IRR - Definitions, Uses, Formulas with Examples

Internal Rate of Return (IRR)

IRR is a metric which used in capital budgeting to estimate the profitability of an investment for the project. The internal rate of return is the annualized effective compounded return rate or rate of return that make the net present value (NPV) of all cash flows from a particular investment equal to zero. 

OR, IRR of an investment is the discounted rate at which that the net present value of the costs of the investment equals the net present value of the benefits of the investments. IRR calculation rely on the same formula as NPV does.

Uses

The internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment. This is in contrast with the net present value, which is an indicator of the value or magnitude of an investment. An investment is considered acceptable if its internal rate of return is greater than an established minimum acceptable rate of return or cost of capital. In a scenario where an investment is considered by a firm that has equity holders, this minimum rate is the cost of capital of the investment (which may be determined by the risk-adjusted cost of capital of alternative investments). This ensures that the investment is supported by equity holders since, in general, an investment whose IRR exceeds its cost of capital adds value for the company (i.e., it is economically profitable). Any project with an IRR that exceeds the RRR will likely be deemed a profitable one, although companies will not necessarily pursue a project on this basis alone. Rather, they will likely pursue projects with the highest difference between IRR and RRR, as these likely will be the most profitable.

Examples

If your company's cost of capital is 6 percent, then any investment or project that will yield an internal rate of return higher than 6 percent is feasible. If your company is presented with an opportunity to purchase long-term Treasury bonds at 4 percent, this IRR of 4 percent is below your cost of capital and, therefore, is an unwise investment. However, say another investment opportunity arises which, upon further analysis, your accountant determines will yield an IRR of 10 percent. Your company should invest in that project, because the internal rate of return exceeds 6 percent.

Calculation :

Invest ₹2,000 now, receive 3 yearly payments of ₹100 each, plus ₹2,500 in the 3rd year.

Let us try 10% interest:

• Now: PV = -₹2,000
• Year 1: PV = ₹100 / 1.10 = ₹90.91
• Year 2: PV = ₹100 / 1.10^² = ₹82.64
• Year 3: PV = ₹100 / 1.10^³ = ₹75.13
• Year 3 (final payment): PV = ₹2,500 / 1.10^³ = ₹1,878.29

Adding those up gets:

NPV = -₹2,000 + ₹90.91 + ₹82.64 + ₹75.13 + ₹1,878.29 = ₹126.97

(continued) at 12.4% interest rate

• Now: PV = -₹2,000
• Year 1: PV = ₹100 / 1.124 = ₹88.97
• Year 2: PV = ₹100 /1.124^² = ₹79.15
• Year 3: PV = ₹100 / 1.124^³ = ₹70.42
• Year 3 (final payment): PV = ₹2,500 / 1.124^³= ₹1,760.52

Adding those up gets:

NPV = -₹2,000 + ₹88.97 + ₹79.15 + ₹70.42 + ₹1,760.52 = -₹0.94

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