Cost Benefit Analysis : Cost Benefit Analysis Arjun Shivanand K.
Arvind Pradeep S. Introduction : Introduction Cost-benefit analysis is a term that refers to:
Helping to appraise, or assess, the case for a project, programme or policy proposal.
An approach to making economic decisions of any kind. Theory : Theory The process involves, whether explicitly or implicitly, weighing the total expected costs against the total expected benefits of one or more actions in order to choose the best or most profitable option.
The formal process is often referred to as either CBA (Cost-Benefit Analysis) or BCA (Benefit-Cost Analysis). Theory : Theory Benefits and costs are often expressed in money terms, and are adjusted for the time value of money(the value of money figuring in a given amount of interest earned over a given amount of time), so that all flows of benefits and flows of project costs over time (which tend to occur at different points in time) are expressed on a common basis in terms of their “present value.” Principles : Principles There Must Be a Common Unit of Measurement
CBA Valuations Should Represent Consumers or ProducersValuations As Revealed by Their Actual Behavior
Benefits Are Usually Measured by Market Choices
Gross Benefits of an Increase in Consumption is an Area Under the Demand Curve
The Analysis of a Project Should Involve a With Versus Without Comparison
Decision Criteria for Projects Principles : Principles Common Unit of Measurement:
To the desirability of a project all aspects of the project, positive and negative, must be expressed in terms of a common unit; i.e., there must be a "bottom line." The most convenient common unit is money. This means that all benefits and costs of a project should be measured in terms of their equivalent money value. Process : Process NPV (net present value)
PVB (present value of benefits)
PVC (present value of costs)
BCR (benefit cost ratio = PVB / PVC)
Net benefit (= PVB - PVC) Example : Example To illustrate how CBA might be applied to a project, let us consider a highway improvement such as the extension of Highway 101 into San Jose.
The local four-lane highway which carried the freeway and commuter traffic into San Jose did not have a median divider and its inordinate number of fatal head-on collisions led to the name "Blood Alley."
The improvement of the highway would lead to more capacity which produces time saving and lowers the risk. But inevitably there will be more traffic than was carried by the old highway. Example : Example Example : Example The data indicates that for rush-hour trips the time cost of a trip is $5 without the project and $3 with it. It is assumed that the operating cost for a vehicle is unaffected by the project and is $4.
The project lowers the cost of a trip and the public responds by increasing the number of trips taken. There is an increase in consumer surplus both for the trips which would have been taken without the project and for the trips which are stimulated by the project.
For trips which would have been taken anyway the benefit of the project equals the value of the time saved times the number of trips.
For the rush-hour trip the project saves $2 and for the nonrush-hour trip it saves $0.80. For the trips generated by the project the benefit is equal to one half of the value of the time saved times the increase in the number of trips. Example : Example Example : Example To convert the benefits to an annual basis one multiplies the hourly benefits of each type of trip times the number of hours per year for that type of trip.
There are 260 week days per year and at six rush hours per weekday there are 1560 rush hours per year. This leaves 7200 non-rush hours per year. Example : Example Example : Example The value of the reduced fatalities may be computed in terms of the equivalent economic value people place upon their lives when making choices concerning risk and money.
If the labor market has wages for occupations of different risks such that people accept an increase in the risk of death of 1/1,000 per year in return for an increase in income of $400 per year then a project that reduces the risk of death in a year by 1/1000 gives a benefit to each person affected by it of $400 per year.
The implicit valuation of a life in this case is $400,000. Thus benefit of the reduced risk project is the expected number of lives saved times the implicit value of a life. For the highway project this is 6x$400,000= $2,400,000 annually. Example : Example Let us assume that this level of benefits continues at a constant rate over a thirty-year lifetime of the project.
The cost of the highway consists of the costs for its right-of-way, its construction and its maintenance.
For purposes of this example the cost of right-of-way is taken to be $100 million and it must be paid before any construction can begin.
At least part of the right-of- way cost for a highway can be recovered at the end of the lifetime of the highway if it is not rebuilt. For the example it is assumed that all of the right-of-way cost is recoverable at the end of the thirty-year lifetime of the project.
The construction cost is $200 million spread evenly over a four-year period. Maintenance cost is $1 million per year once the highway is completed. Example : Example Example : Example The benefits and costs are in constant value dollars; i.e., there was no price increase included in the analysis.
Therefore the discount rate used must be the real interest rate.
If the interest rate on long term bonds is 8 percent and the rate of inflation is 6 percent then the real rate of interest is 2 percent. Present value of the streams of benefits and costs discounted at a 2 percent back to time zero are as follows Example : Example Example : Example The positive net present value of $50.35 million and benefit/cost ratio of 1.2 indicate that the project is worthwhile if the cost of capital is 2 percent.
When a discount rate of 3 percent is used the benefit/cost ratio is slightly under 1.0. This means that the internal rate of return is just under 3 percent. When the cost of capital is 3 percent the project is not worthwhile. Conclusion : Conclusion By reducing the positive and negative impacts of a project to their equivalent money value Cost-Benefit Analysis determines whether on balance the project is worthwhile.
The equivalent money value are based upon information derived from consumer and producer market choices; i.e., the demand and supply schedules for the goods and services affected by the project.
Care must be take to properly allow for such things as inflation.
When all this has been considered a worthwhile project is one for which the discounted value of the benefits exceeds the discounted value of the costs; i.e., the net benefits are positive. This is equivalent to the benefit/cost ratio being greater than one and the internal rate of return being greater than the cost of capital.