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Civil Systems Planning Benefit/Cost Analysis Scott Matthews Final Review Courses: 12-706 and 73-359 Lecture 21 - 12/2/2002 1 Admin PS 4 Returned Today PS 5 Due Friday Lecture 21: 11/28/01 12-706 and 73-359 2 Test Notes Is cumulative, but “end-weighted” 3-4 questions (2 decided already) ‘One’ of these might actually be a series of short questions Open book, notes, lecture notes Can Bring calculators (no laptops - shouldn’t need them) All slides in this talk from earlier classes Lecture 21: 11/28/01 12-706 and 73-359 3 Test Hints I will not try to ‘trick’ you Will be designed for 100 mins, but will have 3 hours to finish - don’t feel need to use whole time Do not re-read text - skim familiar areas, ensure knowledge of others Re-familiarize yourself with handouts And ‘energy problems’ Look for ‘shortcuts’ (e.g. relative NPV) Lecture 21: 11/28/01 12-706 and 73-359 4 Three Legs to Stand On Pareto Efficiency Make some better / make none worse Kaldor-Hicks Program adopted (NB>0) if winners COULD compensate losers, still be better Fundamental Principle of CBA Amongst choices, select option with highest net benefit Lecture 21: 11/28/01 12-706 and 73-359 5 $100 The ‘pareto frontier’ is the set of allocations that are pareto efficent. Try improving on (25,75) or (50,50) or (75,25)… We said initial alloc. mattered - e.g. (100,0)? $25 0 Lecture 21: 11/28/01 $100 $25 12-706 and 73-359 6 Gross Benefits with WTP Price A A B P* B 0 1 2 3 4 Q* Quantity Total/Gross Benefits = area under curve = A+B = willingness to pay for all people = Social WTP = their benefit from consuming Lecture 21: 11/28/01 12-706 and 73-359 7 Consumer Surplus Changes Price A CS2 P* B P1 0 1 2 Q* Q1 Quantity CS2 is the new consumer surplus when price decreases to (P1, Q1) Change in CS = Trapezoid P*ABP1 = gain = Lecturepositive 21: 11/28/01 net benefits 12-706 and 73-359 8 Elasticities of Demand Measurement of how “responsive” demand is to some change in price or income. Slope of demand curve = Dp/Dq. Elasticity of demand, e, is defined to be the percent change in quantity divided by the percent change in price. e = p Dq / q Dp Lecture 21: 11/28/01 12-706 and 73-359 9 Social Surplus Social Surplus = consumer surplus + producer surplus Losses in Social Surplus are Dead-Weight Losses! P S P* D Q* Lecture 21: 11/28/01 12-706 and 73-359 Q 10 General Terms FV = $X (1+i)n X : present value, i:interest rate and n is number of periods (eg years) of interest Rule of 72 PV = $X / (1+i)n NPV=NPV(B) - NPV(C) (over time) Real vs. Nominal values Lecture 21: 11/28/01 12-706 and 73-359 11 Notes on Estimation Move from abstract to concrete, identifying assumptions Draw from experience and basic data sources Use statistical techniques/surveys if needed Be creative, BUT Be logical and able to justify Find answer, then learn from it. Apply a reasonableness test Lecture 21: 11/28/01 12-706 and 73-359 12 Equivalent Annual Benefit EANB=NPV/Annuity Factor Annuity factor (i=5%,n=70) = 19.343 Ann. Factor (i=5%,n=35) = 16.374 EANB(1)=$25.73/19.343=$1.330 EANB(2)=$18.77/16.374=$1.146 Still higher for option 1 Note we assumed end of period pays Lecture 21: 11/28/01 12-706 and 73-359 13 Internal Rate of Return Defined as the discount rate where NPV=0 Graphically it is between 8-9% But we could solve otherwise E.g. 0=-100k/(1+i) + 150k /(1+i)2 100k/(1+i) = 150k /(1+i)2 100k = 150k /(1+i) <=> 1+i = 1.5, i=50% -100k/1.5 + 150k /(1.5)2 <=> -66.67+66.67 Lecture 21: 11/28/01 12-706 and 73-359 14 Relative NPV Analysis If comparing, can just find ‘relative’ NPV compared to a single option E.g. homework 2 copier problem Solutions NPV(1)=-$18k , NPV(2)=-$16k Net difference between them was $1,536 Alternatively consider ‘net amounts’ Copier cost =-3k, salvage 2k, annual +1k -3k+(2k/1.14)+(+1k/1.1)+..+(+1k/1.14) -3k+(2k*.683) +3.1699k = $1,536 Lecture 21: 11/28/01 12-706 and 73-359 15 After-tax cash flows Dt= Depreciation allowance in t It= Interest accrued in t + on unpaid balance, - overpayment Qt= available for reducing balance in t Wt= taxable income in t; Xt= tax rate Tt= income tax in t Yt= net after-tax cash flow Lecture 21: 11/28/01 12-706 and 73-359 16 Chap 5 - Social Discount Rate Discounting rooted in consumer preference We tend to prefer current, rather than future, consumption Marginal rate of time preference (MRTP) Face opportunity cost (of foregone interest) when we spend not save Marginal rate of investment return Lecture 21: 11/28/01 12-706 and 73-359 17 Tradeoff of Car Problem Comfort 10 The slope of the line between M and V is -1/5, I.e. you must trade one unit less of comfort for 5 units more of fuel efficiency. 5 0 Lecture 21: 11/28/01 10 20 12-706 and 73-359 M(25,10) -1 V(30,9) 5 T C 30 Fuel Eff 18 How many variables? Choosing ‘variables’ instead of ‘constants’ for all parameters is likely to make model unsolvable Partial sens. Analysis - change only 1 Equivalent of dy/dx Do for the most ‘critical’ assumptions Can use this to find ‘break-evens’ Lecture 21: 11/28/01 12-706 and 73-359 19 Best and Worst-Case Analysis Does any combination of inputs reverse the sign of our answer? If so, are those inputs reasonable? E.g. using very conservative ests. Monte carlo sens. Analysis Draw inputs from prob. Dist’ns What is resulting dist’n of net benefits? Lecture 21: 11/28/01 12-706 and 73-359 20 Cost-Effectiveness Testing Generally, use when: Considering externality effects or damages Alternatives give same result - eg ‘reduced x’ Benefit-Cost Analysis otherwise difficult Instead of finding NB, find “cheapest” Want greatest bang for the buck Find cost “per benefit” (e.g. lives saved) Allows us to NOT include ‘social costs’ Lecture 21: 11/28/01 12-706 and 73-359 21 The CEA ratios CE = C/E Equals cost “per unit of effectiveness” e.g. dollars per lives saved, tons CO2 reduced Want to minimize CE (cheapest is best) EC = E/C Effectiveness per unit cost e.g. Lives saved per dollar Want to maximize EC 12-706 and 73-359 No real difference between 2 ratios Lecture 21: 11/28/01 22 WTP versus WTA Economics implies that WTP should be equal to ‘willingness to accept’ Turns out people want MUCH MORE in compensation for losing something WTA is factor of 4-15 higher than WTP! Also see discrepancy shrink with experience WTP formats should be used in CVs Only can compare amongst individuals Lecture 21: 11/28/01 12-706 and 73-359 23 Life Saving Metrics Dollars/life saved Dollars/life-year saved Know how to calculate and interpret each one (see notes from those lectures for details) Lecture 21: 11/28/01 12-706 and 73-359 24 Value - travel time savings Many studies seek to estimate VTTS Can then be used easily in CBAs Book reminds us of Waters 1993 (56 studies) Many different methods used in studies Route, speed, mode, location choices Results as % of hourly wages not a $ amount Mean value of 48% of wage rate (median 40) North America: 59%/42% Lecture 21: 11/28/01 12-706 and 73-359 25