Transcript Final Review

Civil Systems Planning
Benefit/Cost Analysis
Scott Matthews/Joe Marriott
Final Review
Courses: 12-706 and 73-359
Lecture 22 - 12/1/2004
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Admin
PS 4 Returned Today
PS 5 Due Dec 10 (at final: last chance)
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Test Notes
Is cumulative, but “end-weighted”
About 4 questions (2 decided already)
‘One’ may be a series of short questions
Some HW questions were ‘previous year final questions’
E.g. CARB, DGPS, cash flows
Open book, notes, lecture notes
Can Bring calculators (no laptops - shouldn’t need them
- I will provide P|F,i,n values)
All slides in this talk from earlier classes
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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! Please!
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 better
Fundamental Principle of CBA
Amongst choices, select option with highest
net benefit
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$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
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$100
$25
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Gross Benefits with WTP
Price
A
A
B
P*
B
0
1
2
3
4
Q*
Quantity
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
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 =
Lecturepositive
21: 11/28/01 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 = 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
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Social Surplus
Social Surplus = consumer surplus + producer surplus
Losses in Social Surplus are Dead-Weight Losses!
P
S
P*
D
Q*
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Q
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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 72
PV = $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 needed
Be creative, BUT
Be logical and able to justify
Find 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=$1.330
EANB(2)=$18.77/16.374=$1.146
Still higher for option 1
Note 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
Comfort
10
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.
5
0
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M(25,10)
-1
V(30,9)
5
T
C
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Fuel Eff
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MCDM via AHP
Formal, quantitative framework for solving
multi-criteria problems
Uses survey/system of preferences to
incorporate values
Recall how to apply AHP model (matrixbased priorities and weights)
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Sens. Anal - # of 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
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
Randomly draw from probability distributions
What is resulting dist’n of net benefits?
Understand trend towards mean value, etc.
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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
Different rates for business and leisure
Range of values (e.g. 50-100%)
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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 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
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No real difference
between
2 ratios
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Multiple Effectiveness
 In Option 2, its not relevant to simply divide total costs (TC)
by # deaths, # injuries, e.g. CE1 = TC/death, CE2 = TC/injury
 Why?
Misrepresents costs of each effectiveness
 Instead, we need a method to allocate the costs (or to
separate the benefits) so that we have CE ratios relevant to
each effectiveness measure
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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
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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)
Know how to do annuity factors, etc.
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