This document discusses discounting in cost-benefit analysis of investment projects and climate change adaptation investments. It covers the general methodology of discounting, including calculating the present value of costs and benefits that occur over different time periods. It addresses questions about setting the time horizon (T) of analysis, how to handle infinite time horizons, accounting for inflation, and theories on which discount rate to use. The document provides outlines, explanations, and examples related to discounting in economic analysis.

1. Photo credit: UNDP Climate Change Adaptation
ECONOMICS OF CLIMATE CHANGE
ADAPTATION
BLOCK 2 TRACK 2
Cost-Benefit Analysis of Investment
Projects and of Climate Change
Adaptation Investments
SESSION 9
Discounting

2. 8/21/2017 2
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

3. 8/21/2017 3
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

4. 8/21/2017 4
Session 9
General methodology
Principle of discounting
Discounting is simply a technique that allows us to compare costs and
benefits that happens at different point in time into a common unit of
measurement.
Assume 10% return on investment
Year
0
Year
1
Year
2
110 121100
Compounding
Discounting
Calculate Present Value

5. 8/21/2017 5
Session 9
General methodology
Typically, the flows of costs and benefits of a project look like this:
C0
1nvestment
costs
Benefits
C1 C2 C3 C4 C5 C6Costs C7
Operational
costs
0 0 0 B3 B4 B5 B6 B7

6. 8/21/2017 6
Session 9
General methodology
Net benefits
Benefits
Costs

7. 8/21/2017 7
Session 9
General methodology
C0
Benefits
C1 C2 C3 C4 C5 C6Costs C7
0 0 0 B3 B4 B5 B6 B7
PV of
Costs
PV of
Benefits

8. 8/21/2017 8
Session 9
General methodology
C0 C1 C2 C3Costs
PV of
Costs
Technique of discounting
r Is referred to as the discount rate (in real
terms).
Is referred to as the discount factor.
3
3
2
21
0
)1()1()1( r
C
r
C
r
C
C





=
t
r)1(
1


9. 8/21/2017 9
Session 9
General methodology
PV =
More generally
Suppose a flow of benefits (or costs) Bt from t = 0 until t = T, then the
present value of this flow is:
T
T
r
B
r
B
r
B
r
B
B
)1(
...
)1()1()1( 3
3
2
21
0










 
Tt
t
t
t
r
B
0 )1(PV =

10. 8/21/2017 10
Session 9
General methodology
PV of costs =
So, for any given project or policy, we will have:
PV =
T
T
r
C
r
C
r
C
r
C
C
)1(
...
)1()1()1( 3
3
2
21
0










 
Tt
t
t
t
r
C
0 )1(
T
T
r
B
r
B
r
B
r
B
B
)1(
...
)1()1()1( 3
3
2
21
0







PV of benefits
=


 
Tt
t
t
t
r
B
0 )1(
PV =

11. 8/21/2017 11
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

12. 8/21/2017 12
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

13. 8/21/2017 13
Session 9
Four questions
What is T?
In theory, all benefits and costs of a project should be measured, even
when they extend indefinitely.
However, at least in the case of infrastructure project, the common practice
is set the time horizon of the analysis (T) to coincide with the expected
lifetime of the key (most important) component of the infrastructure project.
For example:
• Expected lifetime of a road (before it needs major repair – so major that it
may as well be considered a new road): 40 years
• Expected lifetime of a bridge: 75 to 100 years
• Expected lifetime of a coal-fired power plant: 25 to 40 years
And so, the time horizon of the analysis is set to coincide with these
expected lifetimes.

14. 8/21/2017 14
Session 9
Four questions
What is T?
Or in situation where the Government will provide a concession to build and
run a project (e.g. a power plant, a forestry or mining concession), then very
often the time horizon of the cost-benefit analysis is set to coincide with the
duration of the concession. For example if:
• Duration of a concession of a build and operate power plant 25 years.
Or if:
• Duration of a mining concession: 40 years
• Then the time horizon of the analysis is set to coincide with these
durations (25 years or 40 years respectively).

15. 8/21/2017 15
Session 9
Four questions
What is T?
Warning:
As a principle, this approach for setting the time horizon of the economic
analysis is wrong.
The selection of the time horizon for the CBA should be guided by one
question: How long will the impacts (positive or negative) last? And the
answer to this question may or may not coincide with the lifetime of the
infrastructure or duration of the concession.
This may or may not matter in terms of assessing the economic desirability
of the project or policy. If the infrastructure lifetime or duration of the
concession is long enough, and if the discount rate being used is relatively
high, then whatever happens after the CBA is truncated (after say 40 years)
may not matter very much.

16. 8/21/2017 16
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

17. 8/21/2017 17
Session 9
Four questions
$A $A $A $A $A $A $A
Year
$A
What if T is infinite?
Suppose the following:
0 1 2 3 4 5 … ∞
For example, if A = $100 and if r = 10%, then the present value of A is:
100*(1.1)/0.1 = $1,100.
PV =
PV =









)1(
...
)1()1()1( 32
r
A
r
A
r
A
r
A
A
r
r
A
)1(
*


18. 8/21/2017 18
Session 9
Four questions
$A $A $A $A
Year
$A
What if T is infinite?
Suppose the following:
0 1 2 3 4 5 … ∞
How would you calculate the PV of $A?

19. 8/21/2017 19
Session 9
Four questions
$A $A $A $A
Year
$A
What if T is infinite?
Suppose the following:
0 1 2 3 4 5 … ∞
Discounted to Year 0, it will be: r
r
A
)1(
*

)1(
3
r
PV to Year 3 =
A *
(1+r)
r

20. 8/21/2017 20
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

21. 8/21/2017 21
Session 9
Four questions
What about inflation? (nominal vs. real?)
Should we include inflation in this work? If we do, then what discount rate to
use?
So, suppose that prices are expected to rise at rate ‘g’ for the duration of
the project.
Suppose that the nominal discount rate is m (the real discount rate is r).

22. 8/21/2017 22
Session 9
Four questions
PV =
What about inflation? (nominal vs. real?)
Then, the present value of a flow of benefits from t = 0 to t = T is:
According to Fisher’s Law: (1 + m) = (1 + r)(1 + g). So we have:
T
T
T
m
gB
m
gB
m
gB
m
gB
B
)1(
)1(
...
)1(
)1(
)1(
)1(
)1(
)1(
3
3
3
2
2
21
0












PV = TT
T
T
gr
gB
gr
gB
gr
gB
gr
gB
B
)1()1(
)1(
...
)1()1(
)1(
)1()1(
)1(
)1)(1(
)1(
33
3
3
22
2
21
0












Which is the same as:
PV =
T
T
r
B
r
B
r
B
r
B
B
)1(
...
)1()1()1( 3
3
2
21
0









23. 8/21/2017 23
Session 9
Four questions
What about inflation? (nominal vs. real?)
If all costs and benefits are measured in nominal values, then use nominal
discount rate. If all costs and benefits are measured in real values, then use
real discount rate. It does not matter.
However, in practice, most of the time we do the analysis in real terms. In
doing so, there is one less variable we need to make projections for, the
annual inflation rate for each year of the time horizon of the analysis.
Note: Doing the analysis in real terms does not necessarily in constant
prices.
.
Message is:

24. 8/21/2017 24
Session 9
Four questions
Adjust past value for US
inflation to find today’s US
value
Taking values from the
past
What about inflation? (nominal vs. real?)
Today
Do analysis in real
terms
Taking values from the
past
Adjust past value for national
inflation to find today’s value
Use exchange rate today to transfer in
national value today
Do analysis in real
terms
Do analysis in real
terms

25. 8/21/2017 25
Session 9
Outline of presentation
2.1 What is T?
1 General methodology
2.2 What if T is infinite?
2.3 What about inflation? (nominal vs. real?)
2.4 Which discount rate to use: theory and
practice
2 Four questions

26. 8/21/2017 26
Session 9
Four questions
Which discount rate to use: theory
Consumers have utility function defined over consumption today and in the
future.
Where and stand for consumption today and tomorrow.
Two things about this function:
In a perfect world:
1 The higher or , the higher is utility.
2 The marginal utility of consumption is declining. It implies that
consuming everything today or tomorrow will not maximize utility
(consumption smoothing is preferred).

27. 8/21/2017 27
Session 9
Four questions
Which discount rate to use: theory
The Marginal Rate of Substitution (MRS) tells us by how much future
consumption must be increased to compensate for a loss of consumption
today.
Where U is marginal utility with respect to C and U with respect to C
The MRS is also interpreted as the individual’s rate of time preference.
In a perfect world:
It is the slope of the indifference between present and future consumption.
1100

28. 8/21/2017 28
Session 9
Four questions
The slope of this Indifference curve is the marginal rate of substitution.
However, if I have a limited
amount of C0 and you are taking
one unit away, I will need a large
increase in C1 to be
compensated.
If I have lots of C0 and you take
away one unit of C0, I do not
need a large increase in C1.
In a perfect world:
C0
C1
-1
-1
Which discount rate to use: theory

29. 8/21/2017 29
Session 9
Four questions
We can transform today’s consumption into future consumption.
In a perfect world:
If we invest one unit of C0, we will obtain additional units of C1 according
to the marginal productivity of capital.
Which discount rate to use: theory

30. 8/21/2017 30
Session 9
Four questions
The slope of this Indifference curve is the marginal rate of substitution.
The slope of this
function is the marginal
rate of transformation.
In a perfect world:
C0
C1
Which discount rate to use: theory

31. 8/21/2017 31
Session 9
Four questions
In a perfect world:
C0
C1
Which discount rate to use: theory
C1
C0

32. 8/21/2017 32
Session 9
Four questions
The optimal consumption path (which maximizes lifetime utility) is
such that the marginal rate of transformation is equal to the
marginal rate of substitution.
In a perfect world:
Marginal rate of
transformation
Which discount rate to use: theory
If we introduce perfectly competitive capital markets, we can show
that a competitive equilibrium in capital markets is such that the
market interest rate (which is the opportunity cost of capital)
equals the marginal productivity of capital.
Individual’s rate of time
preference
Opportunity cost of
capital
Marginal productivity of
capital
=
=

33. 8/21/2017 33
Session 9
Four questions
And so now we finally have:
In a perfect world:
Market interest rate
Which discount rate to use: theory
Opportunity cost of
capital
Individual’s rate of
time preference
=
= Marginal productivity
of capital
=

34. 8/21/2017 34
Session 9
Four questions
Suppose G comes in and wants to undertake a public project. The
project will decrease consumption and/or private investment today,
and increase consumption tomorrow.
In a perfect world:
Which discount rate to use: theory
What should be the discount rate to evaluate the benefits of future
additional consumption?
Answer is:
The project will either displace consumption or private investment.
Hence, the discount rate to use will depend on what G project is
displacing.

35. 35
Session 9
Four questions
If the project displaces current consumption, the discount rate should be
the rate of time preference.
In a perfect world:
Which discount rate to use: theory
If the project displaces other investments, the discount rate should be the
marginal productivity of capital.
If the project displaces both consumption and investment, the discount rate
should be a weighed average of the marginal productivity of capital and the
rate of time preference.
But in this perfect world, both the rate of time preference and the marginal
productivity of capital equals the market interest rate.
Thus we get:
Discount rate = Market Interest Rate (risk free)

36. 36
Session 9
Four questions
We may base the selection of the discount rate either on the rate of
society’s time preference or on the social opportunity cost of capital or on a
weighed average of those two.
In a less than perfect world:
Which discount rate to use: theory
Most financial/treasury/planning institutions would understand using the
social opportunity cost of capital to set the discount rate.
For example, from ADB’s CBA guidelines:
“A project investment is economically justified if the estimated economic
internal rate of return (EIRR) exceeds the economic opportunity cost of
capital (EOCC) for the country.”

37. 37
Session 9
Four questions
All of welfare economics is based on the presumption that policy choices
aim to maximize society’s welfare.
However:
Which discount rate to use: theory
If this is correct, then upon noting (1) that society’s welfare is made of some
aggregation of individual’s welfare (utility) and (2) that utility is defined over
consumption, then the value of the social discount rate should be based the
rate of society’s time preference – not the opportunity cost of capital.
This approach gives rise to the Ramsey Rule.

38. 38
Session 9
Four questions
Ramsey Rule (from Ramsey), 1928)
Where:
is the social discount rate
is the rate at which society discounts the utility of present versus future consumption
(impatience)
is the relative aversion to intertemporal inequality.
is the growth rate of per capita consumption.

39. 8/21/2017 39
Session 9
Four questions
Upon applying the Ramsey Rule:
Which discount rate to use: theory
Weitzman (2007) 2% 2 2% 6%
Nordhaus (2005) 1% 2 2% 5%
Stern (2006) 0.1% 1 1.3% 1.4%
U.K. (since 2003) 1.5% 1 2.0% 3.5%
France (since 2005) 0% 2 2.0% 4.0%

40. 8/21/2017 40
Session 9
Four questions
MDBs:
MDBs Discount rates
World Bank 10%
Asian Development Bank 12%
Inter-American Development Bank 12%
European Bank (EBRD) 10%
Note: All projects, irrespective of sectors (be it transport, energy, environment,
health, water supply, agriculture, etc.) and irrespective of countries, must use the
same discount rate.
Which discount rate to use: practice

41. 8/21/2017 41
Session 9
Four questions
MDBs::
MDBs:
MDBs Discount rates
World Bank 10%
Asian Development Bank 12%
Inter-American Development Bank 12%
European Bank (EBRD) 10%
ADB: “Given the difficulty of estimating country-specific economic opportunity costs
of capital (EOCC), the EOCC for all ADB DMCs is 12%.”
World Bank: “ It is justified as a notional figure for evaluating Bank-financed
projects. This notional figure is not necessarily the opportunity cost of capital in
borrower countries, but is more properly viewed as a rationing device for World
Bank funds" (Operational Core Services Network Learning and Leadership Center,
1998).
Which discount rate to use: practice

42. 8/21/2017 42
Session 9
Four questions
Some countries
Countries Discount rates
Philippines 15%
India 12%
Pakistan 12%
Which discount rate to use: practice

43. 8/21/2017 43
Session 9
Four questions
Line ministries (or operational departments in MDBs) would prefer to have
their policies or projects accepted.
Incentives to over-estimate benefits and under-estimate costs.
Set a high discount rate.
Which discount rate to use: practice
Strategic reaction from those who allocate resources:

44. 8/21/2017 44
Session 9
Four questions
Some countries
Which discount rate to use: practice
Countries Discount rates
Philippines 15%
India 12%
Pakistan 12%
New Zealand 10% (until 2008); now 8%
United States OMB: 10% (until 1992); 7% (until now); 3% for sensitivity
(since 2003); NOAA: 3%: EPA: 3%
European Union 6% (until 2006); now 5%
Germany 4% (until 2004); now 3%
France 8% (until 2005); now 4%

45. 8/21/2017 45
Session 9
Four questions
In the USA:
On the selection of 7% in 1992:
“This new rate of 3% is justified by the social rate of time preference. If we take the
rate that the average saver uses to discount future consumption as our measure of
the social rate of time preference, then the real rate of return on long-term
government debt may provide a fair approximation” (OMB, (2003).
The 3% corresponds to the average real rate of return of 10- year Treasury notes
between 1973 and 2003.
Which discount rate to use: practice
On the selection of 3% in 2003:
“7% is an estimate of the average before-tax rate of return to private capital in the
U.S. economy” (OMB (2003).

46. 8/21/2017 46
Session 9
Four questions
U.K. since 2003
Which discount rate to use: practice
0.5%
1.0%
1.5%
2.0%
2.5%
3.0%
3.5%
100 200 300 400 500
Rationale: We cannot presume that future
generations will be better off than today’s
generation.

47. 8/21/2017 47
Session 9
Four questions
Canada:
TBS currently recommends the use of 3% (“social” rate) and 7% (“real” rate) as
CBA discount rates.
TBS now allows for the option to use 3% discount rate as a central value for health
and environmental CBAs.
Which discount rate to use: practice

48. 8/21/2017 48
Session 9
Four questions
Applying the Ramsey Rule in Canada:
Which discount rate to use: practice
Mid - point 1% 1.5 1.7% 3.5%
Range 1 – 2 1.5% – 2.0% 2.5% - 5.0%
Source: Boardman et al (2008)

49. 8/21/2017 49FOOTER GOES HERE
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