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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. 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

Civil Systems PlanningBenefit/Cost Analysis

Scott Matthews

Final Review

Courses: 12-706 and 73-359

Lecture 21 - 12/2/2002

admin
Admin
  • PS 4 Returned Today
  • PS 5 Due Friday

12-706 and 73-359

test notes
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

test hints
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

three legs to stand on
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

slide6

$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

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gross benefits with wtp

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

consumer surplus changes
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

elasticities of demand
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

social surplus

Social Surplus = consumer surplus + producer surplus

Losses in Social Surplus are Dead-Weight Losses!

P

S

P*

D

Q*

Q

Social Surplus

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general terms
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

notes on estimation
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

equivalent annual benefit
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

internal rate of return
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

relative npv analysis
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

after tax cash flows
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

chap 5 social discount rate
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

tradeoff of car problem
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

how many variables
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

best and worst case analysis
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

cost effectiveness testing
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

the cea ratios
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

wtp versus wta
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

life saving metrics
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

value travel time savings
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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