Presentation on theme: "Engineering Economic Analysis Canadian Edition"— Presentation transcript:
1Engineering Economic Analysis Canadian Edition Chapter 9:Other Analysis Techniques
2Chapter 9 …Develops additional alternate methods to solve engineering economic problems:future valuebenefit-cost ratiopayback periodsensitivity analysisLinks the future value method to the present value and equivalent annual value methods.Uses spreadsheets to perform sensitivity and breakeven analyses.
3Present and Future Value Methods Net Present Value (NPV)What is the present value of future activity?Project cash flows are discounted to an equivalent value, usually at the start of the project (see Chapter 5).Net Future Value (NFV)What is the future value of current activity?Project cash flows are converted to a future value, usually at the end of the project.
4Future Value12345$750$1500$1000$500FV = ?5≡Find the value of the cash flows at the end of the 5th year if the rate of interest is 10% compounded annually. (Answer= $ )
5Economic Criteria Projects are judged against an economic criterion. SituationCriterionFixed inputMaximize outputFixed outputMinimize inputNeither fixedMaximize difference(output input)
6Economic Criteria Restated for Future Value Techniques SituationCriterionFixed inputAmount of capital available is fixedMaximize future value of benefitsFixed outputAmount of benefits is fixedMinimize future value of costsNeither fixedNeither capital nor benefits is fixedMaximize net future value(NFV)
7Type of Projects Independent Mutually exclusive Contingent (dependent) The selection of a project is independent of the decision to undertake any other project(s).Mutually exclusiveAt most one project (including the status quo, or “do nothing” option) can be selected amongst competing alternatives.Contingent (dependent)The selection of a project is dependent on the selection of at least one other project.
8Problem: Find NFV (i = 10%) + $2000(1.10)6+ $3000(1.10)5+ $2500(1.10)4+ $2000(1.10)3+ $1500(1.10)2+ $1000(1.10)+ $500= $20,060.62(or find NPV, then (1.10)8)YEARCASH FLOW$01$10002$20003$30004$250056$150078$500
9NFV and Independent Projects Select all projects with non-negative net future value (NFV).if NFV > 0, accept projectif NFV < 0, reject projectif NFV = 0, marginally accept projectIf all projects have NFV < $0, select the status quo (do nothing) option; invest available funds at the prevailing risk-free interest rate.The selection of independent projects is usually constrained by a capital budget (limited funds).
10NFV and Independent Projects … The NFV is the amount that remains at the end of a project after the annual cash flows are accumulated into the unrecovered capital, plus required returns, throughout the project.Example: find the NFV and the NPV of a project that requires an investment of $500K and has the cash flows shown below if the MARR is fourteen percent. (Answer: NFV = $149,131.52; NPV = $88,297.83).Year1234Cash Flow$150K$300K$225K$125K
11Future Value and Present Value Analysis PARAMETERSPROJECT APROJECT BPROJECT CInvestment$2500$3500$5000Annual cost$900$700$ (G=$100)Salvage value$200$350$600Life (years)5Annual revenue$1800$1900$2100 (15% growth)MARR10%
12Future Value and Present Value Analysis … Calculate the NPV and the NFV for Projects A, B, and C.NPVA = $ ; NFVA = $NPVB = $ ; NFVB = $NPVC = $ ; NFVC = $
13Useful Lives Analysis Period Project A has a three-year life. Project B has a four-year life. Both projects are valid since each has NFV > $0 (i = 10%).Which project is better?YearProject AProject B$1000$20001$500$720234NFV$324.00$413.32
14Useful Lives ≠ Analysis Period … Because Projects A and B have different lives, the NFV criterion requires that they be evaluated over a common period of analysis (12 years).Hence, Project A will be repeated four times (after the initial invest-ment at t=0) and Project B three times.YearProject AProject B$1000$20001$500$72023$5004$128056789101112NFV =$$
15Benefit-Cost RatioBy restating the NPV, NFV, and EACF criteria, we know that an investment is acceptable at a given MARR provided:PV(positive CFs) – PV(negative CFs) ≥ 0FV(positive CFs) – FV(negative CFs) ≥ 0EACF(positive CFs) – EACF(negative CFs) ≥ 0These provisions can be put in terms of the benefit-cost ratio (BCR):BCR = PV(positive CFs)/PV(negative CFs) = EACF(positive CFs)/EACF(negative CFs)If its BCR 1, an investment is acceptable.
16Benefit-Cost Ratio …Example: a firm is considering a project that requires an investment of $600K and has the cash flows shown below. Decide whether the firm should accept this project if its MARR is 15%. Use NPV, EACF, NFV, IRR, and BCR criteria. (Answer: the firm should not accept the project. NPV = $23, < 0; EACF = $ < 0; NFV = $40, < 0; IRR = % < 15%; BCR = < 1).Year1234Cash Flow$150K$300K$225K$125K
17Economic Criteria Restated for Benefit-Cost Ratio Method SituationCriterionFixed inputAmount of capital avail-able is fixedMaximize BCRFixed outputAmount of benefit is fixedNeither fixedNeither capital nor benefits are fixed1 candidate: BCR ≥ 1.2 or more alternatives: use incremental BCR.
18BCR and Incremental BCR (∆BCR) The BCR and other criteria such as the NPV, NFV, EACF, and IRR lead to the same conclusion regarding whether to accept individual projects.Similar to the IRR case, we use incremental BCR (∆BCR) to determine the best alternative among two or more competing alternatives.The BCRs of competing alternatives can not be compared directly even if the lifetimes or analysis periods are equal, as they can for the NPV and NFV cases.
19BCR and ∆BCR …Example: a company needs a new network and it is considering two systems. System M costs $120K to acquire/install; they estimate its annual net benefit will be $45K for four years. System N’s estimated net benefit will be $40K per year for three years at a cost of $85K to acquire/install. Determine which system the company should acquire if they use a 10½ percent rate of return. Use the BCR. (Answer: acquire System M. BCRM = ; BCRN = ; BCRMN = )
20BCR and Competing Alternatives Example: Moose County has three alterna-tives for a new road. Benefits and costs are shown below. Expected road life is 50 years and MARR = 10%. Apply BCR and ∆BCR.RoadFirst CostAnnualBenefitsAnnual Operating CostsA$25,000$3200$200B$35,000$3800$250C$50,000$6050$350
21Payback PeriodDefined as the time taken for the cumulative cash flows of an investment to reach zero.Accept an investment if its payback period ≤ the maximum allowable payback period.Notes about payback period:Payback is an approximate method that ignores the time value of money.After the maximum allowable payback period, all cash flows are ignored.The payback method will not necessarily produce a recommended alternative that is consistent with valuation and rate of return methods.
22Payback Period …Focuses exclusively on liquidity (no concern for profitability).Liquidity: how quickly the investment can be recovered from the project’s cash flows.All other methods of project evaluation focus on profitability (not liquidity).Ignores the time-value of money, i.e. implicitly assumes that MARR = 0%.The opportunity cost of the project balance, or the unrecovered portion of the capital investment, is ignored.Project Balance = –P + ∑(ORi – OCi), i = 0,1, … N.
23Payback Period … Project balance at any point during its life is: Simple payback: a project’s unrecovered investment without discounting.Discounted payback: a project’s unrecovered investment taking into account the opportunity cost (i.e., interest charges or required return) of the unrecovered investment.Generally, annual net cash flows (revenues less costs) will cause a project’s balance to become more positive over time.The project balance is negative until the initial investment has been fully recovered.
24Payback Period … t* Project Balance = $0 + t3 t1 t2 – –t1t2t3t*First CostYear 1: Benefits – Costs
25Payback Period … Year Cash Flow: Project A Cash Flow: Project B –$15,0001$1000$30002$200034$40005$50006$60007$70008$8000
26Payback Period …Projects A and B both have payback period = 5 years (project balance = 0 after five years).They have very different profitability profiles: Project A is more profitable than Project B by the end of its lifetime.Since we focus only on liquidity (how fast the initial investment is recovered), the payback method makes us indifferent between projects A and B.
27Payback Period … Payback period = 3 + 300/1000 = 3.3 years. Compare 3.3 years to an industry threshold to determine if the project is acceptable.If similar investments require, on average, three years to recover, this project would be rejected.YearCash FlowProject Balance–$10001–$500–$15002+$5003+$700–$3004+$1000
28Payback Period … Discounted Payback Period Year Cash Flow Opportunity Cost (10%)Project Balance–$150001$3500–$1500–$130002–$1300–$108003–$1080–$83804–$838–$57185–$571.8–$2789.86–$278.98$431.22
29Payback Period …Discounted payback period = 5 + $2789.8(1.1)/$3500 = years.If the industry average discounted payback period for this type of project is > years, this project is acceptable. Otherwise, it is not.We can see that the NFV is $ (> 0), therefore the project should be considered acceptable.
30Payback Period …We can also use a present value approach for the discounted payback period. Find the point at which the cumulative PVs of the cash flows becomes 0.For the same example. Discounted payback period = years (same as above). Note, the NPV = $If the discounted payback period ≤ the life-time, a project should be considered accep-table since this means that NPV ≥ 0. Regret-tably, such a criterion is not always specified.
31Sensitivity & Break-even Analysis Economic data represent projections of expenditures and returns.These projections ultimately affect our decisions.To consider our choice of a decision more fully, we should play a “what if” game to determine the amount of change in a project parameter that might alter the decision.This allows us to make an assessment of the inherent risk in a project, i.e. the probability of different outcomes due to uncertainty in the project variables.
32Sensitivity & break-even analysis … Projected and actual cash flows may differ due to:Technological change: changes to production costsChanges in the size and number of competing firmsIntroduction of new products: substitutes or complementsChanges to key macroeconomic variables, e.g. inflation, unemployment, economic growth, exchange rateInternational events
33Sensitivity & break-even analysis … Sensitivity example: System cost = $200,000; annual profit = $36,000; salvage value = $23,500; lifetime = 10 years; MARR = 12%. Use sensitivity analysis to determine which project components affect the NPV most.
34Sensitivity & break-even analysis … Break-even example: using the information from the sensitivity example, find the break-even values for the initial investment and for the annual profit (the parameters to which the NPV is most sensitive).
35Sensitivity & break-even analysis … Scenario example: using the information from the sensitivity example, perform a scenario analysis. Worst case: $210,000 investment, $33,000 annual profit, $17,500 salvage value, lifetime eight years, MARR 13%. Best case: $195,000 investment, $37,500 annual profit, $26,500 salvage value, lifetime eleven years, MARR 11½%.