Presentation on theme: "Dealing With Uncertainty"— Presentation transcript:
1 Dealing With Uncertainty CHAPTER 10Dealing With Uncertainty
2 RISK Risk and uncertainty are similar Both present the problem of not knowing what future conditions will beRisk offers estimates of probabilities for possible outcomesUncertainty does not provide estimates of probabilities for possible outcomesThis book treats them as interchangeable
3 Four Major Sources Of Uncertainty Possible inaccuracy of cash-flow estimates used in the studyHow much source information is availableHow dependable is the source informationType of business relative to the future health of the economySome businesses will typically be more at risk when there is a general decline in the economyType of physical plant and equipment involvedSome equipment have more definite lives and MV than the others (general lathe machine vs. mining equipment)Length of study periodThe longer the study period, the greater the level of uncertainty of a capital investment
4 Sensitivity AnalysisSensitivity – The degree to which a measure of merit (I.e., PW, IRR, etc…) will change as a result of changes in one or more of the study factor valuesSensitivity Analysis TechniquesBreakeven AnalysisSensitivity Graph (spiderplot)Combination of factors
5 Breakeven AnalysisUseful for choosing among alternatives when costs or revenues are highly sensitive to a single factor that is hard to estimate (e.g., operating hours per year, useful life, etc.)General Procedure:Write an expression of equivalent worth for each alternative in terms of the common factor.Equate the equivalent worths and solve for the value of the common factor. This value is the breakeven point (B.E.P.).Estimate whether the actual factor value will be higher or lower than the B.E.P. and then choose the appropriate alternative.
6 Breakeven Problem Involving Two Alternatives Indifference between alternatives (EWA = f1(y); EWB = f2(y)EWA = EWB; f1(y) = f2(y) : Solve for yEconomic acceptability of engineering projectEWp = f(z) = 0The value of ‘z’ is the value at which we would be indifferent between accepting or rejecting the project
7 ExampleSuppose that there are two alternative electric motors that provide 100 hp output. An Alpha motor can be purchased for $12,500 and has an efficiency of 74%, an estimated life of 10 years, and estimated maintenance cost of $500 per year. A Beta motor will cost $16,000 and has an efficiency of 92%, a life of 10 years, and annual maintenance costs of $250. Annual taxes and insurance costs on either motor will be 1-1/2% of the investment. If the minimum attractive rate of return is 15%, how many hours per year would the motors have to be operated at full load for the annual costs to be equal? Assume that salvage values for both motors are negligible and that electricity costs $0.05 per kilowatt-hour.
9 Sensitivity Graph (Spiderplot) Makes explicit the impact of uncertainty in the estimates of each factor of concern on the economic measure of meritAnnual revenue and expensesRate of returnMarket (or salvage) valueEquipment LifeCapacity utilization
10 ExampleA machine for which most likely cash flow estimates are given in the following list is being considered for immediate installation. Because of the new technology built into this machine, it is desired to investigate its PW over a range of 40% in:(a) initial investment, (b) annual net cash flow, (c) salvage value, and (d) useful lifeBased on these estimates, how much can the initial investment increase without making the machine an unattractive venture?Draw a diagram that summarizes the sensitivity of present worth to changes in each separate parameter when the MARR = 10% per year
11 Example: SolutionPW(10%) = -11, ,000(P|A,10%,6) + 1,000(P|F,10%,6)= $2,130a) When the Initial Investment varies by ±p%PW=(1± p% /100)(-11,500) + 3,000(P|A,10%,6)+ 1,000(P|F,10%,6)b) When Net Annual Cash Flow varies by ±a%PW = -11,500+(1± a% /100)(3,000)(P|A, 10%,6)+1,000(P|F,10%,6)c) When Salvage Value varies by ±s%PW = -11,500+3,000(P|A,10%,6)+(1± s% /100 )(1,000)(P|F,10%,6)d) When the Useful Life varies by ±n%PW = -11,500+3,000[P|A,10%,6(1± n% /100 )]+1,000[P|F,10%,6(1± n% /100)]
12 Sensitivity Graph (Spiderplot) Of Four Factors PW (10%)7000Capital Investment60005000Annual Net Cash Flow, A$2130Useful Life, N40003000Market Value, MV2000%Deviation Changes in Factor Estimate% DeviationChanges inFactorEstimate1000-1000-2000-3000-4000
13 Revelations Of Spiderplot Shows the sensitivity of the present worth to percent deviation changes in each factor’s best estimateOther factors are assumed to remain at their best estimate valuesThe relative degree of sensitivity of the present worth to each factor is indicated by the slope of the curves (the “steeper” the slope of a curve the more sensitive the present worth is to the factor)In this example:Present worth is insensitive to MVPresent worth is sensitive to I, A, and N
14 Measuring Sensitivity By A Combination Of Factors Develop a sensitivity graph for the projectUse sensitivity graph to select most sensitive project factors.Analyze combined effects of these factors on project’s economic measure of merit
15 Example - Continued Which parameter is most sensitive to change? PW(10%) = 0 when Initial Investment increases 18.5%PW(10%) = 0 when Net Annual CF decreases 16.3%PW(10%) = 0 when Salvage Value decreases 378%Note: requires a negative Salvage ValuePW(10%) = 0 when Useful Life decreases 21.7%
16 Optimistic - Pessimistic Estimates Exploring sensitivity by estimating one or more factors in a favorable direction and in an unfavorable direction to investigate the effect on study results.Optimistic - 95th percentile (desirable)Pessimistic - 5th percentile (undesirable)Not only do we examine the Equivalent Worth (EW) for all three estimation conditions, we examine the EW for all combinations of estimated outcomes for the key factors being estimated.
17 Problem (page 455)Suppose for an engineering project the optimistic, most likely, and pessimistic estimates are as shown belowOptimistic Most Likely PessimisticCapital Investment -$80,000 -$95,000 -$120,000Useful Life 12 years 10 years 6 yearsMarket Value $30,000 $20,000 0Net Annual CF $35,000 $30,000 $20,000MARR 12%/yr 12%/yr 12%/yra) What is the AW for each of the three estimation conditions?b) It is thought the most critical elements are useful life and net annual cash flow. Develop a table showing the AW for all combinations of estimates for these two factors, assuming that all other factors remain at their most likely values.
18 Problem Set upAW(12%) =Set up a table to illustrate summary results:Useful LifeNet Annual O ML PCash Flow (12 yrs) (10 yrs) (6 yrs)O $35,000ML $30,000P $20,000
19 Dealing with Uncertainty Uncertainty causes factors to become random variable in engineering economy analysisRisk-Adjusted MARRA widely used industrial practice for including some consideration of uncertainty is to increase the MARRReduction of useful lifeBy dropping from consideration those revenues (savings) and expenses that may occur after a reduced study period, heavy emphasis is placed on rapid recovery of capital in early years of a project’s lifeThis method is closely related to the discounted payback technique and suffers from most of the same deficiencies