Benefit-Cost RatioThe benefit-cost ratio (BCR) represents the ratio of total benefits over total costs, both discounted as appropriate. The formula for calculating BCR is:

For example, a BCR value of 1.2:1 will indicate that for every $1 invested (costs), society would gain $1.2 (benefits). Example: CBA of School-Based Tuberculin Screening ProgramThis study was conducted in 1995 to compare tuberculin screening strategies:

screening of all kindergartners and high school entrants (screen-all strategy), versus screening limited to high-risk children (targeted screening).

The tuberculosis incidence in the United States declined for three decades as a result of school-based screening programs for tuberculosis infection recommended by the U.S. Public Health Service. As the screening programs were revised to focus on persons at high risk of infection, the majority of health departments discontinued tuberculin screening of schoolchildren. But such screening had a resurgence beginning in 1985. This study considered the costs and benefits of two alternative school-based tuberculosis screening strategies to help in making decisions regarding initiation or continuation of screening programs. Table 1 shows the results of the study: Table 1. Impact of two programs of tuberculin screening of kindergartners and high school entrants in Santa Clara County, California, with baseline assumptions

Strategy Group Program cost($) Benefits($)

Cases prevented

(discounted cases

prevented)

Net annual cost(net

benefits)($)

Benefit-costratio

Screen-all Kindergartners 183,868 58,201 11.1 (3.9) 125,628 0.31

  High school entrants 287,452 217,176 37.2 (16.1) 70,276 0.76

  Both 471,320 275,377 48.3 (20.0) 195,904 0.58

Targeted screening Kindergartners 42,218 41,099 7.9 (2.7) 1,119 0.97

  High school 155,925 169,136 28.9 (11.3) (13,211) 1.08

entrants

  Both 198,143 210,235 38.6 (11.3) (12,092) 1.06Source: Boetani M. JAMA 1995; 274(8): 613–9.

Findings: Tuberculin ScreeningFor the two tuberculin screening programs:

The program cost of the screen-all program is $471,320 per year, and the net cost is $195,904.

The targeted screening program costs less, $198,143, and produces a net saving of $12,090.

For each dollar invested in the screen-all program, $0.58 is saved (BCR = 0.58).

For each dollar invested in the targeted screening program, $1.06 is saved (BCR = 1.06).

On the other hand, the screen-all program results in more cases prevented than does the targeted screening.

These findings should be considered when deciding which strategy to employ in school-based tuberculosis screening programs. Advantages and Limitations of BCR as a Summary Measure Benefit-cost ratio is a simple summary measure that allows a straightforward communication of results of a CBA for decision making. However, many researchers have highlighted these two shortcomings of BCR that limit its usefulness when comparing the results of various cost benefit analyses:

1. BCR is sensitive to how costs and benefits of a project are classified. Let us consider the previous example, with an additional assumption that the analyst classified the benefits from costs averted for high school entrants as a negative cost for the program. Table 2 presents the results of calculating BCRs for both classifications:

Table 2. Benefit-cost ratios for screen-all versus targeted screening programs

Strategy Group

Classification A(screen-all)

Classification B(targeted screening)

Cost($) Benefits($)

Benefit-costratio

Cost($) Benefits($)

Benefit-costratio

Screen-all

Kindergartners

183,868 58,201 0.31 183,868 58,201 0.31

  High school 287,45 217,176 0.76 (287,45 0 0

entrants 2

2 – 217,176

) =70,276

  Both 471,320 275,377 0.58 254,144 58,201 0.23

Targeted screening

Kindergartners 42,218 41,099 0.97 42,218 41,099 0.97

  High school entrants

155,925 169,136 1.08

(155,925 –

169,136) =

–13,211

0 0

  Both 198,143 210,235 1.06 29,007 41,099 1.42

The reclassification of some benefits as negative costs changed the BCRs of both strategies:

For every dollar invested in the screen-all program:

the return in benefits fell from $0.58 to $0.23, and the BCR for the targeted screening program increased from 1.06 to 1.42.

2. BCR is scale sensitive, i.e., it is sensitive to sizes of the numerator and denominator in the ratio.

One reason that the targeted screening strategy with original classification has a higher BCR than the screen-all strategy (represented by Classification A in the table above) is that its costs and benefits are much lower than those of the screen-all strategy.

Therefore, a BCR is a good summary measure when we consider only one program relative to no program, in which scale (how large or small) is not a factor. The same is true when we are interested in determining whether an intervention would have a BCR exceeding or falling short of a certain value and thus are not interested in scale considerations. Advantages and Limitations of NPV as a Summary MeasureUnlike a BCR, an NPV is not sensitive to classification of benefits and costs because it measures the absolute difference between them. This is one of the main reasons that most economists prefer to use NPV as the summary measure of a CBA. Furthermore, by using NPV as summary measures of CBA we can compare alternatives among a group of projects and pick the preferred alternatives that meet our budget constraints.

This can be done both for programs equally successful in achieving a desired health outcome and for those with different health outcomes. Choosing the alternative(s) with the largest NPV that does not exceed a given budget is the decision rule for selecting the preferred program(s). To make the right choice when the additional consideration of budget constraint is a factor in a CBA, we have to provide information on a project's resource requirements. Presenting the discounted costs together with the NPV of a project provides this information and allows decisionmakers to make informed choices about resource use. Incremental Summary MeasuresWhen we are conducting a CBA of a project or intervention, we are comparing it to a "no intervention" baseline. NPV can also be used to consider the benefits and costs of alternatives such as:

expanding an existing program, adopting an intervention to replace an existing intervention, or the alternative with respect to a program which will definitely be adopted.

Incremental NPV is a summary measure that is used to compare programs under those circumstances. It is calculated as follows: Incremental NPV = ( PV BenefitsB – PV BenefitsA ) – ( PV CostsB – PV CostsA )

Incremental NPV = NPVB – NPVA

Here the baseline, intervention A, is either the existing intervention or the intervention deemed to be less effective. Example: Incremental NPV for the Screen-All StrategyWe can calculate the incremental NPV for the screen-all strategy with respect to targeted screening in a school-based tuberculosis screening program. Using the Costs and Benefits values from Table 1 , the incremental net present value for screening all kindergartners versus targeted screening is: Incremental NPV = ( PV

BenefitsAll– PV BenefitsTS ) – ( PV

CostsAll– PV

CostsTS)

  = ( $58,201 – $41,099 ) – ( $183,868 –

$42,218 )

  = – $124,509The results of similar calculations for high school entrants and both groups of students are shown in Table 3. Table 3. Incremental net present value (NPV) for the screen-all strategy

Strategy Group Program cost($) Benefits($)

Incrementalannual cost

(incremental benefit)($)

Screen-all Kindergartners 183,868 58,201 124,509

  High school entrants 287,452 217,176 57,065

  Both 471,320 275,377 183,812

Targetedscreening Kindergartners 42,218 41,099 . . .

  High school entrants 155,925 169,136 . . .

  Both 198,143 210,235 . . .As is evident, the incremental costs exceed incremental benefits when comparing the screen-all strategy with targeted screening. Conducting a Sensitivity AnalysisHaving estimated the summary measures, we can then study the impact of different input variables on the results of our analyses by conducting a sensitivity analysis. Sensitivity analysis takes into account the uncertainty associated with the assumptions and parameters of CBA by studying how changes in variable values impact the results. A conclusion of CBA is considered "robust" with respect to a variable if a relatively large change in the value of the variable does not change the conclusion. We can conduct both one-way and multi-way sensitivity analyses, in which a single variable or multiple variables are altered, respectively. The results of a multi-way sensitivity analysis will be more informative, however, because our estimates involve interdependent epidemiologic, clinical, and economic data. The results of simultaneous changes in more than one variable are bound to more accurately reflect interactions between these variables and their impact on conclusions of our CBA. Please see the Sensitivity Analysis section of the cost analysis tutorial for more detail. Advantages and Limitations of CBAAs a decision-making tool that helps allocate scarce resources to programs that maximize societal economic benefit, CBA compels analysts to study the full economic impact of all potential outcomes of an intervention. Expressing the results of this comprehensive analysis in purely monetary terms makes it possible to compare:

different programs having different health outcomes, or health programs to nonhealth programs.

Furthermore, the identification of all resource requirements (costs) and benefits of an intervention or program allows analysts to examine its distributional aspects, (e.g., who will receive these benefits and who will bear the costs). The major limitation of CBA is the empirical difficulty associated with assigning monetary values to benefits (e.g., extended human life, improved health, and reduced health risks). Besides the complexity of various methods designed to value these benefits, analysts usually confront controversy over the appropriateness of attaching a certain monetary value to human life. Measuring the cost per unit of health outcome in CEA circumvents the need to make an explicit valuation of human life. Nevertheless, when decisions are to be made as to whether to implement a life-saving intervention based on its cost-effectiveness measure, policy makers must make the implicit

decision as to whether the investment is worth the lives it will save. CBA makes this consideration explicit. Finally, as in any other study, the results of CBA are only as good as the assumptions and valuations on which they are based. Hence, understanding the implications of analysis assumptions and methods is essential for a correct interpretation of results. Test Your UnderstandingPlease answer the questions before you look at the "Our Answers" section.

1. A negative net present value (NPV) implies that benefits exceed costs.

True   False

2. NPV is a ratio of the computed present values.

True   False

3. The table below is a summary of a CBA study for two competing projects: A and B.

Projects A B

Costs (million $) 2.2 8.5

Benefits (million $) 6.0 14.1

4. Assuming that all costs and benefits: are present values, and were computed for the same time period,

please answer these questions:

C. Compute the benefit-cost ratios (BCRs) for each project.

D. How would you interpret the results to the policy maker, using layman's language?

E. Based solely on the results from the preceding question, which project would you recommend?

F. Compute the NPV for each project.

G. Interpret the results of the answers to the previous question.

H. Based on those results, what would be your recommendation?

I. Do these change your previous recommendations? Why or why not?

5. Why do we conduct sensitivity analyses?

Our Answers

1. A negative net present value (NPV) implies that benefits exceed costs.

False. A negative NPV implies that costs exceed benefits.

2. NPV is a ratio of the computed present values.

False. NPV is the difference between computed present values. Benefit-cost ratio is a ratio.

3. The table below is a summary of a CBA study for two competing projects: A and B.

Projects A B

Costs (million $) 2.2 8.5

Benefits (million $) 6.0 14.1

4. Assuming that all costs and benefits: are present values, and were computed for the same time period,

please answer these questions:

C. Compute the benefit-cost ratios (BCRs) for each project.

BCRA = 6 / 2.2 = 2.7:1

BCRB = 14.1 / 8.5 = 1.7:1

D. How would you interpret the results to the policy maker, using layman's language?

One dollar spent on Project A returns 2.7 dollars.

One dollar spent on Project B returns 1.7 dollars.

E. Based solely on the results from the preceding question, which project would you recommend?

Project A has a higher return per dollar spent so we would recommend it over Project B.

F. Compute the NPV for each project.

NPVA = 6 – 2.2 = $3.8

NPVB = 14.1 – 8.5 = $5.6

G. Interpret the results of the answers to the previous question.

Project A gives us a net benefit worth $3.8 million.

Project B gives us a net benefit worth $5.6 million.

H. Based on those results, what would be your recommendation?

Society gains more from Project B than from Project A.

Therefore we would recommend Project B.

I. Do these change your previous recommendations? Why or why not?

Yes. However, other relevant factors need to be taken into consideration:

Project B has about four times the capital outlay of Project A. Society might not be able to implement Project B because of limited

resources. Political or societal support might also play a part.

5. Why do we conduct sensitivity analyses?

We conduct sensitivity analyses to test the robustness of the results.

Our conclusions are robust if they do not change when we vary parameter values over ranges that reflect the uncertainty in the underlying assumptions/data.