Mathematically the IRR is defined as any discount rate that results in a net present value of zero of a series of cash flows.

If the internal rate of return is less than the cost of borrowing used to fund your project, the project will clearly be a money-loser. However, usually a business owner will insist that in order to be acceptable, a project must be expected to earn an IRR that is at least several percentage points *higher* than the cost of borrowing, to compensate the company for its risk, time, and trouble associated with the project.

*C _{t}* = cash flow in period

*t*, and

*N*= the number of periods.

##### Example:

Assume that a company has following cash flows for 5 periods ahead.

Year | 0 | 1 | 2 | 3 | 4 |

Cash Flow | -100 | +30 | +35 | +40 | +45 |

The IRR of an investment is the interest rate that will give it a net present value of zero.

Oddly, IRR is calculated trough trial and error method. For the example above, the IRR is 17.09

IRR analysis is generally used to evaluate the project's cash flows, rather than the income from the project that would be shown on an income statement (also known as the profit and loss statement). Why? Because income on a P&L reflects depreciation, but depreciation is not an out-of-pocket expense. For instance, if revenue of $10,000 is reduced to $7,000 of income because of a $3,000 depreciation deduction, you still have the use of the full $10,000. So the cash flow figure of $10,000 is usually the more instructive one to look at. However, if you are very concerned about the appearance of your income statement (for example, if you anticipate putting the business up for sale or seeking major financing in the future, or if you're under stockholder pressure for increased income) you may decide that the income figure is more appropriate to use.

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