Civil systems planning benefit cost analysis
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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

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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


Civil systems planning benefit cost analysis

$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


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

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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

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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

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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’

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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?

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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’

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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

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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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