Internal Rate of Return

10 Key excerpts on "Internal Rate of Return"

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  Fundamentals of Engineering Economic Analysis

  • John A. White, Kellie S. Grasman, Kenneth E. Case, Kim LaScola Needy, David B. Pratt(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  The more common name, however, is Internal Rate of Return (IRR). Math- ematically, investment j’s Internal Rate of Return, denoted i j * , satisfies the following equality: 0 = ∑ t=0 n A jt (1 + i j * ) n−t (6.1) In words, the Internal Rate of Return is the interest rate that makes the future worth of an investment equal 0. Likewise, it is the interest rate that equates the present worth and annual worth to 0. If the Internal Rate of Return is at least equal to the MARR, the invest- ment should be made. 6.1.1 IRR Calculations—Single Alternative As with other DCF methods, when applied to a single alternative, IRR is used to determine whether the investment opportunity is preferred to the do-nothing alternative. Video Lesson: Rate of Return Internal Rate of Return (IRR) The interest rate that makes the present worth, the future worth, and the annual worth equal to 0. Also referred to as the discounted cash flow rate of return, the cash flow rate of return, the rate of return (ROR), the return on investment (ROI), and the true rate of return. EXAMPLE 6.1 The Surface Mount Placement Machine Investment Recall the manager of an electronics manufacturing plant who was asked to approve the purchase of a surface mount placement (SMP) machine having an initial cost of $500,000 in order to reduce annual operating and maintenance costs by $92,500 per year. At the end of the 10-year planning horizon, it was estimated that the SMP machine would be worth $50,000. Using a 10% MARR and Internal Rate of Return analysis, should the investment be made? Key Data Given The cash flows shown in Figure 6.1; MARR = 10%; planning horizon = 10 years Find The IRR of the investment.

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  Finance

  Capital Markets, Financial Management, and Investment Management

  • Frank J. Fabozzi, Pamela Peterson Drake(Authors)
  • 2009(Publication Date)
  • Wiley

    (Publisher)

  The index value is greater than one, which means that the investment produces more in terms of benefits than costs. An advantage of using the profitability index is that it translates the dollar amount of NPV into an indexed value, providing a measure of the benefit per dollar investment. This is helpful in ranking projects in cases in which the capital budget is limited.

  The decision rule for the profitability index depends on the PI relative to 1.0, which means

  Internal Rate of Return

  Suppose an investment opportunity requires an initial investment of $1 million and has expected cash inflows of $0.6 million after one year and another $0.6 million after two years. This opportunity is shown in Figure 14.3 using a time line.

  The return on this investment (denoted by Internal Rate of Return or IRR, in the next equation) is the discount rate that causes the present values of the $0.6 million cash inflows to equal the present value of the $1 million cash outflow, calculated as

  Another way to look at this is to consider the investment’s cash flows discounted at the IRR of 10%. The NPV of this project if the discount rate is 13.0662% (the IRR in this example), is zero:

  An investment’s Internal Rate of Return is the discount rate that makes the present value of all expected future cash flows equal to zero. We can represent the IRR as the rate that solves Going back to Project X, the IRR for this project is the discount rate that solves Using a calculator or a computer, we get the answer of 10.172% per year.

  FIGURE 14.3

  Timeline of Investment Opportunity

  Looking back at the investment profiles of Projects X and Y, each profile crosses the horizontal axis (where NPV = 0) at the discount rate that corresponds to the investment’s IRR. This is no coincidence: by definition, the IRR is the discount rate that causes the project’s NPV to equal zero.

  The IRR is a yield—what is earned, on average, per year. How do you use it to decide which investment, if any, to choose? Let’s revisit Projects X and Y and the IRRs we just calculated for each. If, for similar risk investments, owners earn 10% per year, then both Projects X and Y are attractive. They both yield more than the rate owners require for the level of risk of these two investments:

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  Strategic Finance for Criminal Justice Organizations

  • Daniel Adrian Doss, William H. Sumrall III, Don W. Jones(Authors)
  • 2017(Publication Date)
  • Routledge

    (Publisher)

  In Missoula, Montana, the consideration of a 20% to 25% rate of return was considered regarding public capital initiatives. Only projects that demonstrated a potential rate of return of at least 20% were categorized as acceptable. This rate of return would only be applicable to initiatives that demonstrated “very little risk and uncertainty,” and contracting firms would also “seek a return closer to 40 percent for projects with moderate risk.” † From the perspective of law enforcement use, the IRR is a tool through which potential capital investments may be examined. Such capital investments often are associated with the planning, structuring, and implementation of retirement systems. The use of the IRR may be applied to considerations of retirement systems and retirement planning among agencies and personnel. During 2009, the Fort Lauderdale Police and Fire Pension Board considered the use of such returns within the context of retirement projections among city personnel. ‡ Similarly, the cities of Richmond Heights, Missouri, § and Lakeland, Florida, ¶ also considered the rate of return as a method through which its retirement valuations occurred. These examples show the potency of the IRR method as a tool through which capital budgeting decisions may be embellished. The use of the IRR method provides a tool through which an additional examination of capital initiatives may occur through considerations of whether potential capital initiatives are worthwhile investment pursuits through time. Regardless, the IRR is a tool through which organizational leaders may examine a rate with respect to the characteristics of the considered problem domain. 7.3 Internal Rate of Return (IRR) Method The IRR is a capital budgeting tool that is used primarily to determine the potential profitability of capital investments through time. The period of time may be either strategic or tactical. Regardless, the basic concepts of the IRR are applicable within both situations

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  Financial Intelligence for Entrepreneurs

  What You Really Need to Know About the Numbers

  • Karen Berman, Joe Knight(Authors)
  • 2008(Publication Date)
  • Harvard Business Review Press

    (Publisher)

  In our example, you are proposing to invest $3,000, and your business will receive $1,300 in cash flow at the end of each of the following three years. You can’t just use the gross total cash flow of $3,900 to figure the rate of return because the return is spread out over three years. So we need to do some calculations.

  First, here’s another way of looking at IRR: it’s the hurdle rate that makes net present value equal to zero. Remember, we said that as discount rates increase, NPV decreases. If you did NPV calculations using a higher and higher interest rate, you’d find NPV getting smaller and smaller until it finally turned negative, meaning the project no longer passed the hurdle rate. In the preceding example, if you tried 10 percent as the hurdle rate, you’d get an NPV of about $233. If you tried 20 percent, your NPV would be negative, at – $262. So the inflection point, where NPV equals zero, is somewhere between 10 percent and 20 percent. In theory, you could keep narrowing in until you found it. In practice, you can just use a financial calculator or a Web tool, and you will find that the point where NPV equals zero is 14.36 percent. That is the investment’s Internal Rate of Return.

  IRR is an easy method to explain and present because it allows for a quick comparison of the project’s return to the hurdle rate. On the downside, it does not quantify the project’s contribution to the overall value of the company, as NPV does. It also does not quantify the effects of an important variable, namely how long the company expects to enjoy the given rate of return. When competing projects have different durations, using IRR exclusively can lead you to favor a quick-payback project with a highpercentage return when you should be investing in longer-payback projects with lower-percentage returns. IRR also does not address the issue of scale.

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  Fundamentals of Corporate Finance

  • Robert Parrino, David S. Kidwell, Thomas Bates(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  The payback period is the length of time it will take for the cash flows from a project to recover the cost of the THE FUNDAMENTALS OF CAPITAL BUDGETING 356 5. Be able to compute the Internal Rate of Return (IRR) for a capital project, and discuss the conditions under which the IRR technique and the NPV technique produce differ-ent results. The IRR is the expected rate of return for an investment project; it is calculated as the discount rate that equates the present value of a project’s expected cash inflows to the present value of the project’s outflows – in other words, as the discount rate at which the NPV is equal to zero. Calculations are shown in Section 10.5 and Learning by Doing Application 10.3. If a project’s IRR is greater than the required rate of return, the cost of capital, the project is accepted. The IRR rule often gives the same investment decision for a project as the NPV rule. However, the IRR method does have operational pitfalls that can lead to incorrect decisions. Specifically, when a project’s cash flows are unconventional, the IRR calculation may yield no solution or more than one IRR. In addition, the IRR technique cannot be used to rank projects that are mutually exclusive because the project with the highest IRR may not be the project that would add the greatest value to the firm if accepted – that is, the project with the highest NPV. 6. Explain the benefits of a post-audit review of a capital project. Post-audit reviews of capital projects allow management to determine whether the project’s goals were met and to quantify the benefits or costs of the project. By conducting these reviews, managers can avoid similar mistakes and possibly better recognise opportunities.

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  Financial Mathematics for Actuaries

  • Wai-Sum Chan, Yiu-Kuen Tse;;;(Authors)
  • 2017(Publication Date)
  • WSPC

    (Publisher)

  For simplicity, we assume the cash flows occur at regular intervals, say, annually. The project lasts for n years and the future cash flows are denoted by C 1,···, C n. We adopt the convention that cash inflows to the project (investments) are positive and cash outflows from the project (withdrawals) are negative. We define the Internal Rate of Return (IRR) (also called the yield rate) as the rate of interest such that the sum of the present values of the cash flows is equated to zero. Denoting the Internal Rate of Return by y, we have where j is the time at which the cash flow C j occurs. This equation can also be written as The right-hand side of the above equation is the present value of future outflows (withdrawals) minus the present value of future inflows (investments). Thus, the net present value of all future withdrawals (injections are negative withdrawals) evaluated at the IRR is equal to the initial investment C 0. Example 4.1: A project requires an initial cash outlay of $2,000 and is expected to generate $800 at the end of year 1 and $1,600 at the end of year 2, at which time the project will terminate. Calculate the IRR of the project. Solution: If we denote we have, from (4.2) or Dropping the negative answer from the quadratic equation, we have Thus, Note that v < 0 implies y < − 1, i.e., the loss is larger than 100%, which will be precluded from consideration. ■ Equation (4.1) is formally the same as the equation of value (1.36), with the focus being on the solution of y given the cash flows C j, j = 0,···, n. Indeed, Example 4.1 is similar to Example 1.23, with the problem viewed as one on investment rather than loan. In many practical situations, the cash flows can be calculated or estimated, and the IRR provides a measure of the attractiveness of the project. There is generally no analytic solution for y in (4.1) when n > 2, and numerical methods have to be used. The Excel function IRR enables us to compute the answer easily

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  Business Planning and Control

  Integrating Accounting, Strategy, and People

  • Bruce Bowhill(Author)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  The formula to be followed with linear interpolation is shown below: IRR = lowest discount rate + difference in discount rate × NPV at lowest discount rate difference in NPVs For this example: IRR = 10% + (25% − 10%) × £525,000 (£525,000 − ( − £111,000)) = 10% + 12% = 22%. Figure 4.6 Internal Rate of Return for project A [ 94 ] C H A P T E R 4 Activity 4.5 Calculate the IRR of projects B and C. The advantages and disadvantages of Internal Rate of Return Advantages 1. For most projects IRR actually gives the same project selection as NPV. 2. IRR may be better for communicating than NPV. A comment such as ‘the Internal Rate of Return is 22% on this project’ may seem more meaningful than ‘the NPV of this project is £525,000’. Note that the percentage return is not the same as the ARR. Disadvantages The IRR technique can have more than one IRR, also some projects have no IRR. Activity 4.6 It has been argued that in order to evaluate a project to see if it leads to an increase in shareholder wealth, it is necessary to satisfy the following criteria: 1. The amount of all cash flows should be considered. 2. The timing of the cash flows should be considered. 3. The risk of the cash flows should be considered. Which technique(s) satisfy the three criteria identified above? Decision rule for accepting projects It is possible to accept any combination of projects as long as they comply with the decision rules of the organization (unless the projects are mutually exclusive, i.e. it is only possible to accept one of the options). Payback method : Each organization should decide on how quickly an investment must pay back its cash. If payback must be within 3 years, then 3 years is the cut-off point for the organization. Any investment which took longer than 3 years to pay back would not be accepted. ARR method : Projects with ARRs greater than or equal to the organization’s hurdle rate should be accepted.

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  Financial Intelligence for HR Professionals

  What You Really Need to Know About the Numbers

  • Karen Berman, Joe Knight(Authors)
  • 2008(Publication Date)
  • Harvard Business Review Press

    (Publisher)

  Another potential drawback—the art of finance, again—is simply that NPV calculations are based on so many estimates and assumptions. The cash flow projections can only be estimated. The initial cost of a project may be hard to pin down. And different discount rates, of course, can give you radically different NPV results. Still, the more you understand about the method, the more you can question somebody else’s assumptions—and the easier it will be to prepare your own proposals, using assumptions that you can defend. Your financial intelligence also will be clear to others—your boss, your CEO, whomever—when you present and explain NPV in a meeting to discuss a capital expenditure. Your understanding of the analysis will allow you to confidently explain why, or why not, the investment should be made.

  Internal Rate of Return Method

  Calculating Internal Rate of Return is similar to calculating net present value, but the variable is different. Rather than assuming a particular discount rate and then inspecting the present value of the investment, IRR calculates the actual return provided by the projected cash flows. That rate of return can then be compared with the company’s hurdle rate to see whether the investment passes the test.

  In our example, the company is proposing to invest $3,000, and it will receive $1,300 in cash flow at the end of each of the following three years. You can’t just use the gross total cash flow of $3,900 to figure the rate of return because the return is spread out over three years, so we need to do some calculations.

  First, here’s another way of looking at IRR: it’s the hurdle rate that makes net present value equal to zero. Remember, we said that as discount rates increase, NPV decreases. If you did NPV calculations using a higher and higher interest rate, you’d find NPV getting smaller and smaller until it finally turned negative, meaning the project no longer passed the hurdle rate. In the preceding example, if you tried 10 percent as the hurdle rate, you’d get an NPV of about $233. If you tried 20 percent, your NPV would be negative, at – $262. So the inflection point, where NPV equals zero, is somewhere between 10 percent and 20 percent. In theory, you could keep narrowing in until you found it. In practice, you can just use a financial calculator or a Web tool, and you will find that the point where NPV equals zero is 14.36 percent. That is the investment’s Internal Rate of Return.

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  Multiple Interest Rate Analysis

  Theory and Applications

  • M. Osborne(Author)
  • 2014(Publication Date)
  • Palgrave Pivot

    (Publisher)

  et al . (2011) contains a classic statement of the arguments and lists four pitfalls.

     1    An IRR, by itself, does not indicate whether a project involves borrowing or lending;

     2    Some cash flows cause the IRR equation to solve for more than one plausible IRR, resulting in ambiguity about which IRR to use as a criterion;

     3    NPV and IRR do not always rank mutually exclusive projects the same; the consensus opinion is that ranking by NPV is reliable, and therefore ranking by IRR is not;

     4    A non-flat yield curve provides more than one cost of capital with which to compare IRR leading to uncertainty about which cost of capital to employ.

  Despite the pitfalls there is considerable empirical evidence that the majority of practitioners continue to use IRR as an investment criterion and performance measure. For example, in the context of capital budgeting there is the study of US data by Graham and Harvey (2001) and the similarly executed study of European data by Brounen et al . (2004). Many studies of capital budgeting practice are published every year containing similar results for various countries. In the context of IRR as a performance measure for private equity firms, hedge funds, and venture capitalists see the works by Phalippou (2008), Phalippou and Gottschalg (2009), Dichev and Yu (2011), and Achleitner et al.

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  Economic Feasibility of Projects

  Managerial and Engineering Practice

  • S.L. Tang(Author)
  • 2003(Publication Date)
  • The Chinese University of Hong Kong

    (Publisher)

  From the private investor’s viewpoint, however, the criterion may be different. Under the circumstances of limited availability of funds, the highest IRR should be a suitable criterion for n n n n n R B BR B I R I R I B C ) ( ) ... ( ) ( 2 2 1 1 -+ -+ + + + ----n n n n R I R I R I C ) ... ( 2 2 1 1 + + + + ---n n i I i I i I C ) 1 ( ... ) 1 ( ) 1 ( 2 2 1 + + + + + + + - 5. Comparison of Multiple Alternatives 85 private investment decisions. The IRR varies as the financial arrangement varies. As is seen above, the NPW functions as an economic indicator while the IRR functions as a financial indicator. If the IRR of an investment is ever used to reflect the economic viability, it must be calculated on the basis of the cash flows of an all-equity case (i.e. without loan). The evaluation of Financial-IRR (FIRR) and Economic-IRR (EIRR) can be found in Chapter 8. It should be noted that there is only one EIRR (a constant value) but there are different FIRRs for a single capital investment under different financial arrangements. This fact is consistent with the theory that the readers have read in this chapter. 5.8 Problems 1. There are six alternative ways to improve a production line. The capital costs needed, the extra annual OMR costs required and the extra annual benefits generated from the improvement are as follows: Alternatives (1) (2) (3) (4) (5) (6) Capital cost of improvement 150,000 170,000 200,000 350,000 500,000 650,000 Extra annual OMR costs needed 10,000 12,000 15,000 25,000 40,000 50,000 Extra annual benefit generated 41,800 46,500 56,000 93,000 132,000 160,500 Assuming the life of the project to be 10 years and the discount rate to be 12% p.a., find the alternative which gives: (a) the highest net annual benefit, (b) the highest net present worth, (c) the highest direct B/C ratio, (d) the highest direct IRR. Use the following methods to find the best alternative: (e) the incremental benefit-cost ratio method, (f) the incremental IRR method.

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