Cost Benefit Analysis

Cullis and Jones chap 6

• Future benefits and costs discounted at present value.• The individuals are not indifferent between certain sum of

money today and the receipt the same in future.• If r is interest rate and n is number of years the discount factor

is 1/(1+r)n• Assume that there are monetary benefits received each years

are converted into present value and added, the PV is the stream of earnings:

• The costs are split into initial cost I0 and current costs C1, C2,…..which occur during the lifetime of project

• The net benefits are discounted to evaluate net present value

• The projects are ranked according to their NPV.• The best project are with highest NPV. .Project are selected if

NPV>=0

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• The Internal rate of return is the value of r that makes the stream of discounted net benefits equal to initial capital cost.

• The projects with high NPV have also high IRR.• It is preferable to rank projects according to NPV• Because there is no unique solution of IRR, there are

more than one discount rate make stream of earning equal to zero.

• Mutually exclusive projects, IRR will select the project not chosen by NPV.

• In public sector project different benefits, costs and discount rate are calculated. Based on welfare economics.

• When for public expenditure project NPV is positive it means that if the project is undertaken the beneficiaries from the investment will gain more than the losers

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• Real vs. Pecuniary Impact• CBA looks at social costs and social benefit rather than pure

private costs.• Example The CBA study underground railway line include reduced

congressional the road were added to the revenue to measure social benefit. In search of new airport, the cost of aeroplane noise is directly taken account of.

• In education the direct tangible benefits may be increased future earning of the students and the indirect in-tangible benefits would be reduction in the cost of crime or more informed electorate.

• Technical and pecuniary externalities: A technical externality in one where the production function of the effected producer is altered

• Pecuniary externality is visible in the form of changed prices, wages and profit, not change the technological possibility of production and consumption.

• CBA include technical externalities, example diseconomy of motorway to cut the farmer holding in to two, not pecuniary externalities like increasing the resale value of businesses.

• Cost and benefits may be tangible where they are measured in the market or in-tangible where no market exist and shadow price is used for example scenic or environment improvement for example.

• Evaluation of Benefit Consumer Surplus• CBA is concerned with maximizing social welfare.• Consumer surplus is used for Pareto value judgment, how

much the consumer is prepared to pay for the project.• To estimate consumer surplus area under the demand curve is

used.• This estimates is inadequate because the price changes in

other markets ere not included.• In example of public sector transport project which reduce price

form P1 to P2, an increase in consumer surplus by P1ABP2.• Some travelers substitute public transport to private transport. • The demand curve of private transport shift to the left.• Due to reduction in the congestion on the road the price of

private cost fall , where cost is average cost of journey.• This creates gain for those motorist who remain in private

transport, and is a technical externality for the project, the associated gain is marginal P1CDP2 and must be added to P1ABP2 to record the full gain.

• Shadow Prices• When there is market failure market prices may not reflect true marginal social cost

or benefits, the social prices or shadow prices are used which do not really exist in the market.

• The theory of second best is that market prices will not be useful when there are known imperfections in the market.

• First, market distortions that would lead to make amendment to the prices we use in the cost-benefit study, but prices exist.

• Second, if the good is provided publicly, it is unlikely that preference of that good is not revealed in the market and there exist no prices

• Shadow prices of inputs in to a project provided by monopolist, the market price of input will not be equal to marginal social cost of inputs.

• A solution to this problem is to is considering the alternate use of the input, example cement for project of public school purchased from monopolist.

• If possible to increase the output of the good, the value of the good to public sector is equal to the amount paid in private sector.

• If the supply is elastic, and can be expanded we use value of MC of resource involved.

• If supply is inelastic than the opportunity cost of the resources is the value that would be paid in the private sector.

• The valuation of labor at the wage rate requires the assumption that represents the opportunity cost of labor.

• If unemployment opportunity cost is zero.• Taxes and subsidy, consider the intermediate goods

used in the project, the output of the good is valued at market prices where the output is used in some other project, it will be valued at the cost of inputs, net of taxes, where they are provided for the project.

• For developing economies, market prices are unreliable as guides to accounting opportunity cost, because of uneven income distribution, market distorting taxes, subsidy, quotas, monopolies and other imperfections..

• The appraisal mechanism is based on the border or international trade prices. International trade add productive sector in the economy.

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• Shadow Pricing: Creating Prices• Intangible benefits: There is distinction between valuation

of an intermediate good and final good. When the good is entered in the utility function as final good the benefits are much more difficult to measure, for example value of the environmental improvement in terms of increasing utility that individual derive from a pleasant view.

• Value of Human Life: valuation of human life is issue in cost-benefit studies of medical care and road safety.

• The cost effective analysis is sufficient to choose between alternative projects that save same number and quality of life years.

• How much investment to be undertaken, is to explicitly or implicitly weigh the costs of investment against benefits.

• The first approach to valuation of human life is loss of output that occurs when the life is lost.

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• Using lost output approach ignore the consumption aspect of life, pain and discomfort due to ill health.

• A decision has to be made whether or not the analyst is concerned with the welfare of the group of individuals that currently exist (including the person whose life is at stake or the remaining individuals who will survive. Then the net output is estimated as

• The Pareto concept requires the shadow prices should reflect the value that individuals themselves place on the good and resources. In projects of medical care and road safety, how much any individual pay for the reduction in probability of the loss of life.His expected utility is contingent on the chances that he will live to consume the wealth or die

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• Discounting and Cost of Capital• A high discount rate reduce the value of the stream of earnings of the

project turn NPV negative and bias choice between projects. • If no imperfections rate of interest on loan able funds is discount rate.• The social rate of discount reflects society’s rate of time preference,

which is equal to the MRS consumption in the current period Ct and consumption in the next period Ct+1.

• The social discount rate deal with allocation of resources between private and public sectors. The social opportunity cost rate of discount, is the rate that reduces to zero the NPV in social terms of the best alternatives private use of the fund.

• The supply curve S reflects how much individual save at different rate of interest and I reflects the demand for investment. When markets are perfect and Pareto optimality condition apply, the equilibrium rate of return is on the point of intersection of two curves.

• The equilibrium rate is at the same time act as indicator of social time preference rate and social opportunity rate of discount.

• Due to imperfections in the market, for example corporate tax. The tax reduce the level of investment as the rate of return must be high enough to enable the investor to pay the saver an adequate return and pay a tax. The wedge is between rate of interest that must be paid to consumers r(STP)-which is social time preference rate and the rate of return that the project earns, which is social opportunity cost rate of discount r(SDC).

• Social Time Preference rate should be positive, uncertainty, mortality in future and prospects of economic growth with diminishing MU of consumption all support this proposition.

• If markets are perfect market rate of interest can be used as proxy for STP

• Social Opportunity Cost Rate• The social opportunity cost rate of discount should be weighted

average of the rate of return earned in private sector projects.SDC=x1r1+x2r2

• Taxes: If the private project has to cover 50% corporate tax, then the SOC rate must be double the rate of return shown in the project in the private sector.

• Risk: Alliance must be made for element of risk in private project. Public projects are less risky because the unexpected losses in one project are compensated by unexpected gains in others and the cost of the project is split over many tax-payers.

• Social cost and benefits: the private projects are evaluated at market price. The social opportunity cost rate of discount is based on social rate of return earned by project in private sector. The private rate of return is based on private cost of project. If social opportunity cost is greater than the market price, the private rate of return will be higher than the social rate of return and social rate of discount will be lower than the private rate of return.

• Though these adjustments are necessary, some cost-benefit analysis estimating social opportunity cost by using government long term borrowing rate as proxy for opportunity cost of funds to the government which is not appropriate.

• Opportunity Cost• Opportunity cost is the value of alternative use of funds.• The criteria for investment

PVr(B)>SOC(k)

• The present value of the benefits discounted at the social time preference rate should exceed the social opportunity cost of capital used.

• SOC(k)=Ak(x)

• A=θ1(p/r)+(1-θ1)• This arguments says that opportunity cost of capital should

allow for the fact that not all of the resource used in the public sector would represent lost investment in the private sector.

• Due to many difficulties there is line of argument that suggests there is no requirement at all to discount for investment.

• Risk and Uncertainty• The uncertainty is about the state of the world arising that can not be

anticipated.• Risk the probability distribution is attached to some outcomes and expected

outcome can be predicted.• The expected value of cost or benefit is used.• The discount rate is higher than the normal to reflect degree of risk

aversion.• PV(B)=p1r1+p2r2/(1+0.1+r`)

• The r` varies with degree of risk aversion.• Another approach is to calculate the certainty equivalent of uncertain

positive NPV and than rank the projects.• The trade off between variance and uncertainty.

• If I0, I1, I2, I3 are risk averter who is prepared to accept • greater risk only when expected NPV is higher.• A should be rejected and C, D, B ranked.• It is difficult to get IC map.• It is that ex-ante cost-benefit calculations are rejected to bear a close

correspondence to ex-post or realized outcome.• The main emphasis is that CBA is concerned with distributional

consequences of the project.

• Pareto Improvement• The basic principle of CBA , as the compensating

variation for gainers is the maximum sum they are prepared to pay rather than go without the project and the compensating variation of the losers is the minimum sum required for them to put up with the project, then the Pareto criteria is represented by sum of compensating variations.

• If the NPV of cost-benefit analysis is positive then sum of CV is positive and the project is accepted meeting the Pareto Criteria.

• Let two groups A and B, A is road user B are those who live near the projected road. Initially NPV of road project is positive, .A can compensate B.

• B is employed during construction of road and their income improves relative to A.

• After the construction of the road the cost of noise is higher so the B is in a position to compensate A not to have road.

• CBA analysis is more problems when distribution of income comes in.

• CBA is appropriate for small projects.• The Pareto improvement does not deal with interpersonal welfare.

Deal with it to use distributional weights• Two ways in which weights can be estimated. First rely upon the

past decisions of the society. Second, weight can be constructed on explicit normative criteria and decision maker left to chose whether or not they are significant.

• In the first approach use of marginal rate of income tax to create distributional weights. Since progressive tax structure the inference may be that society regards smaller tax payment by the poor as equivalent in sacrifice to higher tax payment.

• For second approach the weights may be simply from the ratio of their personal income to the average national personal income.