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# What is IRR (Internal Rate of Return) | Formula, Examples

What is Internal Rate of Return | Meaning, Calculation? In the previous articles, we have given Definitions and New Rates of CRR, SLR, Repo Rate, Reverse Repo Rate and Partnership Firm Registration Procedure in IndiaToday we are discussing what is IRR, and it’s formula with examples. Internal Rate of Return (IRR) is a financial metric for cash flow analysis, primarily for evaluating investments, capital acquisitions, project proposals, programs, and business case scenarios. Like other cash flow metrics (net present value, payback period, and return on investment), IRR takes an “investment view” of expected financial results. As a result, each of these Financial Metrics compares the magnitudes and timing of cash flow return

As a result, each of these Financial Metrics compares the magnitudes and timing of cash flow return on cash flow costs, while each makes the comparison in its own way, and each carries a unique message about the value of the action. An internal rate of return is a discount rate that makes the net present value(NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.

The following is the formula for calculating NPV: where:

Ct = net cash inflow during the period t

Co= total initial investment costs

r = discount rate, and

t = number of time periods

The formula for IRR is:

0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and IRR equals the project’s internal rate of return.

Let’s look at an example to illustrate how to use IRR.

Assume Company ABC must decide whether to purchase a piece of factory equipment for \$300,000. The equipment would only last three years, but it is expected to generate \$150,000 of additional annual profit during those years. Company ABC also thinks it can sell the equipment for scrap afterward for about \$10,000. Using IRR, Company ABC can determine whether the equipment purchase is a better use of its cash than its other investment options, which should return about 10%.

Here is how the IRR equation looks in this scenario:

0 = -\$300,000 + (\$150,000)/(1+.2431) + (\$150,000)/(1+.2431)2 + (\$150,000)/(1+.2431)3 + \$10,000/(1+.2431)4

The investment’s IRR is 24.31%, which is the rate that makes the present value of the investment’s cash flows equal to zero. From a purely financial standpoint, Company ABC should purchase the equipment since this generates a 24.31% return for the Company –much higher than the 10% return available from other investments.

A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function.

Uses of IRR

Profitability of an Investment

Corporations use 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 a project’s IRR, the more desirable it is to undertake the project. If all projects require the same amount of up-front investment, the project with the highest IRR would be considered the best and undertaken first.

Maximizing Net Present Value

The internal rate of return is an indicator of the profitability, efficiency, quality, or yield of an investment. This is in contrast with the net present value, which is an indicator of the net value or magnitude added by making an investment.

Applying the internal rate of return method to maximize the value of the firm, any investment would be accepted, if its profitability, as measured by the internal rate of return, is greater than a minimum acceptable rate of return. The appropriate minimum rate to maximize the value added to the firm is the cost of capital, i.e. the internal rate of return of a new capital project needs to be higher than the company’s cost of capital. This is because an investment with an internal rate of return which exceeds the cost of capital has a positive net present value.

However, the selection of investments may be subject to budget constraints, or they may be mutually exclusive competing projects, such as a choice between or the capacity or ability to manage more projects may be practically limited. In the example cited above, of a corporation comparing an investment in a new plant versus an extension of an existing plant, there may be reasons the company would not engage in both projects.

Fixed Income

IRR is also to calculate yield to maturity and yield to call.

Liabilities

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

Capital Management

Corporations use internal rate of return to evaluate share issues and stock Buyback programs. Share repurchase proceeds if returning capital to shareholders has a higher internal rate of return than candidate capital investment projects or acquisition projects at current market prices. Funding new projects by raising new debt may also involve measuring the cost of the new debt in terms of the yield to maturity(internal rate of return).

Private Equity

IRR is also used for private equity, from the limited partners’ perspective, as a measure of the general partner’s performance as an investment manager. This is because it is the general partner who controls the cash flows, including the limited partners’ draw-downs of committed capital.

Net Present Value vs Discount Rate: The graph shows that increasing the discount rate lowers NPV for both streams. The graph also shows how cash flow streams with a positive total net cash flow can produce NPVs that are either positive or negative, depending on discount rate.

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