ANALISA EKONOMI TEKNIK

ANALISA EKONOMI TEKNIKPresent Worth AnalysisAnnual Cash Flow AnalysisRate of return AnalysisANALISA EKONOMI TEKNIK 1 Present Worth AnalysisKita sdh bahas:Konsep ekivalensiArus KasBunga majemukSelanjutnya:Memahami kriteria ekonomi.Penggunaan metoda present worth .Asumsi2 dalam solusi analisa ekonomi teknik.

EGR 403 - Cal Poly Pomona - SA74Economic Decision Making Problems Fall Into Three CategoriesThree criteria that apply to all of our analysis techniques:For fixed input situations, maximize the benefits or other outputs. For fixed output situations, minimize the costs or other inputs.Where inputs and outputs vary, maximize = benefits costs.First step is to decide which category applies.See the back inside cover of the text.

EGR 403 - Cal Poly Pomona - SA75Economic Criteria Restated Present Worth TechniquesMaximize net present worth: NPW Max NPW = PWB - PWCNeither capital nor $ benefits are fixedNeither fixedMinimize present worth of costs: PWCMin PWC$ amount of benefit is fixed or fixed outcomeFixed outputMaximize present worth of benefits : PWBMax PWBAmount of capital available fixedFixed inputCriterionSituationEGR 403 - Cal Poly Pomona - SA76Economic Criteria - ExamplesCBAAltMaximize the profit - The biggest margin between benefit & cost. Maximize PWB - PWC Purchasing rental propertyNeither fixedNegotiate for minimum cost/sq ft. Minimize input20,000 sq ft building neededFixed outputPurchase the most you can for the money. Maximize output.$150,000 budgeted for raw materialsFixed inputCriterionExampleSituationEGR 403 - Cal Poly Pomona - SA77Applying Present Worth TechniquesWith PW analysis the analysis period used is a major consideration. Several cases:Useful life of the alternative(s) equals the analysis period.Alternatives have useful lives different from the analysis period.The analysis period is infinite or long enough to be treated as infinite, n = .EGR 403 - Cal Poly Pomona - SA78Useful Lives Equal the Analysis PeriodExample 5-1: Require a project to last five years.The equipment and tooling will last five years.Calculate the PW or NPW over a five year span and junk the equipment at the end of the five years (salvage value = 0).Two alternatives with cost of $1000 and useful live of 5 years. Assume i = 7%.

EGR 403 - Cal Poly Pomona - SA79Example 5-1: Fixed input, therefore maximize PW of Benefits.Alternative AFind the PW of all cash flows related to benefits of Alternative A. Also include additional costs that come later.PW of Benefits = 300 (P/A, 7%, 5) = 300 (4.100) = $1230

EGR 403 - Cal Poly Pomona - SA710Example 5-1: Fixed input, therefore maximize PW of Benefits (contd)Alternative B - Here we have a combination of a uniform series (A = 400) and a negative gradient (G = 50). Decompose to use the factors available.PW of Benefits = 400 (P/A, 7%, 5) - 50 (P/G, 7%, 5) =400 (4.100) - 50 (7.647) = $1257.65

EGR 403 - Cal Poly Pomona - SA711Example 5-1 ContdPWB Alternative A = $1230.00PWB Alternative B = $1257.65Since our criteria was to maximize PW of Benefits, Alternative B is preferred.Notice that each alternative provided the same total cash flow, but alternative B provided it sooner so that it was available sooner to the company to use. MONEY NOW IS BETTER THAN MONEY LATEREGR 403 - Cal Poly Pomona - SA712More ExamplesExample 5-2: Two stage construction. Fixed output so Minimize PW of CostUse PW factors to find PW of second stage costs and benefits at time 0.Example 5-3: Salvage value includedFixed output, so Minimize PW of CostUse PW factors to find PW of salvage value. Operating & maintenance costs were assumed equal.Example 5-4: Neither input nor output fixedMaximize (PWB - PWC) or Maximize NPWSalvage value treated as a negative cost ( a benefit)EGR 403 - Cal Poly Pomona - SA713Useful Lives Different From the Analysis PeriodConsider (based on Example 5-3):Speedy: Useful life = 5 years. P = 1500, S = 200, PWC = $1357Allied: Suppose useful life = 10 years instead of 5 years. P = 1600, Salvage value = 325. PWC = $1435.If we have two alternatives with different useful lives, is it proper to compare PWB and/or PWC directly?Answer: No, because we have 5 additional years of benefits for Allied that would be ignoredSolution: Require the project to last 10 years.For Speedy assume that you will purchase new equipment and tooling twice: At the beginning of year one and six. Junk the equipment and tooling at the end of each five year period and replace with the same equipment.

EGR 403 - Cal Poly Pomona - SA714Useful Lives Different From the Analysis PeriodCalculate the PW or NPW over a 10 year span.Speedy: PWC = $2325Now Allied is the preferred choice since PWC is less than for SpeedyEGR 403 - Cal Poly Pomona - SA715Techniques for Dealing with Unequal Useful LivesRepeated Project Policy - We will assume the same costs and benefits and repeat a project all the way to the end of the analysis period. This is a major part of PW analysis.Least Common Multiple - Find useful life that coincides with multiple lives of each alternative under consideration: e.g. If useful lives are 3 years and 4 years, then the least common multiple is 12 years.EGR 403 - Cal Poly Pomona - SA716Techniques for Dealing with Unequal Useful LivesTerminal year Sometimes the least common multiple method (LCM) creates an unrealistic useful life (e.g., 13 years and 7 years = LCM of 91 years). Instead, pick a terminal year and repeat all projects up until the terminal year.Truncate all costs and benefits after the terminal year(See Figure 5-1 on page 175 for an illustration)EGR 403 - Cal Poly Pomona - SA717Infinite Analysis PeriodFor n = infinity, A = i PTherefore:P = A / ii = A / PWhen you have a very long analysis period, use the infinity assumption to simplify problems.Example 5-6: If we can resolve our desired task or service into an equivalent A, then we can use P = A / i to simplify the process of finding P.EGR 403 - Cal Poly Pomona - SA718Assumptions in Solving Economic Analysis ProblemsEnd-of-year (or period) convention (simplifies calculations) Viewpoint (generally the firm)Sunk costs (past has no bearing)Borrowed money (consider investing only)Effect of inflation (prices are not stable)Income taxes (must be considered for realism)ANALISA EKONOMI TEKNIK 2Annual Cash Flow AnalysisEGR 403 - Cal Poly Pomona - SA820Annual Cash Flow CalculationsResolving a Present Cost to an Annual CostSimplest case is to convert the PV to an A-series (annual worth):A = P(A/P, i, n)Where there is salvage value:A = F(A/F, i, n)

A is -PMT in EXCEL.To duplicate the A/P factor, put the value for P in place of PV in the PMT fields: PMT(rate, nper, pv, fv, type)(fv and type are 0)

To duplicate the A/F factor, put the value for F in place of FV in: PMT(rate, nper, pv, fv, type)(pv and type are 0)See Examples 6 -1 & 2EGR 403 - Cal Poly Pomona - SA821Annual Cash FlowFour Essential PointsEUAC = PWC(A/P, i, n)EUAB = PWB(A/P, i, n)EUAW = EUAB - EUACEUAW isDecreased by a cost.Increased by a benefit.In MS Excel use -PMT to calculate EUAW (remember the minus sign)For an irregular cash flow over the analysis period first determine the PW then convert to EUAW.

EGR 403 - Cal Poly Pomona - SA822Annual Cash Flow AnalysisMaximize EUAWNeither capital nor $ benefits are fixedNeither fixedMinimize EUAC$ amount of benefit is fixedFixed outputMaximize EUABAmount of capital available fixedFixed inputCriterionSituationEGR 403 - Cal Poly Pomona - SA823These two examples further illustrate:The equivalency of PW and EUAW. Example 6-5 (Example 5-1)Example 6-6 EUAW

Two More Examples of Resolving a PW to an EUAWEGR 403 - Cal Poly Pomona - SA824Analysis Period ConsiderationsAnalysis period equal to alternative lives.Analysis period a common multiple of alternative lives.Analysis period for a continuing requirement.Some other period such as project life.

EGR 403 - Cal Poly Pomona - SA825Analysis Period Equal to Alternative Lives.Base the comparison on the life of the alternatives.This is the case we have most often considered in our examples.This is rarely the case in real life organizations.

EGR 403 - Cal Poly Pomona - SA826Analysis Period a Common Multiple of Alternative Lives.When the lives of the equipment in the two alternatives varies, use a common multiple of the two lives.Example 6-7 However, calculations are simplified. You only need to use one useful life to get the EUAW.

EGR 403 - Cal Poly Pomona - SA827Analysis Period for a Continuing Requirement.Where the project will last forever (nothing does) use an infinite time period.In most analyses organizations often use a representatively long time period to get a reasonable estimate.Example 6-9: Alt A has infinite analysis period. Use A = P iEGR 403 - Cal Poly Pomona - SA828Some Other Period Such AsProject Life.Most often physical equipment has a useful life that varies from the project life.In this case use the project life as the analysis period.This is the most common case in real organizations.ANALISA EKONOMI TEKNIK 3Rate of Return AnalysisEGR 403 - Cal Poly Pomona - SA930Three Major Methods of Economic AnalysisPW - Present WorthAW - Annual WorthIRR - Internal Rate of ReturnIf P = A(P/A, i, n)Then (P/A, i, n) = P/ASolve for (P/A, i, n) and look up interest in Compound Interest TablesEGR 403 - Cal Poly Pomona - SA931Internal Rate of Return (IRR)The interest rate paid on the unpaid balance of a loan such that the payment schedule makes the unpaid loan balance equal to zero when the final payment is made. Ex: P = $5000, i = 10%, n = 5

EGR 403 - Cal Poly Pomona - SA932Calculating Rate of ReturnThe IRR is the interest rate at which the benefits equal the costs. IRR = i*PW Benefit - PW Cost = 0PW Benefit/PW Cost = 1NPW = 0EUAB - EUAC = 0PW Benefit = PW CostEGR 403 - Cal Poly Pomona - SA933Calculating IRR - Example 7-1PWB/PWC = 12000(P/A, i, 5)/8200 = 1(P/A, i, 5) = 8200/2000 = 4.1From Table, IRR = 7%

3.9938%4.1007%4.2126%(P/A,i,5)Interest rateFrom Compound Interest Tables

EGR 403 - Cal Poly Pomona - SA934Calculating IRR - Example 7-2Sometimes we have more than one factor in our equation. When that happens we cannot solve for just one factor.

If we use: EUAB - EUAC = 0100 + 75(A/G, i, 4) - 700(A/P, i, 4) = 0

EGR 403 - Cal Poly Pomona - SA935Calculating IRR - Example 7-2 (contd)No direct method for calculating. Use trial and error and iterate to get answer.Try i = 5%:100 + 75(A/G, 5%, 4) - 700(A/P, 5%, 4) = + 11+ 11 is too high. The interest rate was too lowTry i = 8%100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = - 6- 6 is too low. The interest rate was too highTry i = 7%100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = 0Therefore IRR = 7%EGR 403 - Cal Poly Pomona - SA936Calculating IRR - Example 7-3 Example 7-3 shows a series of cash flows that does not match any of our known patterns. We must use trial and error. Using NPW = 0, suppose we start with i = 10% . NPW = + 10.16, which is too high. Using i = 15%, NPW = - 4.02. IRR is between 10% & 15% The iterations may be graphed and the true IRR will be indicated at the point where the NPW curve = 0.Yr CF0 - 1001 + 202 + 203 + 304 + 405 + 40

EGR 403 - Cal Poly Pomona - SA937Calculating IRR - Example 7-3 (Contd)We can use linear interpolation to find estimate the point where the curve crosses 0.IRR = i* = 10% + (15%-10%)[10.16/(10.16 + 4.02)] = 13.5%This is a linear interpolation of a non-linear function so the answer is slightly inaccurate, but good enough for decision making here (after all, the guesswork in our future cash flows introduces uncertainty in the analysis).EGR 403 - Cal Poly Pomona - SA938Calculating IRR - Example 7-3 (Contd)

To get an exact answer, we can use the IRR function in EXCEL Select the IRR function from the fx icon. Block the column on the spreadsheet that has the cash flows for all years. The function returns the IRR. =IRR(A1:A6)The IRR function in EXCEL allows you to evaluate the return of investments very easily

EGR 403 - Cal Poly Pomona - SA939Calculating IRR for a Bond - Example 7-4aBond Costs and Benefits:Purchase price = $1000Dividends = $40 every six monthsSold after one year for $950

Calculation of Periodic interest rate & IRR:m = 2 compounding periods/year1000 = 40(P/A, i, 2) + 950(P/F, i, 2)By trial and error and interpolation i* 1.5%IRR Nominal rate = 2 x 0.015 = 0.03 (3%)IRR Effective rate = (1 + 0.015)2 - 1 = 0.0302 (3.02%)EGR 403 - Cal Poly Pomona - SA940Example 7-4a EXCEL Solution

Use IRR function to find periodic IRR (i) Find nominal using r = i * m Use EFFECT function to find effective interest rateEGR 403 - Cal Poly Pomona - SA941Rate Of Return (ROR) AnalysisMost frequently used measure of merit in industry.More accurately called Internal Rate of Return (IRR).EGR 403 - Cal Poly Pomona - SA942Calculating RORWhere two mutually exclusive alternatives will provide the same benefit, ROR is performed using an incremental rate of return (DROR) on the difference between the alternatives.You cannot simply choose the higher IRR alternative.Choose lower-cost alternativeDROR < MARRChoose higher-cost alternativeDROR MARRDecisionTwo-alternative situationEGR 403 - Cal Poly Pomona - SA943The Minimum Attractive Rate of Return (MARR)The MARR is a minimum return the company will accept on the money it investsThe MARR is usually calculated by financial analysts in the company and provided to those who evaluate projectsIt is the same as the interest rate used for Present Worth and Annual Worth analysis.EGR 403 - Cal Poly Pomona - SA944ROR on Alternatives With Equivalent Benefits

Example 7-5: Consider the lease vs. buy situation. MARR = 10% Leasco: Lease for five years for 3 annual payments of $1000 each Saleco: Purchase up front for $2783 Both alternatives have a $1200/year benefit for 5 yearsEGR 403 - Cal Poly Pomona - SA945Example 7-5 (Contd) Cannot simply pick the highest IRR if alternatives have different investment costs Must examine the incremental cash flows!! Subtract the cash flows for the Lower First Cost alternative from the cash flows of the Higher First Cost alternative to obtain the Incremental Cash Flow or D. Compute the IRR on the incremental cash flow. This is the DROR. For this problem the DROR is 8.01% which is < MARR, therefore choose the lower cost alternative.EGR 403 - Cal Poly Pomona - SA946Example 7-5 (Contd)Q. Why did we do this?A. Both alternatives were acceptable compared only to the MARR. Since either alternative will work, the question is whether we want to spend the additional $1783 to go from the lower cost to the higher cost alternative. The benefit for doing so is the savings of two years of $1000 lease payments. Essentially we are getting an 8.01% return on that $1783 investment. The company can get 10% ROR on its money elsewhere, so reject the increment. That is, spend $1000 now on Leaseco and invest the other $1783 for a higher return.EGR 403 - Cal Poly Pomona - SA947Analysis PeriodJust as in PW and AW analysis the analysis period must be considered:Useful life of the alternative equals the analysis period.Alternatives have useful lives different from the analysis period.The analysis period is infinite, n = .

7-10For an example of that uses a common multiple of the alternate service lives, see Example 7-10. EXCEL would be useful here because of the irregularity of the cash flows.Sheet1YearAB0-1000-100013004002300350330030043002505300200

Sheet1Pay 1000/yr. prin. + interestYearPrincipalPrin. PaidInt PaidPayment150001000500150024000100040014003300010003001300420001000200120051000100010011006500Balloon payment15000050050025000050050035000050050045000050050055000500050055007500Five equal payments15000818.99500.001318.9924181.0125960263900.89418.101318.9933280.1264516552990.97328.011318.9942289.1516928471090.07228.921318.9951199.07945815791199.08119.911318.996594.94Pay principal & interest at the end150000500025500055003605006050466550665.5057320.507320.50732.058052.558052.55

Sheet100000

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00000

YearPrincipalPrin. PaidInt PaidPayment15000.00818.99500.001318.9924181.01900.89418.101318.9933280.13990.97328.011318.9942289.151090.07228.921318.9951199.081199.08119.911318.9960.000.00

Sheet1-100203020404013.47%

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7-4a7-4aPeriodsCash flowUnrecovered investment at beginning of yearReturn on unrecovered investmentInvestment repayment at end of yearUnrecovered investment at end of year0($1,000.00)1$40.00$1,000.00$15.19$24.81$975.192$990.00$975.19$14.81$975.19$0.003$0.00$0.00$0.00($0.00)$0.004$0.00$0.00$0.00($0.00)$0.005$0.00$0.00$0.00($0.00)$0.00IRR/period1.52%Eff IRR3.06%Total$30.00$1,000.00Periods/year2Trial interest ratesNPW0$30.005($60.90)10($132.23)15($188.38)20($232.64)25($267.52)30($294.95)35($316.42)40($333.09)45($345.89)50($355.56)

7-4a

Net Present Value

7-4b7-4bPeriodsCash flowUnrecovered investment at beginning of yearReturn on unrecovered investmentInvestment repayment at end of yearUnrecovered investment at end of year0($950.00)1$40.00$950.00$41.88($1.88)$951.882$40.00$951.88$41.96($1.96)$953.843$40.00$953.84$42.05($2.05)$955.894$40.00$955.89$42.14($2.14)$958.025$40.00$958.02$42.23($2.23)$960.256$40.00$960.25$42.33($2.33)$962.587$40.00$962.58$42.43($2.43)$965.028$40.00$965.02$42.54($2.54)$967.569$40.00$967.56$42.65($2.65)$970.2110$40.00$970.21$42.77($2.77)$972.9811$40.00$972.98$42.89($2.89)$975.8712$40.00$975.87$43.02($3.02)$978.8813$40.00$978.88$43.15($3.15)$982.0314$40.00$982.03$43.29($3.29)$985.3215$40.00$985.32$43.43($3.43)$988.7616$40.00$988.76$43.59($3.59)$992.3517$40.00$992.35$43.74($3.74)$996.0918$1,040.00$996.09$43.91$996.09($0.00)IRR/period4.41%Eff IRR9.01%Total$770.00$950.00Periods/year2Trial interest ratesNPW0$770.005($63.71)10($401.90)15($542.67)20($599.96)25($619.89)30($622.28)35($616.09)40($605.64)45($593.09)50($579.58)

7-4b

Net Present Value

Sheet1PeriodBuy/sellDividendTotal0-1000-1000140402950409901.52%periodic3.04%nominal3.06%effective

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Sheet3

Sheet1-10020YearCash flow - alternative A (Leaseco)Cash flow - alternative B (Saleco)Cash flow - alternative B - A300-$1,000.00-$2,783.00-$1,783.00201$200.00$1,200.00$1,000.00402$200.00$1,200.00$1,000.00403$1,200.00$1,200.00$0.0013.47%4$1,200.00$1,200.00$0.005$1,200.00$1,200.00$0.00IRR/period48.72%32.60%8.01%

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Sheet1AlternativeXYInitial cost($200.00)($700.00)Uniform annual benefit$95.00$120.00O&M costs$0.00$0.00End-of-useful-life salvage value$50.00$150.00Useful life, in years612XYYearInvestmentBenefitO&MSalvageInvestmentBenefitO&MSalvage0($200.00)($700.00)1$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.002$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.003$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.004$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.005$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.006($200.00)$95.00$0.00$50.00$0.00$120.00$0.00$0.007$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.008$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.009$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.0010$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.0011$0.00$95.00$0.00$0.00$0.00$120.00$0.00$0.0012$0.00$95.00$0.00$50.00$0.00$120.00$0.00$150.00Cash flow on differenceYearCash flow - alternative ACash flow - alternative BCash flow - alternative B-AUnrecovered investment at beginning of yearReturn on unrecovered investmentInvestment repayment at end of yearUnrecovered investment at end of year0($200.00)($700.00)($500.00)1$95.00$120.00$25.00$500.00$6.58$18.42$481.582$95.00$120.00$25.00$481.58$6.34$18.66$462.923$95.00$120.00$25.00$462.92$6.09$18.91$444.014$95.00$120.00$25.00$444.01$5.84$19.16$424.855$95.00$120.00$25.00$424.85$5.59$19.41$405.456($55.00)$120.00$175.00$405.45$5.34$169.66$235.787$95.00$120.00$25.00$235.78$3.10$21.90$213.888$95.00$120.00$25.00$213.88$2.81$22.19$191.709$95.00$120.00$25.00$191.70$2.52$22.48$169.2210$95.00$120.00$25.00$169.22$2.23$22.77$146.4511$95.00$120.00$25.00$146.45$1.93$23.07$123.3812$145.00$270.00$125.00$123.38$1.62$123.38($0.00)IRR/period43.26%14.32%1.32%Total$50.00$500.00MARR =10.00%NPW =$378.56$165.44($213.12)Trial interest ratesNPW0$50.005($105.53)10($193.75)15($244.30)20($272.97)25($288.54)30($296.06)35($298.53)40($297.80)45($295.03)50($290.96)

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Net Present Value

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