Social Discount Rate
12-706 / 19-702
Admin Issues
Schedule changes:
No Friday recitation – will do in class Monday
Pipeline case study writeup – still 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
Similar to Real/Nominal :
Foreign 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 grandchildren can have a
lifestyle similar to yours?
RFF 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
Government Discount Rates
US Government Office of Management and
Budget (OMB) Circular A-94
http://www.whitehouse.gov/omb/circulars/a09
4/a094.html
Discusses how to do BCA and related
performance studies
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
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%
Borrowing, Depreciation, Taxes
in Cash Flow Problems
H. Scott Matthews
12-706 / 19-702
Theme: Cash Flows
Streams of benefits (revenues) and costs over
time => “cash flows”
We need to know what to do with them in terms
of finding NPV of projects
Different perspectives: private and public
We will start with private since its easier
Why “private..both because they are usually of
companies, and they tend not to make studies public
Cash flows come from: operation, financing,
taxes
Without taxes, cash flows simple
A = B - C
Cash flow = benefits - costs
Or.. Revenues - expenses
Notes on Tax deductibility
Reason we care about financing and
depreciation: they affect taxes owed
For personal income taxes, we deduct items like
IRA contributions, mortgage interest, etc.
Private entities (eg businesses) have similar
rules: pay tax on net income
Income = Revenues - Expenses
There are several types of expenses that we
care about
Interest expense of borrowing
Depreciation (can only do if own the asset)
These are also called ‘tax shields’
Goal: Cash Flows after taxes
(CFAT)
Master equation conceptually:
CFAT = -equity financed investment + gross
income - operating expenses + salvage value taxes + (debt financing receipts disbursements) + equity financing receipts
Where “taxes” = Tax Rate * Taxable Income
Taxable Income = Gross Income - Operating
Expenses - Depreciation - Loan Interest - Bond
Dividends
Most scenarios (and all problems we will look at) only deal with
one or two of these issues at a time
Investment types
Debt financing: using a bank or investor’s
money (loan or bond)
DFD:disbursement (payments)
DFR:receipts (income)
DFI: portion tax deductible (only non-principal)
Equity financing: using own money (no
borrowing)
Why Finance?
Time shift revenues and expenses construction expenses paid up front,
nuclear power plant decommissioning at
end.
“Finance” is also used to refer to plans to
obtain sufficient revenue for a project.
Borrowing
Numerous arrangements possible:
bonds and notes (pay dividends)
bank loans and line of credit (pay interest)
municipal bonds (with tax exempt interest)
Lenders require a real return - borrowing
interest rate exceeds inflation rate.
Issues
Security of loan - piece of equipment,
construction, company, government. More
security implies lower interest rate.
Project, program or organization funding
possible. (Note: role of “junk bonds” and rating
agencies.
Variable versus fixed interest rates: uncertainty
in inflation rates encourages variable rates.
Issues (cont.)
Flexibility of loan - can loan be repaid
early (makes re-finance attractive when
interest rates drop). Issue of
contingencies.
Up-front expenses: lawyer fees, taxes,
marketing bonds, etc.- 10% common
Term of loan
Source of funds
Sinking Funds
Act as reverse borrowing - save revenues
to cover end-of-life costs to restore mined
lands or decommission nuclear plants.
Low risk investments are used, so return
rate is lower.
Recall: Annuities (a.k.a uniform
values)
 Consider the PV of getting the same amount ($1) for many years
 Lottery pays $A / yr for n yrs at i=5%
A
A
A
A
PV  1i
 (1i)


..
2
(1i)3
(1i)n
A
A
A
PV * (1 i)  A  (1i)
 (1i)

..
2
(1i)n1
 ----- Subtract above 2 equations.. ------A
PV * (1 i)  PV  A  (1i)
n
n
1
PV *(i)  A(1 (1i)
)

A(1
(1
i)
)
n
PV 
A (1(1i) n )
i
 When A=1 the right hand side is called the “annuity factor”
Uniform Values - Application
Note Annual (A) values also sometimes
referred to as Uniform (U) ..
$1000 / year for 5 years example
P = U*(P|U,i,n) = (P|U,5%,5) = 4.329
P = 1000*4.329 = $4,329
Relevance for loans?
Borrowing
Sometimes we don’t have the money to
undertake - need to get loan
i=specified interest rate
At=cash flow at end of period t (+ for loan
receipt, - for payments)
Rt=loan balance at end of period t
It=interest accrued during t for Rt-1
Qt=amount added to unpaid balance
At t=n, loan balance must be zero
Equations
i=specified interest rate
At=cash flow at end of period t (+ for
loan receipt, - for payments)
It=i * Rt-1
Qt= At + It
Rt= Rt-1 + Qt <=> Rt= Rt-1 + At + It
 Rt= Rt-1 + At + (i * Rt-1)
Annual, or Uniform, payments
Assume a payment of U each year for n
years on a principal of P
Rn=-U[1+(1+i)+…+(1+i)n-1]+P(1+i)n
Rn=-U[((1+i)n-1)/i] + P(1+i)n
Uniform payment functions in Excel
Same basic idea as earlier slide
Example
Borrow $200 at 10%, pay $115.24 at end
of each of first 2 years
R0=A0=$200
A1= -$115.24, I1=R0*i = (200)*(.10)=20
Q1=A1 + I1 = -95.24
R1=R0+Qt = 104.76
I2=10.48; Q2=-104.76; R2=0
Various Repayment Options
Single Loan, Single payment at end of
loan
Single Loan, Yearly Payments
Multiple Loans, One repayment
Notes
 Mixed funds problem - buy computer
 Below: Operating cash flows At
 Four financing options (at 8%) in At section below
t
0
1
2
3
4
5
At
(Operation)
-22,000
6,0 00
6,0 00
6,0 00
6,0 00
6,0 00
2,0 00
10,000
-14,693
At
(Fin ancing)
10,000
10,000
-2,5 05
-800
-2,5 05
-800
-2,5 05
-800
-2,5 05
-800
-2,5 05
-10,800
10,000
-2,8 00
-2,6 40
-2,4 80
-2,3 20
-2,1 60
Further Analysis (still no tax)
t
At
8% (Opera tion )
0
-22 ,000
1
6,000
2
6,000
3
6,000
4
6,000
5
6,000
2,000
NPV 33 17.4 27
10 ,000
-14 ,693
0.1911
At
(Fi nancing at 8%)
10 ,000
10 ,000
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505 -10 ,800
-1.7386
0
10 ,000
-2,800
-2,640
-2,480
-2,320
-2,160
1E-1 2
-12 ,000
6,000
6,000
6,000
6,000
-8,693
2,000
33 17.6 2
A*
(To tal pre-ta x)
-12 ,000
-12 ,000
3,495
5,200
3,495
5,200
3,495
5,200
3,495
5,200
3,495
-4,800
2,000
2,000
33 15.6 9
33 17.4
 MARR (disc rate) equals borrowing rate, so financing
plans equivalent.
 When wholly funded by borrowing, can set MARR to
interest rate
-12 ,000
3,200
3,360
3,520
3,680
3,840
2,000
33 17.4 3
Effect of other MARRs (e.g. 10%)
t
At
10 % (Opera tion )
0
-22 ,000
1
6,000
2
6,000
3
6,000
4
6,000
5
6,000
2,000
NPV 19 86.5 63
10 ,000
-14 ,693
87 6.8
At
(Fi nancing at 8%)
10 ,000
10 ,000
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505 -10 ,800
50 4.08
75 8.16
10 ,000
-2,800
-2,640
-2,480
-2,320
-2,160
48 3.69
-12 ,000
6,000
6,000
6,000
6,000
-8,693
2,000
28 63.3 7
A*
(To tal pre-ta x)
-12 ,000
-12 ,000
3,495
5,200
3,495
5,200
3,495
5,200
3,495
5,200
3,495
-4,800
2,000
2,000
24 90.6 4
27 44.7
 ‘Total’ NPV higher than operation alone for all options
All preferable to ‘internal funding’
Why? These funds could earn 10% !
First option ‘gets most of loan’, is best
-12 ,000
3,200
3,360
3,520
3,680
3,840
2,000
24 70.2 5
Effect of other MARRs (e.g. 6%)
t
At
6% (Opera tion )
0
-22 ,000
1
6,000
2
6,000
3
6,000
4
6,000
5
6,000
2,000
NPV 47 68.6 99
-14 ,693
At
(Fi nancing at 8%)
10 ,000
10 ,000
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505
-80 0
-2,505 -10 ,800
10 ,000
-2,800
-2,640
-2,480
-2,320
-2,160
-97 9.46
-55 1.97
-52 5.1
10 ,000
-84 2.5
-12 ,000
6,000
6,000
6,000
6,000
-8,693
2,000
37 89.2 3
A*
(To tal pre-ta x)
-12 ,000
-12 ,000
3,495
5,200
3,495
5,200
3,495
5,200
3,495
5,200
3,495
-4,800
2,000
2,000
42 16.7 3
39 26.2
Now reverse is true
Why? Internal funds only earn 6% !
First option now worst
-12 ,000
3,200
3,360
3,520
3,680
3,840
2,000
42 43.6 1