Internal Rate of Return (IRR)
The discount rate that will cause the NPV of an investment to equal 0.
Examples of Internal Rate of Return (IRR) in the following topics:

Calculating and Understanding Average Returns
 Average returns are commonly found using average ROI, CAGR, or IRR.
 Average ROI generally does not calculate the actual average rate of return, because it does not incorporate compounding returns.
 The internal rate of return (IRR) is another commonly used method for calculating the average return .
 IRR is the discount rate at which the net present value (NPV) is equal to 0.
 The IRR is calculated by finding the discount rate at which the NPV of the investment equals 0.

Defining the Cost of Capital
 The cost of capital is the rate of return that could be earned on an investment with similar risk.
 The cost of capital can be compared to the internal rate of return (IRR) of a project or investment.
 IRR is the rate of return that makes the net present value of all cash flows from an investment equal zero.
 Equation used to determine net present value, and therefore internal rate of return.
 DPV = discounted net present value, N = total number of periods in which a cash flow occurs, t = the specific period of the cash flow, FV = the value of the future cash flow, and i = internal rate of return.

Defining the IRR
 IRR is a rate of return used in capital budgeting to measure and compare the profitability of investments; the higher IRR, the more desirable the project.
 The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investments.
 It is also called the "discounted cash flow rate of return" (DCFROR) or the rate of return (ROR).
 The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.
 Explain how Internal Rate of Return is used in capital budgeting

Advantages of the IRR Method
 The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investment.
 In other words, 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 addition, the internal rate of return is a rate quantity, it is an indicator of the efficiency, quality, or yield of an investment.
 Internal rate of return is the rate at which the NPV of an investment equals 0.
 Describe the advantages of using the internal rate of return over other types of capital budgeting methods

Ranking Investment Proposals
 An NPV calculated using variable discount rates (if they are known for the duration of the investment) better reflects the situation than one calculated from a constant discount rate for the entire investment duration.
 The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.
 IRR calculations are commonly used to evaluate the desirability of investments or projects.
 ARR calculates the return, generated from net income of the proposed capital investment.
 If the ARR is equal to or greater than the required rate of return, the project is acceptable.

Multiple IRRs
 In a series of cash flows like (−10, 21, −11), one initially invests money, so a high rate of return is best, but then receives more than one possesses, so then one owes money, so now a low rate of return is best.
 Accordingly, Modified Internal Rate of Return (MIRR) is used, which has an assumed reinvestment rate, usually equal to the project's cost of capital.
 It has been shown that with multiple internal rates of return, the IRR approach can still be interpreted in a way that is consistent with the present value approach provided that the underlying investment stream is correctly identified as net investment or net borrowing.
 Apparently, managers find it easier to compare investments of different sizes in terms of percentage rates of return than by dollars of NPV.
 Determine the best way to evaluate a project that has multiple internal rates of return

Disadvantages of the IRR Method
 IRR can't be used for exclusive projects or those of different durations; IRR may overstate the rate of return.
 In addition, IRR assumes reinvestment of interim cash flows in projects with equal rates of return (the reinvestment can be the same project or a different project).
 Therefore, IRR overstates the annual equivalent rate of return for a project whose interim cash flows are reinvested at a rate lower than the calculated IRR.
 This presents a problem, especially for high IRR projects, since there is frequently not another project available in the interim that can earn the same rate of return as the first project.
 Modified Internal Rate of Return (MIRR) does consider cost of capital and provides a better indication of a project's efficiency in contributing to the firm's discounted cash flow.

Calculating the IRR
 Given a collection of pairs (time, cash flow), a rate of return for which the net present value is zero is an internal rate of return.
 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 is zero is an internal rate of return.
 Because the internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero, then the IRR r is given by the formula:
 If the IRR is less than the cost of capital, reject the project.

Calculating the Yield of an Annuity
 The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.
 The second popular method is called the internal rate of return (IRR).
 The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0.
 This investment has an implicit rate of return, but you don't know what it is.
 Calculate the yield of an annuity using the internal rate of return method

Modified IRR
 The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness.
 As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.
 While there are several problems with the IRR, MIRR resolves two of them.
 Firstly, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them.
 To calculate the MIRR, we will assume a finance rate of 10% and a reinvestment rate of 12%.