Dev 567
Project and Program Analysis
Lectures 7: Economic Appraisal of Projects
(continued)
Dr. M. Fouzul Kabir Khan
Professor of Economics and Finance
North South University
Lecture 7
•
•
•
•
•
•
Shadow prices
Project analysis in developing countries
LMST accounting price method in practice
Intermediate goods and asset valuation method
Travel cost method
Social discount rate
Shadow Prices
• When a market does not exist or market failure leads to a
divergence between market price and marginal social cost,
analysts try to obtain estimates of what market price would
be if the relevant good were traded in a perfect market. Such
an estimate is called a shadow price
• Estimates of shadow prices when markets are missing
– Examples: value of a unit of time, statistical life, or the (negative) value
of a particular type of crime
Shadow Prices
Shadow Prices
Shadow Prices
Plug-Ins for Value of Travel Time Saved
Shadow Prices
Plug-Ins for Value of Recreational Activities (in 1999 U.S. dollars)
Shadow Prices
Plug-Ins for Value of Environmental Impact (in 1999 U.S. dollars)
Project Analysis in Developing Countries
• Project Analysis in developing countries have much in common with
Project Analysis in industrialized countries
• The main distinguishing characteristic of Project Analysis in developing
countries is the much grater emphasis on adjusting the market prices of
project output and inputs so that they more accurately reflect their value
to society
– Markets are more distorted in developing countries
•
•
•
•
Segmented labor market
Overvalued exchange rate
Tariffs, taxes, and import controls
Formal and informal credit markets
– Use shadow prices/accounting prices instead of market prices
LMST Accounting Price Method
• Developed by UNIDO, I.M.D Little and J.A. Mirrlees,
synthesized by Lynn Squire and Herman G. van der Tak
• The LMST methodology
– Use world prices as shadow price for all project inputs and outputs
that are classified as tradable
– World prices are less distorted than domestic prices
• Imported input valued at import price, CIF
• Exported output valued at export price, FOB
• Examples
– Steel plant
– Agricultural crop
LMST Method in Practice
• Shadow pricing involves multiplying each market price
by an accounting price ratio
– APR for good i = accounting/shadow price of good i
/market price of good i
– Shadow price of good i = APR of good i *market price of
good i
– Small country assumption
• Shadow price of an imported input or an output that is
an import substitute
• Shadow price of an export
• Shadow price of a non-tradable good (electricity)
Accounting Price of an Import
• CIF price * Exchange rate = World Price in
domestic currency
– Use shadow exchange rate, if there is a big difference
between official and market exchange rates
• Accounting prices
–
–
–
–
–
CIF price: APR = 1
Tariff : APR = 0
Transport cost: APR = 0.5
Distribution cost: APR = 0.8
Weighted APR: 0.85
• Shadow price= Market Price*APR
Accounting Price of an Imported Good
Item
Dollar
Price
Market
Price(Tk)
APR
Accounting
Price
CIF Price
40
2800
1.00
2800
Tariff
-
350
0.00
-
Transport
-
280
0.50
140
Distribution
-
175
0.80
140
3605
0.85
3080
Total
Accounting Price of an Export
• FOB Price
• Export tax is a transfer between foreign
purchaser (no standing) and the government:
APR= 1
• Transport for export: APR= 0.5
• Factory gate price: APR=1
• Shadow price
= 5180*1+70*0.5+1750*1
=Tk. 6965
Accounting Price for Export
FOB Price
Dollar
Price
100
Export tax
25
1750
1.0
1750
Transport
1
70
0.5
35
74
5180
1.0
5180
Item
Market
Price(Tk)
7000
APR
-
Accounting
Price
-
Factory
Gate
Transport(d)
-
120
0.5
60
Distribution(d)
-
300
0.8
240
Accounting Price of Non-tradable
• LMST involves determining the equivalent value
of non-tradables in world prices
• Breaking down the cost of inputs into traded,
non-traded and labor components
• Multiply market price by applicable accounting
price ratio
–
–
–
–
CIF prices: APR =1
Domestic transfer (tariffs and taxes): APR = 0
Labor: APR = 0.6
Standard conversion factor: 0.80
Accounting Price for Electricity Valued or Marginal
Cost of Supply (in thousands of pesos)
Conversion factors
 Semi-input-output analysis
 Consumption conversion factors
Weighted average of accounting price ratios for a
nationally representative market basket of goods
 Standard conversion factors
SCF = (M+X)/[(M+ Tm –Sm)+(X-Tx+Sx)]
Where M= Total value of imports(CIF)
X = Total value of exports(FOB)
Tm = Total tariff on imports
Tx = Total taxes on exports
Sm = Total subsidies on imports
Sx = Total subsidies on exports
Average value of SCF for different countries 0.8
(ranges between 0.59-0.96)
Shadow Pricing when Goods are in Fixed Supply






Constant marginal costs up to capacity level, up to Q1 and then completely inelastic
Whether the fixed supply is binding or not
If not binding (demand with the project within the elastic range), no change in
market price. Would not affect the current consumers of electricity
– Would require additional input to produce additional electricity, use shadow
cost method for non-tradables
If binding, (demand with the project is in the inelastic range), market price will
increase. Current consumers lose surplus and producers gain surplus
Measured in market prices, the cost of electricity would equal [(P1+P2)/2](Q1-Q2)
To convert into shadow price equivalent, multiply the cost by the consumption
conversion factor( weighted average of accounting price ratios for a nationally
representative market basket of goods).
Shadow Pricing when Electricity is Completely
Elastic and Inelastic
The Shadow Price of Labor
 Location of the project
 Source of labor
 Accounting price ratio of type j labor = Shadow price of type j
labor/ the market wage for type j labor
 Shadow price of foreign workers
– SWf = [h + (1-h)(CCF)](PW)
– Where PW is the project wage, h is the fraction of PW sent or taken
home, and 1-h is the fraction spent domestically
 Rural market wage
– RMW = 0.5($50) + 0.25($10) + 0.25($.15) = Tk. 31.25
The Social Discount Rate: Main Issues
• How much current consumption society is willing to give up now in
order to obtain a given increase in future Consumption?
• It is generally accepted that society’s choices, including the choice
of weights be based on individuals’ choices
• Three unresolved issues
– Whether market interest rates can be used to represent how individuals
weigh future consumption relative to present consumption?
– Whether to include unborn future generation in addition to individuals
alive today?
– Whether society attaches the same value to a unit of investment as to a
unit of consumption
• Different assumptions will lead to choice of different discount rate
Does the Choice of Discount Rate Matter?
 Generally a low discount rate favors projects with highest
total benefits, irrespective of when they occur, e.g. project C
 Increasing the discount rate applies smaller weights to
benefits or (costs) that occur further in the future and,
therefore, weakens the case for projects with benefit that are
back-end loaded (such as project C), strengthens the case for
projects with benefit that are front-end loaded (such as
project B).
NPV for Three Alternative Projects
Year
Project A
Project B
Project C
0
-80,000
-80,000
-80,000
1
25,000
80,000
0
2
25,000
10,000
0
3
25,000
10,000
0
4
25,000
10,000
0
5
25,000
10,000
140,000
Total benefits
45,000
40,000
60,000
NPV (i=2%)
37,838
35,762
46,802
NPV (i=10%)
14,770
21,544
6,929
Appropriate Social Discount Rate in Perfect
Markets
●
●
●
●
As individuals, we prefer to consume immediate benefits to ones
occurring in the future (marginal rate of time preference)
We also face an opportunity cost of forgone interest when we spend
money today rather than invest them for future use (marginal rate of
return on private investment)
In a perfectly competitive market:
rate of return on private investment = the market interest rates =
marginal rate of time preference (MRTP)
The rate at which an individual makes marginal trade-offs is called an
individuals MRTP
Therefore, we may use the market interest rate as the social
discount rate
Equality of MRTP and Market Interest Rate
Alternative Social Discount Rate in Imperfect Markets
•Six potential discounting methods
– Social discount rate equal to marginal rate of return on
private investment, rz
– Social discount rate equal to marginal rate of time
preference, pz
– Social discount rate equal to weighted average of pz, rz and i
, where i is the government’s real long-term borrowing
rate
– Social discount rate is the shadow price of capital
– A discount rate that declines over the time horizon of the
project
– A discount rate SG, based on the growth in real per capita
consumption
Alternative Social Discount Rate in Imperfect
Markets
Using the marginal rate of return on private investment
– The government takes resources out of the private sector
– Society must receive a higher rate of return compared to the return in the
private sector
Criticism
– Too high
• Return on private sector investment incorporates a risk premium
– Government project might be financed by taxes, displaces consumption
rather than investment
– Project may be financed by low cost foreign loans
– Private sector return may be high because of monopoly or negative
externalities
– Government investment sometimes raises the private return on capital
Alternative Social Discount Rate in Imperfect
Markets
Using the marginal social rate of time preference, pz
– Numerical values of pz
• Real after-tax return on savings, around 2 percent for the US economy
Criticisms
– Individuals have different MRTP
– How to aggregate such individual MRTP
– Market interest rate reflects MRTP of individuals currently alive
Using the weighted social opportunity cost of capital
WSOC= arz + bi + (1-a-b)pz
– Numerical Value, 3 percent for the US economy
Harberger’s Social Discount Rate
 Social discount rate should be obtained by weighting rz and pz by
the relative size of the relative contributions that investment and
consumption would make toward funding the project
s = arz + (1-a)pz,
where a = ΔI/(ΔI+ ΔC) and (1-a) = ΔC/(ΔI+ ΔC)
 Savings are not very responsive to changes in the interest rate, ΔC
is close to zero

The value of the parameter a is close to one
 The marginal rate of return on private investment rz is a good
approximation of true social discount rate
Alternative Social Discount Rate in Imperfect
Markets
Criticisms of WSOC
 Criticisms applicable to use of rz and pz applies
 Different discount rates for different projects based on source of
financing
Use the shadow price of capital
 Strong theoretical appeal
 Discounting be done in four steps
 Costs and benefits in each period are divided into those that directly affect
consumption and those affect investment
 Flows into and out of investment are multiplied by the shadow price of
capital θ, to convert them into consumption equivalents
 Changes in consumption are added to changes in consumption equivalents
 Discounting the resultant flow by pz
Alternative Social Discount Rate in Imperfect
Markets
• Shadow price of capital

(rz   )(1  f )
p z  rz f   (1  f )
Where rz is the net return on capital after depreciation,
δ is the depreciation rate of capital, f is the fraction of
gross return that is reinvested, and pz is the marginal
social rate of time preference
– Numerical values for the θ,SPC, 1.5-2.5 for the US
economy
– Applying SPC in practice
• Criticism of calculation and use of the SPC
Alternative Social Discount Rate in Imperfect
Markets
 Using time-declining discount rates
 Conclusion, social discounting in imperfect markets
– If all costs and benefits are measured as increments to consumption, use
MSRTP, pz, Boardman et. Al. suggests a value of 2 percent, sensitivity 0-4
percent
– If all costs and benefits are measured as increments to private sector
investment, use MRROI, rz, Boardman et. Al. suggests a value of 8 percent,
sensitivity 6-10 percent
– If all costs and benefits are measured as increments to both consumption
and private sector investment, use SPOC, θ, to increments in investment
and then discount at MSRTP, Boardman et. Al. suggests for SPOC, a value
of 1.65 percent, sensitivity 1.3-2.7 percent; and ΔI = 15 percent and, ΔC=
85 percent, in the absence of information
The Social Discount Rate in Practice
 Many government agencies do not discount at all
 Shadow price of capital is rarely used
 Governments do not use time-varying discount rates
 Constant positive rate that varies from country to country
– US, 7-10 percent
– Canada, 10 percent, sensitivity 5-15 percent
– 0-3 percent for Health and Environment Projects
 ADB, EIRR of 10-12 percent