flows occur at monthly intervals.

Any fixed time can be used in place of the present (for example, the end of an annuity interval); the value obtained is zero if and only if the NPV is zero.

In the case that the cash flows are random variables, as in the case of an annuity, the expected values ​​are placed in the previous formula.

Ways to calculate IRR

Often times, the value of r that satisfies the above equation cannot be found analytically. In this case, numerical or graphical methods must be used.

The IRR in practice is calculated by trial and error. This is because there is no analytical way to calculate when the net present value will equal zero. The calculation of the internal rate of return can be done in three ways:

- Using the IRR function in Excel or other spreadsheet programs

- Use a financial calculator

- Using an iterative process, where the analyst tries different discount rates until the NPV is equal to zero.

Interpretation

The internal rate of return rule is a guide for evaluating whether to proceed with a project or investment.

The IRR rule states that if the internal rate of return on a project or investment is greater than the required minimum rate of return, usually the cost of capital, then the project or investment must continue.

Conversely, if the IRR on a project or investment is less than the cost of capital, then rejecting it may be the best course of action.

How to interpret it

Theoretically, any project with an internal rate of return greater than its cost of capital is beneficial. Therefore, it is in the company's interest to promote such projects.

When planning investment projects, companies will establish an internal opportunity rate (TIO) to determine the minimum acceptable percentage of return that the investment in question must obtain in order to take it into consideration.

Any project that has an IRR greater than the TIO will likely be considered profitable. However, companies will not necessarily search for a project based on this alone.

Rather, they may be pursuing projects with the largest difference between IRR and TIO. These will surely be the ones with the highest profitability.

Also the IRR can be compared with the prevailing rates of return in the stock market.

In the event that a company cannot find projects with an IRR greater than the returns that can be obtained in financial markets, it may prefer to simply invest its retained earnings in these markets.

Although for many the IRR is an attractive indicator, it should always be used in conjunction with the net present value to get a better picture of the value that represents a probable project that a company can start.

Examples

Example 1

Let an investment be defined by the following sequence of cash flows. Then the IRR r is given by:

In this case, the answer is 5.96%, since for the equation to be satisfied, the calculation of r is: r = 0.0596.

Example 2

Suppose you want to open a pizzeria. All costs and profits are calculated for the next two years and then the NPV for the business is calculated at various internal opportunity rates. At 6%, you get a net present value of $ 2,000.

However, the net present value must be zero, so a higher internal opportunity rate is tested, assume 8% interest.

At 8%, the calculation of the NPV gives a net loss of - $ 1,600. Now it is negative. So an internal opportunity rate is tested between the two, say with 7% interest. 7% yields a net present value of $ 15.

That is close enough to zero that the internal rate of return can be estimated to be only slightly above 7%.

References

1. Adam Hayes (2019). Internal Rate of Return (IRR) Definition. Taken from: investopedia.com.
2. Wikipedia, the free encyclopedia (2019). Internal rate of return. Taken from: en.wikipedia.org.
3. CFI (2019). Internal Rate of Return (IRR). Taken from: corporatefinanceinstitute.com.
4. Wall Street Mojo (2019). Internal Rate of Return (IRR). Taken from: wallstreetmojo.com.
5. Investing Answers (2019). Internal Rate of Return (IRR). Taken from: investinganswers.com.
6. The Balance (2019). How to Calculate Your Internal Rate of Return. Taken from: thebalance.com.