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Civil Systems Planning Benefit/Cost Analysis

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Civil Systems PlanningBenefit/Cost Analysis

Scott Matthews

Final Review

Courses: 12-706 and 73-359

Lecture 21 - 12/2/2002

- PS 4 Returned Today
- PS 5 Due Friday

12-706 and 73-359

- 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

- 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

- 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

$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

Price

A

B

P*

0 1 2 3 4 Q*

Quantity

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

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

- 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 = consumer surplus + producer surplus

Losses in Social Surplus are Dead-Weight Losses!

P

S

P*

D

Q*

Q

12-706 and 73-359

- 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

- 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

- 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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- 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

- 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

- 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

- 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

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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