Transcript Borrowing, Depreciation, Taxes in Cash Flow Problems

Social Discount Rate
Guest Lecturer:
Paulina Jaramillo
12-706 / 19-702 /73-359
Lecture 5
Admin Issues
Pipeline case study writeup - due Monday
Format expectations:
Framing of problem (see p. 7!),
Answer/justify with preliminary calculations
Don’t just estimate the answer!
Do not need to submit an excel printout, but
feel free to paste a table into a document
Length: Less than 2 pages.
Real and Nominal Values
 Nominal: ‘current’ or historical data
 Real: ‘constant’ or adjusted data
 Use deflator or price index for real
 Generally “Real” has had inflation/price changes factored in and
nominal has not
 For investment problems:
 If B&C in real dollars, use real disc rate
 If B&C in nominal dollars, use nominal rate
 Both methods will give the same answer
Nominal Discount Rates
Market interest rates are nominal
They ideally reflect inflation to ensure value
Buy $100 certificate of deposit (CD) paying
6% after 1 year (get $106 at the end). Thus
the bond pays an interest rate of 6%. This is
nominal.
Whenever people speak of the “interest rate”
they're talking about the nominal interest rate,
unless they state otherwise.
Real Discount Rates
Suppose inflation rate is 3% for that year
i.e., if we can buy a “basket of goods” today for $100,
then we can buy that basket next year and it will cost
$103.
If buy the $100 CD at 6% nominal interest rate..
Sell it after a year and get $106, buy the basket of
goods at then-current cost of $103, we will have $3 left
over.
So after factoring in inflation, our $100 bond will earn
us $3 in net income; a real interest rate of 3%.
Example
Real rate r, nominal i, inflation m
Real = nominal - inflation
Since inflation usually positive, real < nominal
So Simple method: r ~ i-m <-> r+m~i
(im)
r

More precise:
1m
Example: If i=10%, m=4%
Simple: r=6%, Precise: r=5.77%

Garbage Truck Example
City: bigger trucks to reduce disposal $$
They cost $500k now
Save $100k 1st year, equivalent for 4 yrs
Can get $200k for them after 4 yrs
MARR 10%, E[inflation] = 4%
All these are real values (why?)
See “RealNominal” spreadsheet for
nominal values
Other Real and Nominal Values
Economic metrics like GDP, income, wages, etc. all
come in real, nominal forms
Example: real vs. nominal GDP
If GDP is $990B in $2000.. (this is nominal)
and GDP is $1,730B in $2001 (also nominal)
Then nominal GDP growth = 75%
If 2000 2001 GDP equal to $1450B “in $2000”, then
that is a real value and real growth = 46%
Then we call 2000 a “base year”
Use this “GDP deflator” to adjust nominal to real
GDP deflator = 100 * Nominal GDP / Real GDP
=100*(1730/1450) = 119.3 (changed by 19.3%)
Similar Idea : Exchange Rates /
PPP
Big Mac handout
Common Definition of inputs
Should be able to compare cost across
countries
Interesting results? Why?
What are limitations?
Is it worth to spend $1 million today to
save a life 10 years from now?
How about spending $1 million today so
that your grand children can have a
lifestyle similar to yours?
Discounting Handout
How much do/should we care about
people born after we die?
Ethically, no one’s interests should count
more than another’s: “Equal Standing”
Social Discount Rate
 Rate used to make investment decisions for society
 Most people 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
Intergenerational effects
We have tended to discuss only short
term investment analyses (e.g. 5 yrs)
Economists agree that discounting should
be done for public projects
Do not agree on positive discount rate
Climate Change
 Discussions ongoing about how best to manage global
CO2 emissions to limit effects of global change.
 Should we sacrifice short-run economic growth to do
something to improve environment and leave resources
for the future?
Two Questions
What duty do we have to make sacrifices
for future generations?
If we sacrifice, what is the optimal policy
to maximize benefit?
So we should compare global change
proposals with alternatives
Perhaps higher R&D spending on science or
medicine would have higher benefits!
Government Discount Rates
 US Government Office of Management and Budget (OMB)
Circular A-94
http://www.whitehouse.gov/omb/circulars/a094/a094.h
tml
Discusses how to do BCA and related performance
studies
Match real values with real discount rates, etc
How to do sensitivity analysis / which inputs to vary
What discount, inflation, etc. rates to use
Basically says “use this rate, but do sensitivity analysis
with nearby rates”
OMB Circular A-94, Appendix C
 Provides the current suggested values to use for federal
government analyses
http://www.whitehouse.gov/omb/circulars/a094/a94_appxc.html
Revised yearly, usually “good until January of the next year”
How would the government decide its discount rates?
What is the government’s MARR?
Historic Nominal Interest
Rates (from OMB A-94)
2005
2006
3.7
4.7
4.1
4.8
4.4
4.9
4.6
5.0
5.2
5.2
Real Discount Rates (from A-94)
2005
2006
1.7
2.5
2.0
2.6
2.3
2.7
2.5
2.8
3.1
3.0
What do people think
Cropper et al surveyed 3000 homes
Asked about saving lives in the future
Found a 4% discount rate for lives 100 years
from now
Hume’s Law
Discounting issues are normative vs.
positive battles
Hume noted that facts alone cannot tell
us what we should do
Any recommendation embodies ethics and
judgment
E.g. focusing on ‘highest NPV’ implies net
benefits is only goal for society
Some Issues Arise
Equal standing does not imply different
generations have equal claims to present
resources!
Harsanyi says only do so if their marginal
gain is higher than our loss
If future generations will be better off than us
anyway
Then we might have no reason to make additional
sacrifices
There might be ‘special standing’ in addition to
‘equal standing’
Immediate relatives vs. distant relatives
Different discount rates over time
Why do we care so much about future and ignore some
present needs (poverty)
A Few More Questions
Current government discount rates are
‘effectively zero’
What does this mean for projects and
project selection decisions?
What does it say about intergenerational
effects?
What are implications of zero or negative
discount rates?
Comprehensive Everglades
Restoration Project
Comprehensive project to restore natural
water flow to the Florida Everglades.
Enhance water supply to South Florida
region.
Provide continuous flood protection.
See more info at
http://www.evergladesplan.org/
Indian River Lagoon-South (IRLS)
 Part of Everglades Restoration Project.
 Total Cost of $1.21 billion.
 Annual Benefits of $159 million after project is
completed in 2015.
 Find NPV of first 25 years of project.
IRLS Cash Schedule
$159 per year
00
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
$0.425
16
17
18
19
20
21
22
23
$2.043
$12.62
All values are in millions
$447.3
$748.3
24
25
NPV of Project
$0
3%
7%
20%
-$100
NPV of Project (Millions)
-$200
-$300
-$400
-$500
-$600
-$700
Discount Rate
What would NPV be if we used a negative discount rate?
NPV of Project
$1,000
$800
$600
NPV of Project (Millions)
$400
$200
$0
3%
7%
20%
-$200
-$400
-$600
-$800
Discount Rate
0%
-1%
Next Up:
Friday’s review: microeconomics
Supply, demand, pareto efficiency, etc.
Monday - Pipeline Case
Sensitivity Analysis (next wed)
Skim Clemen Chapter 5
Refers to decision/trees, etc that we have
not done yet (ignore that part)
Next Friday: Using @RISK