Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash
ID: 2705961 • Letter: C
Question
Consider the following two mutually exclusive projects:
Year Cash Flow (A) Cash Flow (B) 0
Explanation / Answer
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)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