[Solution]Cost-Benefit Formula

The basis of the cost-benefit analysis is simple: to determine whether the benefits of a particular project outweigh the costs. The following formula is used:…

The basis of the cost-benefit analysis is simple: to determine whether the benefits of a particular project outweigh the costs. The following formula is used:
NB = B – C
In this formula, NB represents the expected net benefits of a project, B is the expected total benefits from that project, and C is the expected total costs (Finkler, Kovner, & Jones, 2010).
For example, suppose three public health programs—a breast cancer screening program for adult women, a nutrition program for school-aged children, and an anti-smoking program for adolescents—are presented for funding. Suppose, too, that all three programs have been shown to be effective in achieving their intended objectives. A cost-benefit analysis can be applied to estimate the total benefit and costs of the three competing programs to determine the net benefits of each. An estimation of net benefits in terms of a common unit, dollars, makes it possible to discern whether a particular program generates greater net benefits for society than competing projects.
Now, let’s suppose that a nurse executive is deciding whether to implement a shared-governance program to enhance staff-nurse engagement and nursing autonomy and independence. The shared-governance program’s underlying philosophy will be to support clinical practice using the principle of participatory management. The nurse executive can utilize a cost-benefit analysis to identify and measure both the direct and indirect costs of the program and direct benefits to the organization and the nursing staff.
In carrying out a cost-benefit analysis, the nurse executive can ask a series of three practical questions.
1. Which costs should be included in the cost-benefit calculation?
2. Which benefits should be included?
3. How should future costs and benefits be treated?
The costs that should be included in the analysis would consist of: meeting time for nurses to attend unit-based and organization-wide shared-governance meetings, time for nurses to complete projects, staff coverage, materials for completing special projects, and for nurses to attend other hospital-wide meetings. The benefits included in this analysis would be staff- satisfaction scores, retention rate of nurses, patient-satisfaction scores, and project outcomes. If the benefits outweigh the costs, then implementing shared governance is an optimal decision for the nurse executive (Finkler, et al., 2010).
Types of Cost Analysis
In the healthcare literature, several different types of cost analysis are used.
• Cost-benefit analysis—The outcome or benefits of a program are measured in terms of dollars.
• Cost effectiveness—The benefits are measured in terms of health units.
When costs and outcomes are measured in terms of dollars, cost-benefit analysis is the appropriate tool to use. The costs are subtracted from the benefits to determine the net economic benefit. This analysis permits the comparison of alternatives, since all costs and benefits are converted into dollars.
Cost effectiveness is used to evaluate competing programs that are designed to achieve the same or similar objectives. Because the program outputs are assumed to be the same, attention is focused on the identification and estimation of program costs, thus avoiding many of the difficulties of benefits estimation. For example, both physicians and nurse midwives can provide routine prenatal care, but the costs and effectiveness may be very different. Cost-effectiveness analysis can be used to evaluate the relative merits of the two types of healthcare providers who can serve the needs of the same group of patients.
Breakeven Analysis
Break-even analysis is used to determine at what point a new program or service will break-even and then start to make money (Finkler, et al., 2010). The analysis is based on the following formula.
The breakeven quantity (Q) =
Fixed Costs (FC)
Price (P) – Variable Cost per Patient (VC)
Q = FC
P – VC
Where Q is the number of patients needed just breakeven.
FC is the total fixed cost.
P is the assumed average amount collected per patient.
VC is the variable cost per patient.
At a quantity lower that Q, there would be a loss; at a quantity higher than Q, there would be a profit. P is assumed to be the average amount of revenue the organization ultimately receives per patient. The basis for the formula is the underlying relationship between revenues and expenses. If total revenues are greater than expenses, there is a profit. If total revenues are less than expenses, there is a loss. If revenues are just equal to expenses, there is neither a profit nor a loss, and the service is said to just break-even (Finkler, et al., 2010).
Suppose a healthcare organization opens a new home-health agency that charges, on average, $50 per patient visit. The agency has fixed costs of $10,000—salaries, equipment, supplies, and other miscellaneous and overhead. Also, the agency has variable costs of $30 per patient—home instructions based on patient diagnosis, additional office supplies, traveling expenditures per nurse, etc. If there are no patients at all, there is no revenue, but there are fixed costs of $10,000, and there is a $10,000 loss.
Each patient brings in $50 of revenue, but causes the agency to spend $30 more per patient. The difference between the $50 price and the $30 variable cost is $20, and called the contribution margin. The contribution margin from each patient can be used to cover fixed costs.
Let’s say that the agency sees 100 patients. There is a contributing margin of $20 for each of the 100 patients, or a total contribution margin of $2,000. The agency would still be operating at a loss of $8,000. How many patients would the agency need to have to break even? Using the break-even analysis formula:
Q = FC = $10,000 = $10,000 = 500 Patient Visits
P – VC $50 – $30 $20
Five hundred patients would generate $10,000 of contribution margin; exactly enough to cover fixed costs. If the agency sees 500 patients, it will just break even.
Additional Example:
When there are different types of patients, the break-even analysis becomes more complicated. If there are different types of patients with different prices, it is necessary to find the weighted average contribution margin.
Suppose for this new home-health agency, there are three different classes of home visits. The price for the visits is $100, $75, and $50. The variable costs for the visit are $30. The contribution margin for each type of patient can be calculated by subtracting the variable cost from the price as follows.
Price Variable Cost Contributing Margin
Complex $100 – $30 = $70
Moderate $75 – $30 = $45
Simple $50 – $30 = $20
The crucial piece of information for calculating the break even point is the relative proportion of each type of visit. Let’s say that 20% of all visits are complex, 50% are moderate, and 30% are simple. This information can be used to calculate the weighted average contribution margin. This requires multiplying each type of contributing margin by the percentage of patients that make up that type of visit, and then adding the sum of those results to attain the total weighted average contributing margin.
Percentage of Visits Contribution Margin Weighted Average Contribution Margin
Complex 20% x $70 = $14.00
Moderate 50% x $45 = $22.50
Simple 30% x $20 = $6.00
Total Weighted Average Contribution Margin: $42.50
The $42.50 weighted represents the average contribution margin for all types of visits. It can be used to calculate the break-even quantity. Assume that fixed costs are at $10,000.
$10,000 Q = $42.50 = 235 visits
Of the total 235 visits, 47 would be expected to be complex (20%), 118 moderate (50%), and 70 visits as simple (30%). The same weighted average approach could be used to find the break-even volume when there are more than three different types of patients.
Suppose we want to know the exact day when a profit for the new home-healthcare agency will begin. Using the same home-healthcare-agency example, days to break even is calculated as follows.
Days to break even = # of patients to break even
# of patients the agency serves per day
Let’s say that the agency sees 1800 patients during its first year of operation, 20% of which are complex, 50% patients are moderate care, and 30% are simple. The days to break even is calculated as follows.
Price Variable Cost Contributing Margin
Complex $100 – $30 = $70
Moderate $75 – $30 = $45
Simple $50 – $30 = $20
# of Percentage Contribution Weighted Average
Patients of Visits Margin Contribution Margin
Complex 360 20% x $70 = $14.00
Moderate 900 50% x $45 = $22.50
Simple 540 30% x $20 = $6.00
1800 $42.50
Q = $42.50 = 235 visits
# of patients served per day = # of patients seen per year
# of days per year
= 1800 = 4.93 patient per day
Days to break even = # of patients to break even
# of patients the agency serves per day
= 235 = 47.6
The new home-healthcare agency will break even on the 48th day of operation and, on the 49th day of operation, will start to make a profit.

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