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 the Yield of an Annuity
 Calculate the yield of an annuity using the internal rate of return method 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 Internal Rate of Return (IRR) is the discount rate at which the NPV of an investment equals 0.
 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.
 Net Present Value (NPV) (noun) The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision.
 yield (noun) In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return. Yield applies to various stated rates of return on stocks (common and preferred, and convertible), fixed income instruments (bonds, notes, bills, strips, zero coupon), and some other investment type insurance products
 Internal Rate of Return (IRR) (noun) The discount rate that will cause the NPV of an investment to equal 0.

Calculating and Understanding Average Returns
 Differentiate between the different methods for calculating the average return of an investment Average returns are commonly found using average ROI, CAGR, or IRR.
 Internal rate of return (IRR) is the discount rate at which the NPV equals 0.
 The three main methods are Return on investment (ROI) Compound annual growth rate (CAGR) Internal rate of return (IRR).
 The internal rate of return (IRR) is another commonly used method for calculating the average return .
 The IRR is calculated by finding the discount rate at which the NPV of the investment equals 0.
 compounding returns (noun) Returns earned on previous returns. Akin to compounding interest.

Advantages of the IRR Method
 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.
 The internal rate of return is a rate quantity, an indicator of the efficiency, quality, or yield of an investment.
 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.
 Internal rate of return is the rate at which the NPV of an investment equals 0.
 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.
 cost of capital (noun) the rate of return that capital could be expected to earn in an alternative investment of equivalent risk
 capital budgeting (noun) The budgeting process in which a company plans its capital expenditure (the spending on assets of longterm value).

Defining the IRR
 Explain how Internal Rate of Return is used in capital budgeting 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).
 In the context of savings and loans the IRR is also called the "effective interest rate
 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.
 effective interest rate (noun) The effective interest rate, effective annual interest rate, annual equivalent rate (AER), or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.

Multiple IRRs
 Determine the best way to evaluate a project that has multiple internal rates of return When cash flows of a project change sign more than once, there will be multiple IRRs; in these cases NPV is the preferred measure.
 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.
 mutually exclusive (adjective) Describing multiple events or states of being such that the occurrence of any one implies the nonoccurrence of all the others.
 Modified Internal Rate of Return (noun) The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. 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.

Defining Capital Budgeting
 Major methods for capital budgeting include Net present value, Internal rate of return, Payback period, Profitability index, Equivalent annuity and Real options analysis.
 Many formal methods are used in capital budgeting, including the techniques as followed: Net present value Internal rate of return Payback period Profitability index Equivalent annuity Real options analysis Net Present Value Net present value (NPV) is used to estimate each potential project's value by using a discounted cash flow (DCF) valuation.
 Internal Rate of Return The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero.
 One shortcoming of the IRR method is that it is commonly misunderstood to convey the actual annual profitability of an investment.
 Accordingly, a measure called "Modified Internal Rate of Return (MIRR)" is often used.
 APT (noun) In finance, arbitrage pricing theory (APT) is a general theory of asset pricing that holds, which holds that the expected return of a financial asset can be modeled as a linear function of various macroeconomic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factorspecific beta coefficient.
 Modified Internal Rate of Return (noun) The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. 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.

Disadvantages of the IRR Method
 Describe the disadvantages of using IRR for capital budging purposes IRR can't be used for exclusive projects or those of different durations; IRR may overstate the rate of return.
 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.
 Project A has a higher NPV (for certain discount rates), even though its IRR (= xaxis intercept) is lower than for project B 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.
 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.
 mutually exclusive (adjective) Describing multiple events or states of being such that the occurrence of any one implies the nonoccurrence of all the others.
 duration (noun) A measure of the sensitivity of the price of a financial asset to changes in interest rates, computed for a simple bond as a weighted average of the maturities of the interest and principal payments associated with it

NPV Profiles
 The NPV Profile is a graph with the discount rate on the xaxis and the NPV of the investment on the yaxis.
 The discount rate at which the NPV equals 0 is called the internal rate of return (IRR).
 When the value of the outflows is greater than the inflows, the NPV is negative.
 A special discount rate is highlighted in the IRR, which stands for Internal Rate of Return.
 And it is the discount rate at which the value of the cash inflows equals the value of the cash outflows.
 discount rate (noun) The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
 internal rate of return (noun) IRR. The rate of return on an investment which causes the net present value of all future cash flows to be zero.

Defining the Cost of Capital
 IRR is the rate of return that makes the net present value of all cash flows from an investment equal zero.
 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.

Modified IRR
 Calculate a project's modified internal rate of return The MIRR is a financial measure of an investment's attractiveness; it is used to rank alternative investments of equal size.
 MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the 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.
 Firstly, IRR assumes that interim positive cash flows are reinvested at the same rate of return as that of the project that generated them.
 cost of capital (noun) the rate of return that capital could be expected to earn in an alternative investment of equivalent risk
 reinvestment rate (noun) The annual yield at which cash flows from an investment can be reinvested.