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MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 11.011Project Evaluation:Comparing Costs & BenefitsCarl D. MartlandBasic Question: Are the future benefits large enough to justify the costs of the project?Present, Future, and Annual WorthInternal & External Rates of ReturnWhat Is a Project?For the planner (dreamer?):A vision, a dream or a hopeA monumentA way to solve a problemFor the construction company:A specific task to be completed within a specific timeA way to make money through constructionFor the owner: Potential benefits over the life of the projectA way to make money through operationA monumentFor others:Potential improvement in opportunities, environment, etcPotential disruptions and degradation in environmentHow Do We Justify a Project?Is this project worthwhile?Are the benefits greater than the costs?Are MY benefits greater than MY costs?Is this the best way to achieve these benefits (either engineering & institutional options)?Can similar benefits be achieved more efficiently by some other approach?Is this the best place to allocate resources?Do other projects have greater payoff?Are other types of benefits more important?Cash Flow of a Typical CEE ProjectYear-40-30-20-1001020304050Millions of DollarsEvaluating a Time Stream of Monetary Costs & BenefitsKey concepts:Time value of moneyRisk vs. required returnPresent Worth (= Net Present Value)Equivalence (for PW, FW, and AW)Project LifePresent Worth (Net Present Value)The "Present Worth" of a project is commonly referred to as its "Net Present Value".The NPV for the project is obtained by summing the discounted benefits for each year (using a discount rate i = MARR): NPV of Project = PW = Σ[(Bt - Ct)/(1+i)t]We know that this NPV can be transformed into an equivalent annual or future worth.MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 2Reduce all costs and benefits to time 0Compute the equivalent time stream of costs and benefits over the life of the project using standard formulas or spreadsheet commands:Use equations, tables or spreadsheet functions to calculate equivalent annuities (AW or "Equivalent Uniform Annual Benefits") or FWBe careful whether cash flows occur at the beginning or the end of the period (Annuities are generally assumed to be received at the END of the period)Equivalent PW, AW, and FWMeaning of NPVNPV > 0, using a discount rate of i% This project is better than making an investment at i% per year for the life of the projectThis project is worth further considerationNPV < 0, using a discount rate of i%This project does not provide enough financial benefits to justify investment, since alternative investments are available that will earn i% (that is what is meant by "Minimum Acceptable Rate of Return" )The project will need additional, possibly non-cash benefits to be justifiedImportance of the Discount RateVery low rates favor large projects with distant benefitsUsing very low discount rates may lead a country to undertake massive projects while ignoring current needsVery high rates favor staged investments with quick payback Using very high discount rates may prevent a country from ever undertaking large infrastructure investmentsImportance of the Project LifeProjects need to be evaluated over a reasonable project life (and the economic life will be shorter than physical life)However, your choice of a project life should NOT determine the outcome of the analysis (if it does, you must show sensitivity of the results to project life)Because of discounting, the "out years" do not add much to the NPV, so a 20 to 50 year life is usually sufficient for analysisThe proper assumption is that the very long term effects will be positive or neutral - NOT that we can live it up now and let our children and grandchildren worry about the future!Risks increase with timeSo we don't want to be dependent on long-term benefits to recover our investment. -15-10-50510A. Net Cash Flows Over a 10-Year Life-15-10-50510C. Cash Flows Over 25 Years(Increasing Competition & Maintenance) -200204060D. Net Cash Flows Over 50 Years(Rehab and Expansion in Prime Location)-15-10-50510B. Net Cash Flows Over 25 Years (Assuming Steady State After Year 10)Choice of a Project Life Should NOT Determine the Outcome of Your Analysis!Other Ways to Evaluate Cash FlowsBenefit/Cost RatiosNPV(Benefits)/NPV(Costs)Commonly used in public policy analysesRequired in order to ensure that benefits (by SOME measue at least!) are greater than costsA political, not a methodological statement!Internal and External Rates of Return (IRR and ERR)Very common in private sector, but there may be problems with IRR (which can be fixed by using ERR)Payback PeriodHow many years to recoup my investment? (A rather unsatisfactory approach that may be useful for quick assessment of some projects)MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 3Year-40-30-20-1001020304050Millions of DollarsYear050100150200250Millions of DollarsCash Flows, NPV, and Equivalent Uniform Annual Net BenefitsNPVEUANB-40-30-20-1001020304050Millions of DollarsYear050100150200250Millions of DollarsCalculating the Internal Rate of ReturnNPV(i%)EUANB(i%)Choose discount rate such that the NPV = 0NPV(IRR)EUANB(IRR)Problems With theInternal Rate of ReturnIf the cash flows switch signs more than once, there could be two or more IRR for which NPV(IRR) = 0This method assumes that all intermediate cash flows can be discounted/reinvested at the IRRThis is unrealistic when the IRR is very highThe private sector uses this method very commonly despite these problemsA Better Approach:The External Rate of ReturnUse a different discount rate (called the "External Rate of Return") to Discount all expenses to time 0Reinvest all benefits for the remaining time in the project lifeThen compare the NPV of the costs and the Future Value of the benefitsThe external rate of return is the discount rate s.t. the NPV of the costs is equivalent to the FV of the benefitsYear-40-30-20-1001020304050Millions of DollarsNPV Cost FV BenefitsYear-1000100200300400Millions of DollarsCalculating the External Rate of ReturnNPV of Costs,discounted at e%FV of Benefits, invested at e%Are There Alternatives For Achieving the Objectives of this Project?The NPV analysis only shows that a project can be justified relative to the discount rate that is usedThere may be other projects that are even better for


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