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Civil Systems Planning Benefit/Cost Analysis

Civil Systems Planning Benefit/Cost Analysis. Scott Matthews Final Review Courses: 12-706 and 73-359 Lecture 21 - 12/2/2002. Admin . PS 4 Returned Today PS 5 Due Friday. Test Notes. Is cumulative, but “end-weighted” 3-4 questions (2 decided already)

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Civil Systems Planning Benefit/Cost Analysis

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  1. Civil Systems PlanningBenefit/Cost Analysis Scott Matthews Final Review Courses: 12-706 and 73-359 Lecture 21 - 12/2/2002

  2. Admin • PS 4 Returned Today • PS 5 Due Friday 12-706 and 73-359

  3. 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 12-706 and 73-359

  4. 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) 12-706 and 73-359

  5. 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 12-706 and 73-359

  6. $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 $100 $25 12-706 and 73-359

  7. Price A B P* 0 1 2 3 4 Q* Quantity Gross Benefits with WTP A B • Total/Gross Benefits = area under curve = A+B = willingness to pay for all people = Social WTP = their benefit from consuming 12-706 and 73-359

  8. 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 = positive net benefits 12-706 and 73-359

  9. 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 12-706 and 73-359

  10. Social Surplus = consumer surplus + producer surplus Losses in Social Surplus are Dead-Weight Losses! P S P* D Q* Q Social Surplus 12-706 and 73-359

  11. 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 12-706 and 73-359

  12. 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 12-706 and 73-359

  13. 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 12-706 and 73-359

  14. 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 12-706 and 73-359

  15. 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 12-706 and 73-359

  16. 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 12-706 and 73-359

  17. 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 12-706 and 73-359

  18. Tradeoff of Car Problem Comfort M(25,10) 10 -1 V(30,9) 5 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. T 5 C 0 10 Fuel Eff 20 30 12-706 and 73-359

  19. 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’ 12-706 and 73-359

  20. 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? 12-706 and 73-359

  21. 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’ 12-706 and 73-359

  22. 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 • No real difference between 2 ratios 12-706 and 73-359

  23. 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 12-706 and 73-359

  24. 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) 12-706 and 73-359

  25. 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% 12-706 and 73-359

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