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We expect college costs to increase at a 6% annual rate. What will tuition be in 10 years? Tuition of tomorrow = $2000(1 + 0.06)10 = $3582 Vx0x%  U@#Estimating Past Cost with InflationThe cost of a hamburger is $3 today, what did it cost 40 years ago? Assume the average rate of inflation during that time was 5%, Hamburger of yesterday = $3/(1 + 0.05)40 = $0.43D1&  +Why do we Have Inflation?Too many dollars chasing too few goods bid prices up Government creates too much money Money not backed by hard currency Decreasing amounts of raw materials Unreasonable demands by labor Unreasonable price increases by business.DWhy do we Have Inflation? (cont d)Inflationary expectations (Inflationary spiral) Uncertainty about government survival and policies Governments benefit by inflation Borrowed money is easier to pay back Proportion of income taxed goes up in a progressive tax system&dd/Effect of Inflation Is inflation good or bad? It depends on whether you are a borrower or an investor It is confusing for decision makers Can inflation be controlled? It is a primary concern of Alan Greenspan and the Federal Reserve How do we make economic decisions considering inflation?`\B9\B90 Expressing Cash FlowsCash flows may be in real or actual dollars Consider an estimated cash flow n years from today. If the cash flow is expressed in terms of today s dollars, we say the amount is in real (or year-0, or constant) dollars. If the cash flow is expressed in terms of the dollars that will be used in n years, we say the amount is in actual (or year-n, or current) dollars.,B, fn  1!From Real to Actual DollarsAssume a general inflation rate of f per year. If some cash flow at year n is the amount $C expressed in real dollars, the amount in actual dollars isV#%<2"From Actual to Real DollarsqIf some cash flow at year n is the amount $D expressed in actual dollars, the amount expressed in real dollars isHrD3#'Economic Analyses Considering Inflation+The MARR is different with and without inflation We denote the market MARR (with inflation) with ic the real MARR (without inflation) with ir , ic > ir. the inflation rate with f The MARR considering inflation should be ic = ir + f + ir f If f and ic are given, then ir. = ( ic -f )/( 1+f )6;0ZzZ*Z ZZ4Z:& (   *         `&F XAEstimating Cash Flows YB$Changing Estimates to Actual Dollars ZC'Changing Actual Dollars to Real Dollars [DPresent Worth Analysis 6&Cash Flow Analysis with NPWIf cash flows are in actual dollars, Use ic to compute NPW If cash flows are in real dollars, Use ir to compute NPW NPW is the same in both real and actual dollars&$1& $ 1,)6@9( Example 1All components of the cash flow escalate at the same rate as general inflation The investment is $10,000 and the life is ten years with no salvage. Based on today s prices, we estimate operating costs at $500 per year, and revenues at $2000 per year. All costs and revenues are fully responsive to inflation.Escalation rates are the same as general inflation. The MARR without inflation is 4%. The general inflation rate is 5%. Therefore, the MARR with inflation is 0.04 + 0.05 +( 0.04)(0.05) = 0.092 = 9.2%LOZZ= ZO;*$Example 1 (cont d)R<Neglecting InflationSometimes inflation can be neglected For an economic analysis, if all receipts and expenses expand at the same rate as the general inflation rate, forget about inflation. Do the analysis with real dollars and ir (the MARR without inflation)l%  % ?,Different Inflation RatesIf some components of receipts and disbursements do not have the same escalation rate either: Express all cash flows in actual (year-n) dollars and use ic Express all cash flows in real (year-0) dollars and use ir ^x^: 9 $8@- Example 2lSome components of the cash flow escalate at different rates than general inflation The investment is $10,000 and the life is ten years with no salvage. Based on today s prices, we estimate that operating costs as $500 per year and revenues at $2000 per year. We expect the general inflation rate to be 5%. Operating costs escalate at the same rate as general inflation. Revenues do not increase with time. The MARR w/o inflation is 4%.4TcTbA.DExample 2 (cont d): Actual DollarsB/@Example 2 (cont d): Real DollarsC0"Alternative Computation: Short CutComputing NPW when components have different escalation rates Investment - Not affected by inflation A cash flow component that is fully responsive to inflation Use the MARR w/o inflation (ir) A cash flow component that does not change with time (escalation rate is 0) Use the MARR with inflation (ic) A cash flow component that is increasing at a rate ej Use [(1 + ic)/(1 + ej)] - 1n>c L!6>c L 3          bk5 E1Example 2: Using Short CutInvestment is $10,000 Estimate annual costs of $500. They escalate at a 5% rate Estimate annual revenues of $2000. They are fixed and do not escalate. MARR w/o inflation is 4%. Assume general inflation rate is 5%. NPW = -10000 + 2000 (P/A, 0.092, 10) - 500(P/A, 0.04, 10)= -1332 d< :   S=Cash Flow Analysis with NAWTo find the annual worth in actual dollars, Use ic to compute NAW, or Use NAWc = NPW (A/P, ic , N) To find the annual worth in real dollars, Use ir to compute NAW, or Use NAWr = NPW (A/P, ir , N) NAWr (in real dollars) is the most reasonable for comparisonsJ-8+8>-    +     :0 3 :F2Computing the NAWH3Example 2: Revisited with NAWWhen comparing alternatives with the NAW method, it is only rational to compare the NAW expressed in real dollars. Compute the NAW as follows: NAWr = NPW(A/P, ir, n), where ir is the MARR without inflation. NAWr = -1332(A/P, 0.04, 10) = -1332 (0.1233) = -$164 per year.@:      :P   =T>Cash Flow Analysis with RORIf cash flow are in actual dollars, Compute RORc This RORc is with inflation Compare with ic If cash flow are in real dollars, Compute RORr This RORr is without inflation Compare with ir You can find one from the other: %;#="%      #    # "t- +##I4Rate of Return MethodJ5Analysis with TaxesDepreciation does not adjust with inflation. It is always in actual dollars. An after-tax analysis always requires that inflation be considered. Either express after tax cash flows in actual dollars and use ic, or express the after tax cash flows in real dollars and use irr> > ,>L6 Example 3After-tax analysis includes taxes and depreciation. The Investment is $10,000 and the life is ten years with no salvage. Without adjusting for inflation, we estimate that operating costs as $500 per year and revenues at $2000 per year. Both revenue and costs increase at the same rate as general inflation. The general inflation rate is 5%. The asset is depreciated with the straight-line method. The tax rate is 40%. The after tax MARR without inflation is 4%.444M7Example 3: After-Tax AnalysisInflation reduces the attractiveness of investments requiring depreciation Assuming 5% inflation, After-tax MARR w/ inflation = 9.2%, Tax Rate = 40%.*JKN8Summary7When all cash flow components escalate at the general inflation rate, use real dollars and ir. When some cash flow components escalate at different rates, either use real dollars and ir or actual dollars and ic. 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