Dev 567Project and Program Analysis

Lectures 7: Economic Appraisal of Projects (continued)

Dr. M. Fouzul Kabir KhanProfessor of Economics and Finance

North South University

• 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

Lecture 7

• 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)

Shadow Prices

• 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

Project Analysis in Developing Countries

• 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 Accounting Price Method

• 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)

LMST Method in Practice

• 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 Import

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

Total 3605 0.85 3080

Accounting Price of an Imported Good

• 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 of an Export

Item Dollar Price

Market Price(Tk)

APR Accounting Price

FOB Price 100 7000 - -

Export tax 25 1750 1.0 1750

Transport 1 70 0.5 35

FactoryGate

74 5180 1.0 5180

Transport(d) - 120 0.5 60

Distribution(d) - 300 0.8 240

Accounting Price for Export

• 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 of Non-tradable

Accounting Price for Electricity Valued or Marginal Cost of Supply (in thousands of pesos)

Semi-input-output analysis Consumption conversion factorsWeighted 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)

Conversion factors

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 Goods are in Fixed Supply

Shadow Pricing when Electricity is Completely Elastic and Inelastic

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 Shadow Price of Labor

• 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

The Social Discount Rate: Main Issues

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).

Does the Choice of Discount Rate Matter?

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 10,000 140,000Total benefits 45,000 40,000 60,000NPV (i=2%) 37,838 35,762 46,802NPV (i=10%) 14,770 21,544 6,929

NPV for Three Alternative Projects

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 sectorCriticism

– 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 economyCriticisms

– 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 capitalWSOC= arz + bi + (1-a-b)pz

– Numerical Value, 3 percent for the US economy

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

Harberger’s Social Discount Rate

Alternative Social Discount Rate in Imperfect Markets

Criticisms of WSOCCriticisms applicable to use of rz and pz appliesDifferent discount rates for different projects based on source of

financingUse the shadow price of capital

Strong theoretical appealDiscounting 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 equivalentsDiscounting the resultant flow by pz

)1(r)1)((r

z

z

ffpf

z

Alternative Social Discount Rate in Imperfect Markets

• Shadow price of capital

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