2 Chapter Outline Incremental Analysis Graphical Technique in Solving problems with Mutually Exclusive AlternativesUsing Spreadsheets in Incremental Analysis
3 Learning Objectives Define Incremental Analysis Apply Graphical Technique in Solving Problems with Mutually Exclusive AlternativesUse Spreadsheets in Incremental Analysis
4 Internal Rate of Return (IRR) By definition in Chapter 7:Given a cash flow stream, IRR is the interest rate i at which the benefits are equivalent to the costs. This can be expressed mathematically in five different ways.NPW=0PW of benefits - PW of costs =0PW of benefits = PW of costsPW of benefits / PW of costs=1EUAB-EUAC=0
5 ExampleCash flows for an investment are shown in the following figure. What is the IRR to obtain these cash flows?YEARCASH FLOW($500)1$1002$1503$2004$250
11 Mutually Exclusive Alternatives Only one alternative may be implementedAll alternatives serve the same purposeObjective of incremental analysis is to select the best of these mutually exclusive alternatives
12 Incremental AnalysisWhen there are two alternatives, rate of return analysis is performed by computing the incremental rate of return, ΔIRR, on the difference between the two alternatives, as discussed in Chapter 7.
13 Two -Alternative Situations Incremental AnalysisThe cash flow for the difference between alternatives is calculated by taking the higher initial-cost alternative minus the lower initial-cost alternative.The below decision path is made for incremental rate of return (ΔIRR) on difference between alternatives:Two -Alternative SituationsDecisionΔIRR≥MARRChoose the higher-cost alternativeΔIRR<MARRChoose the lower-cost alternative
14 ExampleThe cash flows for four different alternatives are given in table below. If MARR 10%, which is the best alternative?Using the incremental analysis, we need to repeat 3 times, by comparing 2 alternatives at a time.
15 Choose the higher-cost alternative Choose the lower-cost alternative MARR = 10%EUAB =EUAC (Increment)ΔIRR≥MARRChoose the higher-cost alternativeΔIRR<MARRChoose the lower-cost alternative
16 Incremental AnalysisCould be applied to rate of return (IRR), present worth (PW), equivalent uniform annual cost (EUAC), or equivalent uniform annual worth (EUAW) approaches.[Higher-cost alternative] = [Lower-cost alternative] + [Increment between them]The “defender” is the best alternative identified so far in the process, and “challenger” is the next higher-cost alternative to be evaluated.For a set of N mutually exclusive alternatives, (N - 1) “challenger/defender” comparisons must be made.Copyright Oxford University Press 2009
17 ExampleGiven the alternatives below: Select the one best alternative if MARR = 8%. Use incremental rate of returnanalysis.
18 MARR = 8%Since the MARR is 8%, Alt. D may be eliminated, as the ROR is less than 8%Among the remaining alternatives A, B, and C, the two lower cost alternatives are A and B.(A - B) increment:PW of benefit = PW of cost( )(P/A, i, 10) = (4, ,000)(P/A, i, 10) = 1,000/92 = 10.86(C - B) increment:PW of benefit = PW of cost(1, )(P/A, i, 10) = (6, ,000) (P/A, i, 10) = 3,000/489 = 6.13∆ROR is greater than 8%. Therefore, choose the higher-cost alternative, Alt. C
20 Example 8-1 – Continued In column B, input formula: PW LOW = –$10,300 + $3300(P/A,i,5) = –$ pv(A3, 5, –3300)In column C, input formula:PW HIGH = –$13,400 + $4000(P/A,i,5) = –$ pv(A3, 5, –4000)From a3 to a24, input interest from 0 to 0.21In column D, input formula for incremental cost PW HIGH–LOW:= C3 – B3Then draw a line chart!Or use EXCEL function npv(i, value range)npv(A3, $A$28:$A$32)npv(A3, $A$36:$A$40)
21 Example 8-1 – Continued PW LOW= -$10,300 + $3300(P/A,i,5) Interest RateBest Choice0% ≤ i ≤ 4.3%High Capacity4.3 % ≤ i ≤ 18%Low Capacity18% ≤ iDo NothingPW HIGH= -$13,400 + $40000(P/A,i,5)PWhigh-low = -$ $700(P/A, i, 5)IRRIncrement= %4.3IRRIncrement= %4.3IRRHighIRRLow
22 Example 8-2 Net Present Worth Rate Machine X Machine Y 0% $840.00 $890.001.322752.242710.89687.314604.26519.906515.57380.618441.26263.9010378.56165.4412325.3081.8314279.7710.3716240.58-51.0818206.6520177.10MARR = 10%Machine XMachine YInitial Cost$200$700Uniform Annual Benefit$95$120End-of-Useful-Life Salvage Value$50$150Useful Life, in Years612In column C,–700 + pv(A3, 12, –120, –150)In column B,–200 + pv(A2, 6, -95, -50) + pv(A2,6, 0, 200 – pv(A2, 6, -95, -50))
23 Example 8-2 Net Present Worth Rate Machine X Machine Y 0% $840.00 $890.001.322752.242710.89687.314604.26519.906515.57380.618441.26263.9010378.56165.4412325.3081.8314279.7710.3716240.58-51.0818206.6520177.10∆ IRRIncrement =1.3%IRRYMachine XMachine YFor MARR ≤ 1.3%, Machine Y is the right choiceFor MARR ≥1.3%, Machine X is the right choice
24 Example 8-3 Consider the three mutually exclusive alternatives: A B C Initial Cost$2000$4000$5000Uniform Annual Benefit410639700Each alternative has a 20 year life and no salvage value. If the MARR is 6%, which alternative should be selected?
28 Example 8-5 Incremental Analysis (with Do-Nothing option) Machine XMachine YMachine ZInitial Cost$200$700$425Uniform Annual Benefit65110100Useful Life, in years6128IRRY-Z=3.5%If MARR≥23%,Choose “Do-Nothing”If 23%≥MARR≥11%,Choose XIf 11%≥MARR≥3.5%,Choose ZIf 3.5%≥MARR≥0%,Choose YIRRZ-X=11%IRRX=23%XZY
29 Example 8-5 Incremental Analysis (without Do-Nothing option) Machine XMachine YMachine ZInitial Cost$200$700$425Uniform Annual Benefit65110100Useful Life, in years6128IRRY-Z=3.5%If MARR≥11%,Choose XIf 11%≥MARR≥3.5%,Choose ZIf 3.5%≥MARR≥0%,Choose YIRRZ-X=11%IRRX=23%XZY
30 Example 8-6 Incremental Analysis using Graphical Comparison BCDEInitial Cost$4000$2000$6000$1000$9000Uniform Annual Benefit639410761117785IRRC-A=2%Life = 20 yrsIRRA-B=9.6%IRRB=20%
31 Example 8-6 Incremental Analysis using Graphical Comparison BCDEInitial Cost$4000$2000$6000$1000$9000Uniform Annual Benefit639410761117785Calculating Incremental Interest∆IRR(C-A) = $6000-$4000 = ($761 - $639)(P/A, i, 20) = 2%∆IRR(A-B) = $4000-$2000 = ($ $410)(P/A, i, 20) = 9.6%And to find where the NPW of B crosses the 0 axisIRR (B) = $2000 = $410(P/A, i, 20) = 20%
32 Example 8-6 Incremental Analysis using Graphical Comparison BCDEInitial Cost$4000$2000$6000$1000$9000Uniform Annual Benefit639410761117785If MARR≥20%,Choose Do-NothingIf 20%≥MARR≥9.6%,Choose BIf 9.6%≥MARR≥2%,Choose AIf 2%≥MARR≥0%,Choose CIRRC-A=2%IRRA-B=9.6%IRRB=20%
33 Spreadsheet and Incremental Analysis Excel FunctionsPurposeRate (n, A, -P, [F], [Type], [guess])To find rate of return or incremental rate of return given n, P, and AIRR (range, [guess])To find internal rate of return (or incremental rate of return) of a series of cash flow (or incremental cash flow)Excel ToolsPurposeGoal SeekIt varies the value in one specific cell until a formula that's dependent on that cell returns the wanted result.SolverSolver adjusts the values in the changing cells to produce the result from the target cell formula. Constraints are applied to restrict the values Solver can use in the model.