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 Subject: Comparing Investment Criteria Category: Reference, Education and News > Homework Help Asked by: tangothecat-ga List Price: \$20.00 Posted: 04 Jul 2004 15:39 PDT Expires: 03 Aug 2004 15:39 PDT Question ID: 369646
 ```Comparing Investment Criteria. Consider the following two mutually exclusive projects Year Cash Flow (A) Cash Flow (B) 0 -\$210,000 -\$20,000 1 15,000 12,000 2 30,000 10,500 3 32,000 9,500 4 425,000 8,200 Whichever project you choose, if any, you require a 15 percent return on your investment. a. If you apply the payback criterion, which investment will you choose? Why? b. If you apply the NPV criterion, which investment will you choose? Why? c. If you apply the IRR criterion, which investment will you choose? Why? d. If you apply the profitability index criterion, which investment will you choose? Why? e. Based on your answers in (a) through (d), which project will you finally select?```
 ```Hi tangothecat!! a. If you apply the payback criterion, which investment will you choose? Why? Payback (PB) calculation will give us an idea on how long it will take for a project to recover the initial investment. Then if: Y = the year before full recovery of investment I; U = Unrecovered cost at the start of last year; CFi = CF of the year Y+1; PB = Y + U/CFi -Project A: CFi = \$425,000 I = \$210,000 After the year 3 we will have recovered only \$77,000 and we will finish to recover the investment during the year 4, then: Y = 3 and U = \$210,000 - \$77,000 = \$133,000 PB = 3 + 133,000/425,000 = 3.313 (about 3 years and 4 months) -Project B: CFi = \$10,500 I = \$20,000 After the year 1 we will have recovered only \$12,000 and we will finish to recover the investment during the year 2, then: Y = 1 and U = \$20,000 - \$12,000 = \$8,000 PB = 1 + 8,000/10,500 = 1.762 (about 1 year and 10 months) Definition of Payback Criterion: -Accept a project if its payback period is less than maximum acceptable payback period. -Reject a project if its payback period is longer than maximum acceptable payback period. -Mutually Exclusive Projects: Accept the one having the shortest PB. In this case, using the Payback Criterion you must choose the project B, the theory of the Payback Criterion states that projects with shorter paybacks are more liquid, and thus less risky. In general projects with a project with Payback period less than three years is preferred. ----------------------------------------------------------- b. If you apply the NPV criterion, which investment will you choose? Why? Some definitions: Present Value: CF1 CF2 CF3 CF4 PV = --------- + ---------- + ---------- + ---------- (1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4 Net Present Value: NPV = PV - I where I = Initial Investment NPV Decision Rule that says: -General Rule: Accept a project if NPV >= 0. -Mutually Exclusive Projects: Accept the project that has the largest NPV >= 0. -Project A: PV = \$299,763.44 NPV = \$299,763.44 - \$210,000 = \$89,763.44 -Project B: PV = \$29,309.07 NPV = \$29,309.07 - \$20,000 = \$9,309.07 The NPV criterion says that in mutually exclusive projects we must choose the project with the largest positive NPV, in this case the best project by this criterion is the project A. ----------------------------------------------------------- c. If you apply the IRR criterion, which investment will you choose? Why? Some definitions: To calculate the IRR you must find r from the following equation: CF1 CF2 CF3 CF4 PV = --------- + ---------- + ---------- + --------- = I (1 + r)^1 (1 + r)^2 (1 + r)^3 (1 + r)^4 In other words IRR is the discount rate at which the NPV equals zero. You can use one of the following techniques to calculate the IRR: -Trial & Error techniques -Calculator -Computer (spreadsheet) Here is a brief guide to do this using an MS Excel spreadsheet for this problem: 1) Select a column for the project's Cash flows (lets say column "A"). 2) Input the project's Cash Flows starting from the initial investment and followed by the Y1 to Y4 cash flows, each one in one cell of the column. 3) Click on the cell where you want your IRR calculated (say B1). 4) Enter "=IRR(" (without the quotes) and then highlight the column A then close the parenthesis and hit enter. For the project A the column A will have: A1: -210,000 ; A2: 15,000 to A5: 425,000 ; B1 =IRR(A1:A5) We have for Project A: IRR = 26.9% and for project B: IRR = 38.3% The IRR criterion states that you must accept only projects with IRR greater than the cost of capital (required rate of return). If you use this criterion to choose between mutually exclusive projects you must select the acceptable project with the higher IRR. In this case the required rate of return is 15%,then both projects are acceptable, but the project B is the winning by this criterion. ------------------------------------------------------------ d. If you apply the profitability index criterion, which investment will you choose? Why? Definitions: PI = PV/I Profitability Index criterion: This decision criterion leads to accept a project only if it has a Profitability Index (PI) greater than one. Using the profitability index to compare mutually exclusive projects decision rule implies select the acceptable project with the higher PI. For the project A: PI = PV/I = \$299,763.44 / \$210,000 = = 1.427 For the project B: PI = PV/I = \$29,309.07 / \$20,000 = = 1.465 Using the Profitability Index criterion we select the project B. ----------------------------------------------------------- e. Based on your answers in (a) through (d), which project will you finally select? Start summing up the results of the previous questions: Project Payback NPV IRR PI A 3.313 \$89,763.44 26.9% 1.427 B 1.762 \$9,309.07 38.3% 1.465 Selection B A B B The first observation is that both alternatives are acceptable by all criteria but to different degrees. The goal is to select the best of the two. We can see that the NPV and the IRR criteria are in conflict and the PI criterion gives a very similar rank to both projects (PI criterion says to us "see other criterion"). In cases like that we tend to select the project with the highest NPV, this can be summed up as the following statement: "If projects are mutually exclusive and not subject to capital rationing, the project with the higher NPV should be selected." Why this happens? Remember that NPV and PI assume cash flows are reinvested at the required rate of return for the project and IRR assumes cash flows are reinvested at the IRR. This means that "if the IRR method is used, the project must not be accepted only because its IRR is very high. Management must ask whether such an impressive IRR is possible to maintain. In other words, management should look into past records, and existing and future business, to see whether an opportunity to reinvest cash flows at such a high IRR really exists. If the firm is convinced that such an IRR is realistic, the project is acceptable. Otherwise, the project must be reevaluated by the NPV method, using a more realistic discount rate." Quoted paragragh from "WHAT IS CAPITAL BUDGETING?": http://www.exinfm.com/training/capitalbudgeting.doc Then the high IRR of project B (38.3%) can be an unrealistic rate for future reinvestments. A useful approach to a proper decision between two mutually exclusive alternatives is to evaluate the incremental benefits obtained by moving from the less expensive project to the most expensive project, in this case from the project B to project A. This movement implies an additional investment of: I' = \$210,000 - \$20,000 = \$190,000 and additional benefits of: Y1 = \$3,000 Y2 = \$19,500 Y3 = \$22,500 Y4 = \$416,800 This "project movement" has an IRR of 26.22%. This result exceed the required rate of 15% but is not so attractive as the IRR of the project B (the original project in this case). At this point the question is whether the company has other projects that will offer a return higher than 26.22%. Proceeding with the project B you are saving money for other possible projects, but if these possible projects does not exists or does not offer a better return than 26.22% (this high rate will be the required rate of return for these possible projects!!!) the project A must be selected, this last thing almost happens. As a conclusion we can state the following: IRR and NPV always give the same accept/reject signal in respect of independent projects, but sometimes they give conflicting answers to mutually exclusive projects: IRR suggests that project B be selected and NPV suggests tha project A must be selected. This normally happens when both project have different initial outlays, the patterns of cash flow are different, and/or one project has a longer life than another. This situation can be overcome by calculating the incremental yield, in other words, calculating the IRR obtained by moving from the less expensive project to the most expensive one. If the IRR on the additional investment and additional benefits is greater than the required rate of return then the larger project must be selected. NOTE: The payback criterion is not a proper way to select between mutually exclusive projects. It ignores any benefits that occur after the payback period, and worst it ignores the time value of money. ------------------------------------------------------------ Some lectures for reference: "An Overview of the Capital Budgeting Process": http://accfinweb.account.strath.ac.uk/am2/le11to14.doc "Capital Budgeting": http://www.umanitoba.ca/stangeland/9.220/02_lecture%209.ppt "Net Present Value and Other Investment Criteria ": http://members.cox.net/yung2/Chapter09.ppt "Investment Criteria": http://clem.mscd.edu/~mayest/FIN3300/Files/ch9.ppt "Net Present Value and Other Investment Criteria - Making Capital Investment Decisions": http://www.yonsei.ac.kr/TimeTbl212/20012/Lect8.ppt "Project Evaluation and Selection Analysis Techniques": http://cbdd.wsu.edu/kewlcontent/cdoutput/TR505r/page15.htm "Net Present Value Evaluations": http://www.treasury.govt.nz/publicsector/fixedassets/appendix.asp "Capital Investment Appraisal": http://www.cityu.edu.hk/afdragon/teach/capbud.html -------------------------------------------------------------- Search strategy: "Investment Criteria" "mutually exclusive" "Investment Criteria" "Incremental Cash Flows" "Incremental Cash Flows" "capital budgeting" "mutually exclusive" ----------------------------------------------------------------- I hope that this helps you. If you find something unclear, imcomplete or wrong please let me know using the clarification feature giving me the opportunity to complete, clarify, correct or improve this answer if needed before you rate it. I will gladly respond to your requests. Best regards. livioflores-ga```
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