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Internal Rate of Return – Definition

Internal Rate of Return (IRR) Definition

Internal rate of return (IRR) refers to a metric utilized in capital budgeting to estimate how profitable potential investments are. Internal rate of return refers to a discount rate which makes all cash flow’s net present value (NPV) from a specific project equal to zero. Internal rate of return calculations depends on the exact formula NPV relies on.

Below is the formula for calculating Net Present Value:

The formula for calculating NPV.


“Ct” represents net cash flow during the t period

“Co” represents total initial investment costs

“r” represents the discount rate

“t” represents the number of time periods

In order to calculate IRR with the formula, NPV must be stealing equal to zero and then calculate for the (r) discount rate, which is the internal rate of return. Because of the formula’s nature, however, IRR can’t be solved analytically and instead, must be solved either by utilizing a software program or trial-and-error to calculate IRR.

In general, the higher the internal rate of return of a project, the more pleasant it is to take on. Internal rate of return is uniform for various types of investments, thus IRR can be utilized in ranking many likely projects on a somewhat even basis. In a situation where the investment costs are equal among the different projects, the project having the highest IRR will most likely be termed the best and thus, undertaken first.

Sometimes, IRR is referred to as “a discounted cash flow rate of return” or “economic rate of return.” Using “internal” implies external factor omission, like the capital or inflation cost, from the calculation.

A Little More on What is Internal Rate of Return – IRR

You can term internal rate of return as the growth rate a project is meant to generate. While the actual return rate that a specific project eventually generates often differs from its estimated IRR, a project having a substantially higher internal rate of return value than other available alternatives will still have a much better strong growth chance. One common use of IRR is its ability to compare the profitability of setting up new operations with the expanding existing ones. For instance, an energy company may utilize IRR to decide on either opening a new power plant or renovating and expanding a previously existing plant. While the two would possibly add value to the company, one would likely be the more logical decision as stated by IRR.

Theoretically speaking, any project whose IRR exceeds its capital cost is profitable, and thus it’s in the interest of a company to carry out such projects. In organizing investment projects, firms often set up a required rate of return (RRR) in order to ascertain the least acceptable return percentage which the specified investment must earn for it to be important. Any project having an IRR that surpasses the RRR would likely be considered profitable, even though companies won’t necessarily embark on a project solely for this reason. Instead, they would pursue projects having the highest IRR to RRR difference, as these would likely be the most profitable.

Furthermore, IRR can be compared to prevailing return rates in the securities market. In a situation where a firm cannot find any project with IRR surpassing the returns which can be gotten in the financial market, it may just decide on investing it’s retained revenue into the market.

Despite the fact that IRR is a metric that appeals to many, it should be utilized alongside with NPV for clarity of the value represented by a prospective project a firm might undertake.

Internal Rate of Return Issues

While IRR is very a very common metric in calculating a project’s profitability, if used alone, it can be misleading. Depending on the costs of the initial investment, a project may have an IRR that’s low but an NPV that is high. This means that while the company’s pace at seeing returns on the project might be slow, the same project may be adding a high overall value to the company.

A similar issue comes up when utilizing RRR in comparing projects of various lengths. For instance, a short-term project may have a high internal rate of return, making it look like a perfect investment, however, it may have a low net present value. Conversely, a long-term project may have a low internal rate of return, slowly and steadily earning returns, but may have huge additional value to the company eventually.

Another IRR issue is one relating to its common misuse as against an issue that focuses on the metric itself. There may be assumptions that when positive cash flows are created while a project is ongoing, the revenue would be reinvested at the return rate of the project. This can occur rarely. Instead, when there is a reinvestment of positive cash flows, it would be at a rate that is more similar to the cost of capital. When you miscalculate utilizing IRR this way might result in the belief that a project has more profitability that it truly is. This, coupled with the fact that long-term projects with varying cash flows may have many unique IRR values, has initiated the use of a different metric by the name modified internal rate of return (MIRR). In order to correct the issues, MIRR adjusts the IRR thus incorporating capital cost as the cash flow reinvestment rate, and how they exist as a single value. As a result of MIRR’s correction of the previous IRR issue, a project’s MIRR would often be much lower than the IRR of the same project.

Reference for Internal Rate of Return

Academic Research on Internal Rate of Return

The rate of interest, Fisher’s rate of return over costs and Keynes’ internal rate of return, Alchian, A. A. (1955). The American Economic Review, 938-943.

The modified internal rate of return and investment criterion, Lin, S. A. (1976). The Engineering Economist, 21(4), 237-247.

Accountants, too, could be happy in a golden age: the accountants rate of profit and the internal rate of return, Kay, J. A. (1976). Oxford Economic Papers, 28(3), 447-460.

The relevant internal rate of return, Hartman, J. C., & Schafrick, I. C. (2004). The Engineering Economist, 49(2), 139-158.

Uniqueness of the internal rate of return with variable life of investment, Arrow, K. J., & Levhari, D. (1969). The Economic Journal, 79(315), 560-566.

A sufficient condition for a unique nonnegative internal rate of return, Norstrøm, C. J. (1972). Journal of Financial and Quantitative Analysis, 7(3), 1835-1839.

Average internal rate of return and investment decisions: a new perspective, Magni, C. A. (2010). The Engineering Economist, 55(2), 150-180.

Present value versus internal rate of return-an essay in the theory of the third best, Turvey, R. (1963). The Economic Journal, 73(289), 93-98.

Relationship between the accounting and the internal rate of return measures: A synthesis and an analysis, Livingstone, J. L., & Salamon, G. L. (1970). Journal of Accounting Research, 8(2), 199-216.

The internal rate of return as a ranking criterion, Mao, J. C. (1966). The Engineering Economist, 11(4), 1-14.

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