## AN ALGORITHM FOR COST-BENEFIT ANALYSIS

From http://www.unc.edu/~perreira/guide11.html (PUPA 71 @ UNC)

• Determine Standing: The analyst must first decide whose costs and whose benefits should be considered. This will depend on your perspective. We might be interested in costs and benefits to an individual, to a family, to a small community, to a state, to the federal government, or to the world. In general, policy analysts will take the perspective of the government agency they represent or a global perspective that includes all people who could be influenced by the policy change whether or not they actually live in the community where the policy is being enacted. Deciding on the perspective is essential because one persons/agencies cost may be another persons/agencies benefit.
• Select Alternatives for Comparison: At this point the analyst will restrict the analysis to two or three alternatives that are the most politically feasible. Often the analysts is told exactly which project alternatives should be compared.
• Categorize Costs and Benefits: This is often the most contentious step in cost-benefit analysis. The analyst must prepare a complete lists of costs and benefits. The failure to include a potentially significant cost or benefit will subject the analysis to intense criticism and may render it useless. Categories of costs include: (1) Capital/Fixed Costs (e.g. Buildings, equipment Construction), (2) Administrative/Operational Costs (e.g. wages and maintenance of capital), (3) Time Costs, (4) Psychic Costs, (5) Opportunity Costs. Categories of benefit include: (1) Revenues, (2) Operational Savings, (3) Time Savings (4) Psychic Benefits, (5) Option Values, and (6) Physical Benefits (e.g. lives saved, accidents prevented, new products made)
• Predict Net Life-time Value of Project: Once analysts have identified all the relevant costs and benefits, it is time to measure them over the life of the project. Some projects will be implemented for a limited or defined time period. The life-time of other projects may be defined by the life-time of the physical capital invested in the project. All physical capital depreciates over time and eventually wears out or becomes obsolete. At that point, a new investment would need to be considered. Lastly, the life-time of a project may be set arbitrarily at one, five, or ten years. This will depend on the preferences and perhaps election terms of those commissioning the analysis.
• Monetize Costs and Benefits: Valuing inputs to and outputs of a project in monetary terms is a tricky process. Some inputs (e.g., physical inputs and labor inputs) and some outputs (e.g. revenue) are easily valued in monetary terms. Other inputs and outputs are more difficult to measure in monetary term. How do we quantify an increase in leisure/spare time, the value of a life saved, an accident prevented, a lake, or a forest? How do we quantify an increase in equality, an increased sense of security, or the value of fairness? For starters, we can conduct survey research to identify what individuals would be willing to pay to prevent an accident, increase their sense of security, reduce income disparities, or save a life. We can also look act how people actually behave. Per capita charitable contributions might give us a sense of how much individuals in a community value income equality. Decisions to work based on the going wage rate can give us a sense of how individuals value their time. The salary premium a person will accept to work in a high-risk job can provide a sense of how much they are willing to accept to incur an injury or even death. Courts will often value a life by the amount of earning potential and individual has. Similarly, a disability might be valued by the amount of lost earnings. Luckily, there are a wide range of pre-existing studies that can help policy analysts place monetary value on these hard to measure items.
• Calculate Expected Net Value of Project: The net benefit of a project may vary depending on different states of the world. Unexpected events can take place at any point during the duration of a project and change the cost-benefit calculation. Thus, benefits and costs do not always accrue with absolute certainty. Often, they only accrue with some probability. When this is the case, we must calculate the relative cost or benefit as an expected cost or benefit. In other words, the cost (benefit) will be equal to the sum of the costs in each "state" of the world and the probability that the event(s) leading to that "state" will occur. In the simplest case where there are only two states of the world to consider, the expected costs (benefits) can be defined as:

$E (B) = p_1B_1 + p_2B_2$
or
$E (C) = p_1 C_1 + p_2C_2$

where p_1 is the probability of the event happening;
$p_2$ is the probability that the event doesn't happen;
$C_1$ and $C_2$ are the relevant costs when the event occurs and when it does not, respectively; and
$B_1$ and $B_2$ are the relevant benefits when the event occurs and when it does not, respectively.

• Calculate Net Present Value of Project: Often the costs of a project are incurred immediately, but the benefits of the project will not accrue until several years after it is implemented. The present value of a project is the amount that you would be willing to pay today to receive the benefit of the project tomorrow. We are most familiar with using the concept of present value when we consider loaning money to someone. If a friend asks for a loan and promises to pay us back one year from now, we will generally ask them to pay back the loan amount plus some interest. The interest is the price to the borrower of renting our money for one year. We will generally set this price based on the opportunity cost of the money. Assuming that the next best use of the money was to invest it in a Certificate of Deposit earning 5 % annually, then we would break-even by charging our friend 5 % interest on their loan from us.

A project that will yield a net benefit of NB one year in the future has a present value of NB/(1+r), where r is the interest rate. In cost-benefit analysis, this interest rate is called the discount rate. Benefits and costs accruing in the future are worth less than benefits accruing today. Therefore, we discount their value. A project with a stream of net benefits (NB0, NB1, NB2….) over several years (t) will have a present value of:

(1)
\begin{align} PV = NB_0 + \frac {NB_1} {(1+d)^1} + \frac {NB_2} {(1+d)^2 } + ... + \frac {NB_t} {(1+d)^t} \end{align}
• Conduct Sensitivity Analysis: To do any cost benefits analysis, we must make several assumptions. Common assumptions include those regarding the probability of an event (p), the appropriate discount rate (d), and the size of particular costs and benefits. When there is considerable disagreement regarding one or more assumptions made in the analysis, it is helpful to provide an upper and lower bound to the cost-benefit calculation. We can do this by varying the set of assumptions made and testing the sensitivity of our estimates to these assumption.
• Recommend Alternative: The cost-benefit analysis will indicate which alternative has the largest net social benefit. Whether this is the alternative that should be implemented is a normative decision to be made in the political and bureaucratic arenas. The cost-benefit analysis will not consider the political feasibility of adopting and implementing an alternative. It focuses only on the efficiency and effectiveness with which each alternative can achieve a specific set of objectives. These objectives are also defined in the political and social arenas and are not the subject of positive analysis.
page revision: 6, last edited: 16 Jan 2016 20:45