6.3 Benefit-Cost Analysis
A benefit-cost analysis (BCA) (or cost-benefit analysis) is a decision making tool that attempts to balance the components of a project in order to maximize its net benefits and/or minimize its costs. In this analysis, we try to quantify the costs of project factors that do not truly have monetary costs; for example, loss of life is often assigned a monetary value. These values are then incorporated into the analysis along with other financial costs. Using BCA, decision makers try to either maximize benefits for a set cost, minimize costs for a set level of benefit, or find the most beneficial compromise when both costs and benefits are variable. For any project to be worthwhile, the benefits must exceed the costs.
6.3.1 Service Projects vs. Revenue Projects
When evaluating various projects, it is important to draw a distinction between revenue projects and service projects. A revenue project is one that will generate both costs and revenues over its project life. When choosing between multiple revenue projects, you should select the alternative with the highest NPV. Nearly every example we have discussed so far in this text fits the definition of a revenue project.
A service project is one that will generate costs, but not revenues, over its project life, or whose revenues are constant regardless of the project alternative chosen. When choosing between multiple service projects, you should select the alternative that performs the service at the lowest cost. For example, a city contracts a company for residential garbage collection. Since the program generates no revenue for the city, when contracting a company to run the collection program, it should choose the business that will run the program at the lowest cost, or do it themselves.
6.3.2 Economic Sectors
Importantly, the concept of a service project should not be confused with concepts of services or the service sector. As a significant distinction, all types of economic activity are sometimes divided into three sectors: the primary sector, the manufacturing sector, and the service sector. The primary sector involves producing raw materials, and covers activities like mining, fishing, and agriculture. The manufacturing sector involves (as you might have guessed) manufacturing products from those raw materials. Finally, the service sector supplies services to consumers, where a service is anything intangible with economic value.
While the service sector might seem the most abstract of the three economic sectors, it is an enormous part of the economy for any developed country. Even in Canada, which has significant and well-developed natural resources, the service sector accounts for over 70% of the nation’s GDP (Statistics Canada, 2017). The service sector includes a wide-range of industries including retail, transportation, insurance, real estate, health care, and education.
In Chapter 1 we covered how a manufacturing business might set costs for its products. By understanding the direct costs of material and labour for each product, and assigning an appropriate amount of overhead from the other expenses of the business, arriving at an appropriate and competitive price for a product is not overly complicated, at least in theory. However, due to the intangible nature of services, setting prices for them can be a difficult task. For example, imagine an airline that currently charges $300 for a flight from Saskatoon to Fredericton. If the airline wanted to improve its service by enhancing the variety of in-flight entertainment and refreshment options, or increasing the amount of leg room on each flight, how much more would its customers be willing to pay for these improvements? Conversely, if the airline cut back on these same services in order reduce its ticket price, would its customers accept the less comfortable conditions for a $250 ticket? What about for a $150 ticket?
Since the price of services is so sensitive to the interests of consumers, it can be very responsive to pressures of supply and demand, and determining a service’s value can be difficult. This is especially true for services performed in the public sector.
6.3.3 Public Sector vs Private Sector
You may also hear of the public sector and the private sector. While these share the term “sector”, they are not related to the concept of primary, manufacturing, and service sectors. In this distinction, the public sector refers to any business that is owned and operated by the government, while the private sector refers to any business that is not owned by the government. Common examples of public sector organizations include (but are not limited to) government ministries, police departments and libraries. Private sector industries are wide ranging often include manufacturing, retail, entertainment, and trades. Sometimes, private sector companies can be hired by governments to perform work in the public sector, or can partner on projects to create what is known as a public private partnership, or P3. Public and private companies may also compete for consumers in the same industries, such as how private shipping companies like UPS compete with national postal services.
It should be noted that there is no consistent rule about which industries or services are in the public sector or private sector, and this will vary depending on a region and its system of government. For example, most communist countries either fully or significantly limit any activity in the private sector, and any country, province, territory, or state may choose to privatize or nationalize different industries depending on their situation (e.g. during WWII, the Canadian government took direct control over most raw material production and manufacturing in order to support the war effort). Even within Canada, services that are public in one province may be private in another; for instance, Saskatchewan is the only province which still owns a public telecommunications company (SaskTel) which competes for consumers with other private companies.
Public sector services often take the form of not-for-profit, service projects. This makes them especially hard to evaluate because the value of their services is not solely financial. For example, how do you decide if one project is a better investment or more beneficial than another. For this reason, we typically use a benefit-cost analysis to evaluate this kind of project:
6.3.4 Framework for Benefit-Cost Analysis
Evaluating User Benefits
The first step in performing a BCA is to identify the impacts that a project will have on its users or stakeholders. We identify these impacts as benefits if they are positive, and disbenefits if they are negative. It can be useful to rank these benefits and disbenefits as primary or secondary, or in a larger hierarchy, in order to understand their relative importance. Primary benefits are those that have a direct impact, while secondary impacts might have an indirect impact. For example, the primary benefit of having a mountain rescue service is that lost skiers are rescued. A secondary benefit is that knowing such a service exists makes people feel safer about going skiing, and thus encourages tourism. When the benefits and disbenefits of a project are directly quantifiable, we find the total value of the benefits for a project with the following equation:
Total Benefits (B) = ∑(Benefits) – ∑(Disbenefits)
To ensure a complete evaluation of benefits, it is necessary to be diligent when identifying all users or stakeholders of a project, and the full range of effects they will experience. For example, consider a city which plans to construct a new athletics stadium. The benefits would include improved facilities for local sports teams (and their fans), a new space for civic, educational, and corporate events, the opportunity to boost tourism and local industry by hosting larger events, new jobs created in constructing and operating the stadium, and potentially many other positive effects. Disbenefits could include traffic delays surrounding the new stadium, or higher ticket prices for events than at the existing facility. In order to properly assess any large project like this, the process of identifying and ranking user benefits must be thorough and deliberate (and can be quite time consuming).
Evaluating Costs
After evaluating the benefits of a project, we must also consider the costs, which make up the other half of our benefit-cost analysis. Since these costs are often strictly financial, they can be more tangible to calculate than the benefits and disbenefits. It is important to realize that the total costs for a project also incorporate any revenue generated by the project. We find the value of the costs for a project using the following equation:
Total Costs (C) = (Capital Cost) + (Operating & Maintenance Cost)
With our example of a new athletics stadium, the costs would be fairly straightforward to determine. There would be capital costs for the land acquisition and construction of the new building, operating and maintenance costs for its upkeep, and revenue produced from event ticket sales or rental fees of the facility
Quantifying Benefits and Disbenefits
While the equations listed above may make this process look uncomplicated, they gloss over the most difficult aspect of benefit-cost analysis: quantifying the benefits and disbenefits. In section 6.4.1, we gave the example of a new stadium, which would (among other impacts) create new employment opportunities and cause traffic delays. These benefits and disbenefits are easy to list off, but difficult to assign dollar amounts to. How much is the creation of a new job in the maintenance and operation of the stadium worth to the city? What is the equivalent cost of an added 20-minute delay per commuter during a peak traffic time for the stadium? How will the increased tourism from the stadium translate into increased business for local hotels, restaurants, etc.? These questions do not have straightforward answers. However, since BCA requires us to quantify these kinds of abstract impacts, we need to determine an approach that suits our scenario.
The two basic approaches to quantifying benefits/disbenefits are to determine the willingness to pay of consumers, or to set performance metrics for certain impacts of the project.
Willingness to pay
Willingness to pay is the highest price that the average consumer would be willing to pay to obtain a product or service, or to avoid a negative outcome. For instance, imagine an open-air music festival where one vendor is selling umbrellas. On one day, the vendor might find they can only charge $15 per umbrella, and that their sales decline sharply if they raise their prices any higher. However, if a sudden rainstorm strikes the festival, they might be able to raise their prices to $35 per umbrella, because the willingness to pay of their consumers has been affected by their circumstances.
In this case, we would say that the value of the umbrellas was found using the revealed preference technique. This means that the customers of the umbrella vendor were revealing the value of the umbrellas through their purchasing habits. If the price were too high, and the average festival-goer would prefer to save their money and get rained on, then the umbrella would not be worth that amount. If most consumers would gladly exchange the listed price for an umbrella, then the price is acceptable or could be increased. We can also imagine the revealed preference technique working in a reverse situation; if new toll stations were installed on a major commuter bridge, how far out of their way would commuters be willing to travel to avoid the toll? How low would the toll need to be to discourage commuters from taking the detour?
The alternative to the revealed preference technique is the stated preference technique. This approach relies on surveying consumers directly about their willingness to pay. The advantage of this technique is that it gives straightforward answers that can be directly applicable to the situation at hand. Would you change laundry detergent brands if there was an alternative $2 cheaper? How much more would you be willing to pay for internet if your provider upgraded to a high-speed, fiber-optic network? Would a new tax on cigarettes impact your decision to quit (or begin) smoking? Would increased ticket prices for speeding cause you to change your driving habits?
The drawback of this approach is that consumers stated preferences do not always line up well with their actual preferences. For the examples above, a consumer might say they’d switch to a cheaper detergent, but in practice stay with their usual brand out of habit. They might also underestimate their preference for faster internet, overestimate their ability to quit smoking, and quickly forget about the increased speeding fines (until they get written their first ticket). In short, the stated preference technique can be useful for determining willingness to pay, but is not a foolproof option.
Performance Metrics
Another commonly used approach for determining the value of a cost or benefit is to set performance metrics for the impacts of a project. For example, when transportation engineers compare alternative roadway designs, they calculate the expected number of crashes for each design, and the severity of those crashes. Most often, the crashes are classified as either “fatal” crashes, “injury” crashes, or “property damage only (PDO)” crashes, and a certain dollar value is assigned to each type of crash based the severity of the damage done (e.g. a “PDO” crash might be valued around $1000, and a fatal crash might be valued around $1,000,000). Then, by multiplying these values by the expected number of crashes, the relative cost savings (also representing human safety) can be compared to the price to inform whether a project is worthwhile.
For a project with environmental impacts, there are many possible routes for evaluation. If a project generates some kind of pollutant, the metric could be based on the cost of removing that pollutant from the ecosystem, or on the contributing cost to the healthcare system for any negative health outcomes it encourages (e.g. more air pollution might lead to increased respiratory problems). Carbon pricing methods like a carbon tax or a cap-and-trade system are examples of a government attaching a cost metric to an environmental impact (in this case, CO2 emissions) in order to have businesses consider their environmental effects as a tangible cost.
Assigning performance metrics to determine the value of a cost or benefit is not an exact science, and for any given benefit there are likely to be many different ways of quantifying it. The important factor is to quantify the effect on the basis of a logically related cost, and to arrive at a performance metric that scales appropriately with the importance of the impact.
Determining Social Discount Rate
In Chapter 5 we found that many financial evaluation methods are very sensitive to the discount rate applied during analysis. Setting an appropriate interest rate or MARR is a vital step in determining the value of any project. Benefit cost analysis is no different. When performing analysis for a services project, we refer to the discount rate as a social discount rate.
The social discount rate is set slightly differently than other discount rates we have discussed previously. There are two basic approaches to setting the rate, depending on whether the project has private sector involvement:
- For a fully public sector project, the social discount rate should reflect only the prevailing government borrowing rate.
- For a project with private counterparts, the social discount rate should reflect the rate that could have been earned had the funds not been removed from the private sector.
Once the social discount rate has been set, it is used in the same way as the discount rate for any other project: to discount cash flows from different points in the project to a common time frame.
6.3.5 Evaluating Results
Once the benefits and costs of a project have been determined, there are two commonly used indicators for evaluating the project: the benefit cost ratio and the profitability index.
Benefit Cost Ratio
The benefit cost ratio for a project is the present value of the project’s benefits divided by the present value of its costs- ensuring all costs and benefits are compared during the same time scale is an important consideration of this process. Any future amounts can be converted to present values using the determined social discount rate.
If the benefit cost ratio is greater than 1 (i.e. the benefits are greater than the costs), then the project should be accepted. If it is less than 1, then the project should be rejected.
Profitability Index
The profitability index (PI) for a project is slightly different from the benefit cost ratio, since it considers costs and benefits on an annual basis and incorporates the capital investment cost of project separately. Again, the costs and benefits associated with the project must all be considered at their present values.
As with the benefit cost ratio, if the PI is greater than 1, the project should be accepted. Otherwise the project should be rejected.
Comparing Multiple Projects
Suppose you were performing benefit-cost analyses to find the best alternative for the expansion of an existing airport. You considered five alternatives, which returned benefit cost ratios of 1.2, 0.8, 1.15, 1.3, and 0.95. You might assume that the alternative with the 1.3 benefit-cost ratio is the best alternative, since it has the highest ratio. However, the best approach in this situation is to use an incremental analysis technique, consisting of the following steps:
- Eliminate any alternatives with benefit-cost ratios less than 1.
- Arrange the remaining alternatives from lowest cost to highest cost.
- Compute the incremental differences from the paired alternatives.
- Compute the benefit cost ratio again based on the incremental benefits and costs.
- Compare the chosen alternative to the next alternative.
This technique is best demonstrated using an example. Let’s look at the airport expansion example from above, but in greater detail. Using the data provided below, let’s walk through the steps of this analysis.
| Alternative | Initial Investment | Benefits | Costs | Benefit/Cost Ratio |
| A | $1,000,000 | $48,000 | $40,000 | 1.2 |
| B | $1,500,000 | $48,000 | $60,000 | 0.8 |
| C | $800,000 | $40,250 | $35,000 | 1.15 |
| D | $1,250,000 | $58,500 | $45,000 | 1.3 |
| E | $750,000 | $33,250 | $35,000 | 0.95 |
- Eliminate any alternatives with benefit-cost ratios less than 1.
This leaves us with alternatives A, C, and D.
2. Arrange the remaining alternatives from lowest cost to highest cost.
This leaves us with the following table of results:
| Alternative | Initial Investment | Benefits | Costs | Benefit/Cost Ratio |
| C | $800,000 | $40,250 | $35,000 | 1.15 |
| A | $1,000,000 | $48,000 | $40,000 | 1.2 |
| D | $1,250,000 | $58,500 | $45,000 | 1.3 |
3. Compute the incremental differences from the paired alternatives.
4. Compute the benefit cost ratio again based on the incremental benefits and costs.
5.Compare the chosen alternative to the next alternative.