1 Civil Systems Planning Benefit/Cost Analysis Scott Matthews Final Review Courses: and Lecture /2/2002

Lecture 21: 11/28/ and Admin  PS 4 Returned Today  PS 5 Due Friday

Lecture 21: 11/28/ and 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/ and 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/ and 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/ and $100 0 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

Lecture 21: 11/28/ and Gross Benefits with WTP Price Quantity P* Q* A B A B  Total/Gross Benefits = area under curve = A+B = willingness to pay for all people = Social WTP = their benefit from consuming

Lecture 21: 11/28/ and Consumer Surplus Changes Price Quantity P* Q* Q1 A B P1 CS2  CS2 is the new consumer surplus when price decreases to (P1, Q1)  Change in CS = Trapezoid P*ABP1 = gain = positive net benefits

Lecture 21: 11/28/ and Elasticities of Demand  Measurement of how “responsive” demand is to some change in price or income.  Slope of demand curve =  p/  q.  Elasticity of demand, , is defined to be the percent change in quantity divided by the percent change in price.  = p  q / q  p

Lecture 21: 11/28/ and Social Surplus Social Surplus = consumer surplus + producer surplus Losses in Social Surplus are Dead-Weight Losses! Q P Q* P* S D

Lecture 21: 11/28/ and 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/ and 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/ and Equivalent Annual Benefit  EANB=NPV/Annuity Factor  Annuity factor (i=5%,n=70) =  Ann. Factor (i=5%,n=35) =  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/ and 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/ k /(1.5)

Lecture 21: 11/28/ and 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/1.1 4 )+(+1k/1.1)+..+(+1k/1.1 4 )  -3k+(2k*.683) k = $1,536

Lecture 21: 11/28/ and After-tax cash flows  D t = Depreciation allowance in t  I t = Interest accrued in t  + on unpaid balance, - overpayment  Q t = available for reducing balance in t  W t = taxable income in t; X t = tax rate  T t = income tax in t  Y t = net after-tax cash flow

Lecture 21: 11/28/ and 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/ and Tradeoff of Car Problem Fuel Eff Comfort M(25,10) V(30,9) T C 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.

Lecture 21: 11/28/ and 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  y/  x  Do for the most ‘critical’ assumptions  Can use this to find ‘break-evens’

Lecture 21: 11/28/ and 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/ and 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/ and 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

Lecture 21: 11/28/ and 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/ and 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/ and 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%