MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 11.011 Project EvaluationPrices & InflationCarl D. Martland1. Review of prices2. Price indices3. Real vs. nominal discount ratesReview of PricesPrices are determined by the interaction of supply and demandDemand issues:Willingness-to-pay depends upon the VALUE of the service or product, not its COSTThe lower the price, the greater the demandSupply issuesMin price > marginal cost (or supplier won't produce)Avg price > avg cost (or supplier won't make a profit)Choose design, production process, machines, materials for expected volume/demand and desired level of service Lower Costs Allow Lower PricesChoice of process depends upon the relative prices of inputs Input substitutionAverage and marginal costs vary with the size of the projectEconomies of ScaleTechnological change allows lower costs through introduction of new machines, materials, processes, designs, etcTechnological changeMinimum Cost Combination of Inputs to Produce Q0 is Where Isocost Curve is Tangent to Isoquant for QoQ0Q1Production IsoquantsCapitalLaborIsocost = Cc*Capital + Cl*LaborOptimal Input Substitution:As Prices of Inputs Change, Different Processes or Materials are Used Q0Q1Production IsoquantsCapitalLaborIsocost = Cc2*Capital + Cl2*LaborNew OptimalEconomies of Scale: Production Isoquants Are Close TogetherQ0Q1Production IsoquantsCapitalLaborIsocost = Cc*Capital + Cl*LaborOptimal Q3 Q2MIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 2Expansion Path: Optimal Combination of Inputs as Volume Produced IncreasesQ0Q1Expansion PathCapitalLaborIsocost = Cc*Capital + Cl*LaborOptimal Q3 Q2Prices for a Particular Project Will Not Necessarily Follow General Price IndicesRelative changes in prices of inputs may allow input substitutionIncreases in demand may allow economies of scaleNew technologies or designs may reduce costsWhy a Price Index is UsefulWe want to compare $ from different time periods or different countries, and it is desirable to compare $ in terms of purchasing powerWe want to project future costs and revenues taking into account expected changes in prices of inputs and outputse.g. we may expect fuel prices to rise and computer prices to decline relative to laborWe can treat major categories of cost and revenue separatelyCreating a Price Index for a Base Year1. Choose a base year2. Choose a "market basket of goods & services"3. Identify a. Base year prices for each item i = Piob. Base year wieghts Wi (i.e. share of cost of basket)4. Choose a scale factor s.t. base year index = 100PI(0) = Pio*Wi*So, summed over all i Creating a Price Index for Year t1. Choose year t2. For the same "market basket of goods & services", Identify Year t prices for each item i = Pit3. Use the base year weights Wi (i.e. each item is weighted by its share of costs in year 0)4. Calculate the price index for year t:PI(t) = Pit*Wi*So/ Pio*Wi*SoAdjusting the Price IndexThe price index needs to be adjusted periodically:New commodities need to be consideredBecause of relative price changes, the weights need to be revisedThe adjustments can be made annually or at intervals of many yearsMIT Civil Engineering 1.011 -- Project Evaluation Spring Term 2003Carl D. Martland Page 3Nominal vs. Real Discount Ratesir = real discount rate (time value of money & risk)ic = nominal discount rate (include inflation as well)Future price of "market basket" = (1+f)t PoPresent value = (1+f)t Po/(1+ic)tEquivalent future value, 1 year in future:(1+ic)Po = (1+f)(1+ir)Po = (1+ir+f+ir*f)Po1+ic = 1 + ir +f(1+ir) = 1 + f + ir(1+f)So that ic = ir + f +ir*f and ic approx. = ir + f ir = (ic-f)/(1+f) approx. = ic - f if ir = 6% and f= 3%, theIf ir = 6% and f = 3%, thenic = 6% + 3% + .03*6%= 9.18% approx. = 9%Real vs. Nominal Financial AnalysisIf we have calculated IRR using actual $, we can get the IRR in real terms by using: IRR real = (IRR nominal - f)/(1+f)We can use nominal discount rates and current (ie. inflated) costs and benefits, then use the above relationship to adjust the IRR.If costs and revenues inflate at the same rate, then we can use constant dollars for cost and revenue and discount using the real discount rate.Nominal vs. Real Rates in Project EvaluationFinancing from a bank will use nominal interest rates (based upon what the bank and the market anticipate for inflation); you will pay in actual dollars over time (although your payment may in fact be constant)If there is inflation, you generally pay back your loan with cheaper dollars Some care may be needed to get the proper analysis - you need to make sure that all the costs and benefits are expressed in the same kind of dollars and that you use the proper discount rate.Use the Correct Approach!Nominal Interest RateReal Interest RateActual $ CorrectIncorrect (bias toward investment)Constant $Incorrect (bias against
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