Cost Benefit Analysis: Summary Measures

Calculating and Presenting the Summary Measures

After all the benefits and costs have been estimated, the next and final step is the presentation of results in a simple and understandable form for the audience.

The two summary measures typically used are:

net present value (NPV), and
benefit-cost ratio (BCR).

NPV is calculated by summing the dollar-valued benefits and then subtracting all of the dollar-valued costs, with discounting applied to both benefits and costs as appropriate.

Net Present Value

Benefit-Cost Ratio

Example: CBA of School-Based Tuberculin Screening Program

This 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-cost ratio
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 entrants	155,925	169,136	28.9 (11.3)	(13,211)	1.08
	Both	198,143	210,235	38.6 (11.3)	(12,092)	1.06

Source: Boetani M. JAMA 1995; 274(8): 613–9.

Findings: Tuberculin Screening

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:

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)
Strategy	Group	Cost($)	Benefits($)	Benefit-cost ratio	Cost($)	Benefits($)	Benefit-cost ratio
Screen-all	Kindergartners	183,868	58,201	0.31	183,868	58,201	0.31
	High school entrants	287,452	217,176	0.76	(287,452 – 217,176) = 70,276	0	0
	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.

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 Measure

Incremental Summary Measures

When 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 Benefits_B

–

PV Benefits_A

)

–

(

PV Costs_B

–

PV Costs_A

)

Incremental NPV

NPV_B

–

NPV_A

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 Strategy

Strategy	Group	Program cost($)	Benefits($)	Incremental annual 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
Targeted screening	Kindergartners	42,218	41,099	. . .
	High school entrants	155,925	169,136	. . .
	Both	198,143	210,235	. . .

Conducting a Sensitivity Analysis

Advantages and Limitations of CBA

Test Your Understanding

Please enter your answer to each question before you click on "Our Answer".

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

Our Answer

False. A negative NPV implies that costs exceed benefits.
NPV is a ratio of the computed present values.
True False

Our Answer

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

Assuming that all costs and benefits:
- are present values, and
- were computed for the same time period,
please answer these questions:
1. Compute the benefit-cost ratios (BCRs) for each project.
  
  Our Answer
  
  BCR_A = 6 / 2.2 = 2.7:1
  
  BCR_B = 14.1 / 8.5 = 1.7:1
2. How would you interpret the results to the policy maker, using layman's language?
  
  Our Answer
  
  One dollar spent on Project A returns 2.7 dollars.
  
  One dollar spent on Project B returns 1.7 dollars.
3. Based solely on the results from the preceding question, which project would you recommend?
  
  Our Answer
  
  Project A has a higher return per dollar spent so we would recommend it over Project B.
4. Compute the NPV for each project.
  
  Our Answer
  
  NPV_A = 6 – 2.2 = $3.8
  
  NPV_B = 14.1 – 8.5 = $5.6
5. Interpret the results of the answers to the previous question.
  
  Our Answer
  
  Project A gives us a net benefit worth $3.8 million.
  
  Project B gives us a net benefit worth $5.6 million.
6. Based on those results, what would be your recommendation?
  
  Our Answer
  
  Society gains more from Project B than from Project A.
  Therefore we would recommend Project B.
7. Do these change your previous recommendations? Why or why not?
  Our Answer
  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.
Why do we conduct sensitivity analyses?

Our Answer

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.

	=	( $58,201 – $41,099 )	–	( $183,868 – $42,218 )
	=	– $124,509

Projects	A	B
Costs (million $)	2.2	8.5
Benefits (million $)	6.0	14.1