Chapter 11:Cost-Benefit Analysis

Econ 330: Public Finance

Dr. Reyadh Faras

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Cost-Benefit Analysis  How should the government decide whether or not to pursue a particular project? The theory of welfare economics provides a framework for deciding: Evaluate the social welfare function before and after the project, and see whether social welfare increases. If it does, then do the project. Welfare economics provides the basis for cost-benefit analysis:“A set of practical procedures for guiding public expenditure decisions.”

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Cost-benefit analysis allows policymakers to do what markets do automatically (allocate resources to a project as long as the marginal social benefit exceeds the marginal social cost).   

Present Value: Project evaluation usually requires comparing costs and benefits from different time periods.A. Projecting present dollars into the future If $R are invested for T years at an interest rate of r, at the end of T years, it will be worth $R x (1+r)T. This formula shows the future value of money invested now.  3Dr. Reyadh Faras

B. Projecting future dollars into the present (present value) Present value of a future amount is the maximum amount you would be willing to pay today for the right to receive the money in the future. ExampleWhen the interest rate is r, the present value of a promise to pay $R in T years is: $R / (1+r) T.

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Thus, even with no inflation, money in the future worth less than today and must be discounted by an amount that depends on the interest rate and when the money is receivable. r is referred to as the discount rate and (1+r) T as the discount factor for money T periods into the future. The present value (PV) of a stream of payments is found as follows:

PV = R0 + R1 / (1+r) + R2 / (1+r)2 + ….. + RT / (1+r )T

Ignoring discounting makes projects that yield returns in the future appear more valuable than they really are.

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Private Sector Project Evaluation

Suppose a firm has a choice between two projects X and Y.Real costs and benefits (C&B) are realized immediately.Q: Are the projects admissible? A: A project is admissible if its net return is positive (B>C).Q: Which project is preferable?A: The one with the higher net return. In reality, projects involve a stream of real costs and benefits (occur over time). The present value of the stream of income is:PV = B0-C0 + B1-C1 / (1+r) + B2-C2 / (1+r)2 + ….. + BT-CT / (1+r )T

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ExampleIf the discount rate chosen is too high, it tends to discriminate against projects with returns that occur in the relatively distant future and vice versa.

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A.   Internal Rate of Return

The internal rate of return (ρ) is the discount rate that would make the PV of the project just equal to zero. It is defined as the (ρ) that solves the equation: B0-C0 + B1-C1 /(1+ ρ) + B2-C2 /(1+ ρ)2 + .. + BT-CT /(1+ ρ )T = 0

An obvious admissibility criterion is to accept a project if (ρ) exceeds the firm’s opportunity cost of funds, r. If two projects are admissible, choose the one with the higher value of (ρ).

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Problem: when projects differ in size, (ρ) can give poor guidance. In contrast, the PV gives correct answers even when projects differ in size.

B.  Benefit-Cost Ratio The benefit –cost ratio is defined as B / C. Admissibility requires that a project’s cost-benefit ratio exceeds one. This rule always gives correct guidance, that’s because B/C>1 implies that B-C>1, which is just the PV criterion for admissibility.  

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As a basis for comparing admissible projects, however, this ratio is useless.

Conclusion: The internal rate of return and the benefit-cost ratio can lead to incorrect inferences. The present value criterion is more reliable guide.

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Discount Rate for Government Projects

Sensible decision making by the government also requires calculating the PV. There are problems in selecting a public sector discount rate.A.  Rates Based on Returns in the Private Sector If the government extracts $X from a private sector investment (that yields r% return) for a project, society loses $(X x r%) that would have been generated by the private sector project. The opportunity cost of the government project is the (r%) rate of return in the private sector, which is the appropriate discount rate.

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B.  Social Discount Rate Social rate of discount measures the valuation society places on consumption that is sacrificed in the present. Social discount rate is lower than the market rate of return for several reasons:     1. Concern for Future Generations The public sector decision makers care not only about the welfare of current generation but future generations as well, while the private sector cares only about its own welfare. Hence, the private sector devotes few resources to saving, which implies applying high discount rate to future returns.

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2. PaternalismPeople (even with self-interest) may not be farsighted enough to weigh adequately benefits in the future; they discount them at too high rates.

3. Market Inefficiency Private investments generate positive externalities that benefit other firms, this leads to under-provision of investment by private markets.

By applying a discount rate lower than the market’s, the government can correct this inefficiency.

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C.  Government Discounting in Practice The US federal government uses a variety of discount rates, depending on the agency and the type of project.

Federal agencies are required to use a real rate of return of 7%, assuming that this will measure the before-tax rate of return on private sector projects.

However, for many projects involving costs and benefits that come in over long periods of time, a real rate of return of 2% is used; as an approximation to the consumption rate of time preference, that is, the after tax rate of return.

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Valuing Public Benefits and Costs

Evaluating private projects is done by comparing costs and benefits incurred to the firm and it is straightforward; benefits are revenues received and costs are payments for inputs; both are measured at market prices.

The evaluation problem is more complicated for the government because market prices may not reflect social benefits and costs.            

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Ways for measuring the benefits and costs of public sector projects:

A.   Market Prices In well functioning competitive economy, prices reflect the marginal cost of production and its marginal value to consumers.

Problem: in reality, markets have imperfections, (e.g. monopoly  and externalities) which makes prices do not necessarily reflect marginal costs and benefits.    

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B.  Adjusted Market Prices

Prices in imperfect markets do not reflect their marginal social cost.

The shadow price is the underlying social marginal cost and it diverges from market price due to market imperfection.     

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1. Monopoly The monopolist price is higher than the marginal cost (MC), should the government measure input costs at (monopolist) market price or at marginal cost?

Answer: it depends on the impact of government purchase on the market:

a. If production increases by the exact amount used by the project, the social opportunity cost is the value of resources used for the extra production (MC).b. If production does not increase, the government purchase come at the expense of private consumers, who value the good at its demand price.

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2. TaxesQ: When the government purchases an input subject

to sales tax, should the producer's or the purchaser's price be used in calculating the cost?

A: same as the case of monopoly  (if production increases use producer's price, if not use consumer's price).

3. Unemployment If a worker for a public project is hired away from a

private job, then his opportunity cost is the wage rate earned in the private sector. If the worker was involuntarily unemployed, the

wage does not represent the opportunity cost.  

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C.   Consumer Surplus In contrast to the small private firms, public sector projects are relatively large and they may change market prices.

Example, if a public project reduces marginal costs, Q: how should the increase in output valued; at its original price or the new (lower) price?

A: project benefit can be measured using the consumer's surplus: “the difference between the amount the consumer is willing to pay and the amount it actually paid.”

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Games Cost-Benefit Analysts Play

There are additional common errors committed in cost benefit analysis.A. The Chain-Reaction Game Advocates of public projects can make them more attractive by counting secondary profits arising from it as part of the benefits, while ignoring losses induced by the project. Consistency requires counting secondary benefits and losses. A problem with chain-reaction game is that it counts as benefits changes that are merely  transfers.

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B. The Labor Game

Advocates of public projects count wages paid to workers as benefits, while in fact they are costs of projects.

Even in an area with high unemployment, it is unlikely that all project workers would have been unemployed, or they would have remained so for a long time.

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C. The Double Counting If a public project increases the land's value, the government counts as benefits the  increase in land'svalue and the PV of the stream of net income obtained from its use.

Problem: land owner can either sell it or use it, not both.

Under competition, the sale price just equals the PV of the net income obtained from land use.

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