# Internal Rate of Return (IRR) Calculator

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

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

A 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. IRR is also used for private equity , from the limited partners' perspective, as a measure of the general partner's performance as investment manager.

Given a collection of pairs time , cash flow involved in a project, the internal rate of return follows from the net present value as a function of the rate of return. A rate of return for which this function being zero is the internal rate of return. Any fixed time can be used in place of the present e. In the case that the cash flows are random variables , such as in the case of a life annuity , the expected values are put into the above formula.

In this case, numerical methods or graphical methods must be used. Different accounting packages may provide functions for different accuracy levels. Of particular interest is the case where the stream of payments consists of a single outflow, followed by multiple inflows occurring at equal periods. In the above notation, this corresponds to:. In this case the NPV of the payment stream is a convex , strictly decreasing function of interest rate.

There is always a single unique solution for IRR. This is sometimes referred to as the Hit and Trial or Trial and Error method. More accurate interpolation formulas can also be obtained: If applied iteratively, either the secant method or the improved formula always converges to the correct solution. Both the secant method and the improved formula rely on initial guesses for IRR. The following initial guesses may be used:. As a tool applied to making an investment decision, to decide whether a project adds value or not, comparing the IRR of a single project with the required rate of return, in isolation from any other projects, is equivalent to the NPV method.

If the appropriate IRR if such can be found correctly is greater than the required rate of return, then using the required rate of return to discount cash flows to their present value, the NPV of that project will be positive, and vice versa. When the objective is to maximize total value, the calculated IRR should not be used to choose between mutually exclusive projects. In cases where one project has a higher initial investment than a second mutually exclusive project, the first project may have a lower IRR expected return , but a higher NPV increase in shareholders' wealth and should thus be accepted over the second project assuming no capital constraints.

When the objective is to maximize total value, IRR should not be used to compare projects of different duration. For example, the net present value added by a project with longer duration but lower IRR could be greater than that of a project of similar size, in terms of total net cash flows, but with shorter duration and higher IRR.

However, NPV remains the "more accurate" reflection of value to the business. IRR, as a measure of investment efficiency may give better insights in capital constrained situations. However, when comparing mutually exclusive projects, NPV is the appropriate measure. Maximizing total value is not the only conceivable possible investment objective. An alternative objective would for example be to maximize long-term return.

Such an objective would rationally lead to accepting first those new projects within the capital budget which have the highest IRR, because adding such projects would tend to maximize overall long-term return.

To see this, consider two investors, Max Value and Max Return. Max Value wishes her net worth to grow as large as possible, and will invest every last cent available to achieve this, whereas Max Return wants to maximize his rate of return over the long term, and would prefer to choose projects with smaller capital outlay but higher returns.

Max Value and Max Return can each raise up to , US dollars from their bank at an annual interest rate of 10 percent paid at the end of the year. Big-Is-Best requires a capital investment of , US dollars today, and the lucky investor will be repaid , US dollars in a year's time.

Small-Is-Beautiful only requires 10, US dollars capital to be invested today, and will repay the investor 13, US dollars in a year's time. Both investments would be acceptable to both investors, but the twist in the tale is that these are mutually exclusive projects for both investors, because their capital budget is limited to , US dollars. How will the investors choose rationally between the two? So there is no squabbling of who gets which project, they are each happy to choose different projects.

How can this be rational for both investors? The answer lies in the fact that the investors do not have to invest the full , US dollars. Max Return is content to invest only 10, US dollars for now. After all, Max Return may rationalize the outcome by thinking that maybe tomorrow there will be new opportunities available to invest the remaining 90, US dollars the bank is willing to lend Max Return, at even higher IRRs. Even if only seven more projects come along which are identical to Small-Is-Beautiful, Max Return would be able to match the NPV of Big-Is-Best, on a total investment of only 80, US dollars, with 20, US dollars left in the budget to spare for truly unmissable opportunities.

Max Value is also happy, because she has filled her capital budget straight away, and decides she can take the rest of the year off investing. In this case, it is not even clear whether a high or a low IRR is better. Examples of this type of project are strip mines and nuclear power plants, where there is usually a large cash outflow at the end of the project.

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