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Civil Systems PlanningBenefit/Cost Analysis

Scott MatthewsFinal ReviewCourses: 12-706 and 73-359Lecture 21 - 12/2/2002

Lecture 21: 11/28/01 12-706 and 73-359 2

Admin

PS 4 Returned TodayPS 5 Due Friday

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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

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Test Hints

I will not try to ‘trick’ youWill 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)

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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 betterFundamental Principle of CBA

Amongst choices, select option with highest net benefit

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$100

$1000

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

$25

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Gross Benefits with WTPPrice

Quantity

P*

0 1 2 3 4 Q*

A

BA

B

Total/Gross Benefits = area under curve = A+B = willingness to pay for all people = Social WTP = their benefit from consuming

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Consumer Surplus Changes Price

Quantity

P*

0 1 2 Q* Q1

A

BP1

CS2

CS2 is the new consumer surplus when price decreases to (P1, Q1)

Change in CS = Trapezoid P*ABP1 = gain = positive net benefits

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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

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Social Surplus

Social Surplus = consumer surplus + producer surplusLosses in Social Surplus are Dead-Weight Losses!

Q

P

Q*

P*

S

D

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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 72PV = $X / (1+i)n

NPV=NPV(B) - NPV(C) (over time)Real vs. Nominal values

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Notes on Estimation

Move from abstract to concrete, identifying assumptions

Draw from experience and basic data sources

Use statistical techniques/surveys if neededBe creative, BUTBe logical and able to justifyFind answer, then learn from it.Apply a reasonableness test

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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=$1.330EANB(2)=$18.77/16.374=$1.146

Still higher for option 1Note we assumed end of period pays

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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

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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

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

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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

Fuel Eff

Comfort

10

5

0 10 20 30

M(25,10)V(30,9)

T

C

-15

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.

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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’

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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

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 ratiosCE = 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 WTAEconomics implies that WTP should be

equal to ‘willingness to accept’Turns out people want MUCH MORE in

compensation for losing somethingWTA 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

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Life Saving Metrics

Dollars/life savedDollars/life-year savedKnow how to calculate and interpret

each one (see notes from those lectures for details)

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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%