Examples of semi variable costs in healthcare

A n a l y s i s 7 C H A P T E R

DISTINCTION BETWEEN FIXED, VARIABLE, AND SEMIVARIABLE COSTS

This chapter emphasizes the distinction between fixed, variable, and semivariable costs because this knowledge is a basic working tool in financial management. The manager needs to know the difference between fixed and variable costs to compute contribution margins and break-even points. The manager also needs to know about semivariable costs to make good decisions about how to treat these costs.

Fixed costs are costs that do not vary in total when ac- tivity levels (or volume) of operations change. This con- cept is illustrated in Figure 7-1. The horizontal axis of the graph shows number of residents in the Jones Group Home, and the vertical axis shows total monthly fixed cost in dollars. In this graph, the total monthly fixed cost for the group home is $3,000, and that amount does not change, whether the number of residents (the activity level or volume) is low or high. A good example of a fixed cost is rent expense. Rent would not vary whether the home was almost full or almost empty; thus, rent is a fixed cost.

Variable costs, on the other hand, are costs that vary in direct proportion to changes in activity levels (or vol- ume) of operations. This concept is illustrated in Figure 7-2. The horizontal axis of the graph shows number of residents in the Jones Group Home, and the vertical axis shows total monthly variable cost in dollars. In this graph, the monthly variable cost for the group home changes proportionately with the number of residents (the activ- ity level or volume) in the home. A good example of a

After completing this chapter, you should be able to

1. Understand the distinction between fixed, variable, and semivariable costs.

2. Be able to analyze mixed costs by two methods.

3. Understand the computation of a contribution margin.

4. Be able to compute the cost- volume-profit (CVP) ratio.

5. Be able to compute the profit- volume (PV) ratio.

P r o g r e s s N o t e s

variable cost is food for the group home residents. Food would vary directly, depending on the number of individuals in residence; thus, food is a variable cost.

Semivariable costs vary when the activity levels (or volume) of operations change, but not in direct proportion. The most frequent pattern of semivariable costs is the step pat- tern, where the semivariable cost rises, flattens out for a bit, and then rises again. The step pattern of semivariable costs is illustrated in Figure 7-3. The horizontal axis of the graph shows number of residents in the Jones Group Home, and the vertical axis shows total monthly semivariable cost. In this graph, the behavior of the cost line resembles stair steps:

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Figure 7–1 Fixed Costs—Jones Group Home.

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Figure 7–2 Variable Cost—Jones Group Home.

Distinction between Fixed, Variable, and Semivariable Costs 61

thus, the “step pattern” name for this configuration. The most common example of a semi- variable expense in health care is supervisors’ salaries. A single supervisor, for example, can perform adequately over a range of rises in activity levels (or volume). When another su- pervisor has to be added, the rise in the step pattern occurs.

It is important to know, however, that there are two ways to think about fixed cost. The usual view is the flat line illustrated on the graph in Figure 7-1. That flat line represents total monthly cost for the group home. However, another perception is presented in Figure 7-4. The top view of fixed costs in Figure 7-4 is the usual flat line just discussed. The bottom view is fixed cost per resident. Think about the figure for a moment: the top view is dollars in total for the home for the month, and the bottom view is fixed-cost dollars by number of residents. The line is no longer flat but declines because this view of cost declines with each additional resident.

We can also think about variable cost in two ways. The usual view of variable cost is the di- agonal line rising from the bottom of the graph to the top, as illustrated in Figure 7-2. That steep diagonal line represents monthly cost varying in direct proportion with number of residents in the home. However, another perception is presented in Figure 7-5. The top view of variable costs in Figure 7-5 represents total monthly variable cost and is the usual di- agonal line just discussed. The bottom view is variable cost per resident. Think about this figure for a moment: the top view is dollars in total for the home for the month, and the bottom view is variable-cost dollars by number of residents. The line is no longer diagonal but is now flat because this view of variable cost stays the same proportionately for each res- ident. A good way to think about Figures 7-4 and 7-5 is to realize that they are close to being mirror images of each other.

Semifixed costs are sometimes used in healthcare organizations, especially in regard to staffing. Semifixed costs are the reverse of semivariable costs: that is, they stay fixed for a time as activity levels (or volume) of operations change, but then they will rise; then they

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Figure 7–3 Semivariable Cost—Jones Group Home.

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will plateau; then they will rise. Thus, semifixed costs can exhibit a step pattern similar to that of variable costs.1 However, the semifixed cost “steps” tend to be longer between rises in cost. In summary, both semifixed and semivariable costs have mixed elements of fixed and variable costs. Thus, both semivariable and semifixed costs are called mixed costs.

EXAMPLES OF VARIABLE AND FIXED COSTS

Studying examples of expenses that are designated as variable and fixed helps to under- stand the differences between them. It should also be mentioned that some expenses can be variable to one organization and fixed to another because they are handled differ-

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ently by the two organizations. Operating room fixed and variable costs are illustrated in Table 7-1. Thirty-two expense accounts are listed in Table 7-1: 11 are variable, 20 are desig- nated as fixed by this hospital, and 1, equipment depreciation, is listed separately.2 (The separate listing is because of the way this hospital’s accounting system handles equipment depreciation.)

Another example of semivariable and fixed staffing is presented in Table 7-2. The costs are expressed as full-time equivalent staff (FTEs). Each line-item FTE will be multiplied times the appropriate wage or salary to obtain the semivariable and fixed costs for the op- erating room. (The further use of FTEs for staffing purposes is fully discussed in Chapter 9.) The supervisor position is fixed, which indicates that this is the minimum staffing that

Examples of Variable and Fixed Costs 63

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Figure 7–5 Two Views of Variable Costs.

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can be allowed. The single aide/orderly and the clerical position are also indicated as fixed. All the other positions—technicians, RNs, and LPNs—are listed as semivariable, which in- dicates that they are probably used in the semivariable step pattern that has been previously discussed in this chapter. This table is a good example of how to show clearly which costs will be designated as semivariable and which costs will be designated as fixed.

Table 7–1 Operating Room Fixed and Variable Costs

Account Total Variable Fixed Equipment

Social Security $ 60,517 $ 60,517 $ $ Pension 20,675 20,675 Health Insurance 8,422 8,422 Child Care 4,564 4,564 Patient Accounting 155,356 155,356 Admitting 110,254 110,254 Medical Records 91,718 91,718 Dietary 27,526 27,526 Medical Waste 2,377 2,377 Sterile Procedures 78,720 78,720 Laundry 40,693 40,693 Depreciation—Equipment 87,378 87,378 Depreciation—Building 41,377 41,377 Amortization—Interest (5,819) (5,819) Insurance 4,216 4,216 Administration 57,966 57,966 Medical Staff 1,722 1,722 Community Relations 49,813 49,813 Materials Management 64,573 64,573 Human Resources 31,066 31,066 Nursing Administration 82,471 82,471 Data Processing 17,815 17,815 Fiscal 17,700 17,700 Telephone 2,839 2,839 Utilities 26,406 26,406 Plant 77,597 77,597 Environmental Services 32,874 32,874 Safety 2,016 2,016 Quality Management 10,016 10,016 Medical Staff 9,444 9,444 Continuous Quality Improvement 4,895 4,895 EE Health 569 569

Total Allocated $1,217,756 $600,822 $529,556 $87,378

Source: Adapted from J.J. Baker, Activity-Based Costing and Activity-Based Management for Health Care, p. 191, © 1998, Aspen Pub- lishers, Inc.

Analyzing Mixed Costs 65

Another example illustrates the behavior of a single variable cost in a doctor’s office. In Table 7-3, we see an array of costs for the procedure code 99214 office visit type. Nine costs are listed. The first cost is variable and is discussed momentarily. The other eight costs are all shown at the same level for a 99214 office visit: supplies, for example, is the same amount in all four columns. The single figure that varies is the top line, which is “report of lab tests,” meaning laboratory reports. This cost directly varies with the proportion of activity or volume, as variable cost has been defined. Here we see a vari- able cost at work: the first column on the left has no lab report, and the cost is zero; the sec- ond column has one lab report, and the cost is $3.82; the third column has two lab reports, and the cost is $7.64; and the fourth column has three lab reports, and the cost is $11.46. The total cost rises by the same proportionate increase as the increase in the first line.

ANALYZING MIXED COSTS

It is important for planning purposes for the manager to know how to deal with mixed costs because they occur so often. For example, telephone, maintenance, repairs, and utilities are all actually mixed costs. The fixed portion of the cost is that portion representing hav- ing the service (such as telephone) ready to use, and the variable portion of the cost repre- sents a portion of the charge for actual consumption of the service. We briefly discuss two

Table 7–2 Operating Room Semivariable and Fixed Staffing

Total No. Job Positions of FTEs Semivariable Fixed

Supervisor 2.2 2.2 Techs 3.0 3.0 RNs 7.7 7.7 LPNs 1.2 1.2 Aides, orderlies 1.0 1.0 Clerical 1.2 1.2

Totals 16.3 11.9 4.4

Table 7–3 Office Visit with Variable Cost of Tests

99214 99214 99214 99214 Service Code No Test 1 Test 2 Tests 3 Tests

Report of lab tests 0.00 3.82 7.64 11.46

Fixed overhead $31.00 $31.00 $31.00 $31.00 Physician 11.36 11.36 11.36 11.36 Medical assistant 1.43 1.43 1.43 1.43 Bill 0.45 0.45 0.45 0.45 Checkout 1.00 1.00 1.00 1.00 Receptionist 1.28 1.28 1.28 1.28 Collection 0.91 0.91 0.91 0.91 Supplies 0.31 0.31 0.31 0.31 Total visit cost $47.74 $51.56 $55.38 $59.20

66 CHAPTER 7 Cost Behavior and Break-Even Analysis

very simple methods of analyzing mixed costs, then we examine the high–low method and the scatter graph method.

Predominant Characteristics and Step Methods

Both the predominant characteristics and the step method of analyzing mixed costs are quite simple. In the predominant characteristic method, the manager judges whether the cost is more fixed or more variable and acts on that judgment. In the step method, the man- ager examines the “steps” in the step pattern of mixed cost and decides whether the cost appears to be more fixed or more variable. Both methods are subjective.

High–Low Method

As the term implies, the high–low method of analyzing mixed costs requires that the cost be examined at its high level and at its low level. To compute the amount of variable cost in- volved, the difference in cost between high and low levels is obtained and is divided by the amount of change in the activity (or volume). Two examples are examined.

The first example is for an employee cafeteria. Table 7-4 contains the basic data required for the high–low computation. With the formula described in the preceding paragraph, the following steps are performed:

1. Find the highest volume of 45,000 meals at a cost of $165,000 in Septem- ber (see Table 7-4) and the lowest volume of 20,000 meals at a cost of $95,000 in March.

2. Compute the variable rate per meal as

No. of Cafeteria Meals Cost

Highest volume 45,000 $165,000 Lowest volume 20,000 95,000 Difference 25,000 70,000

3. Divide the difference in cost ($70,000) by the difference in number of meals (25,000) to arrive at the variable cost rate:

$70,000 divided by 25,000 meals � $2.80 per meal

Table 7–4 Employee Cafeteria Number of Meals and Cost by Month

No. of Employee Month Meals Cafeteria Cost

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July 40,000 164,000

August 43,000 167,000

September 45,000 165,000

October 41,000 162,000

November 37,000 164,000

December 33,000 146,000

January 28,000 123,000

February 22,000 91,800

March 20,000 95,000

April 25,000 106,800

May 30,000 130,200

June 35,000 153,000

4. Compute the fixed overhead rate as follows: a. At the highest level:

Total cost $165,000 Less: variable portion [45,000 meals � $2.80 @] (126,000) Fixed portion of cost $ 39,000

b. At the lowest level Total cost $ 95,000 Less: variable portion [20,000 meals � $2.80 @] (56,000) Fixed portion of cost $ 39,000

c. Proof totals: $39,000 fixed portion at both levels

The manager should recognize that large or small dollar amounts can be adapted to this method. A second example concerns drug samples and their cost. In this example, a su- pervisor of marketing is concerned about the number of drug samples used by the various members of the marketing staff. She uses the high–low method to determine the portion of fixed cost. Table 7-5 contains the basic data required for the high–low computation. Using the formula previously described, the following steps are performed:

1. Find the highest volume of 1,000 samples at a cost of $5,000 (see Table 7-5) and the lowest volume of 750 samples at a cost of $4,200.

2. Compute the variable rate per sample as

No. of Samples Cost

Highest volume 1,000 $5,000 Lowest volume 750 4,200 Difference 250 $ 800

3. Divide the difference in cost ($800) by the difference in number of samples (250) to arrive at the variable cost rate:

$800 divided by 250 samples � $3.20 per sample

4. Compute the fixed overhead rate as follows: a. At the highest level:

Total cost $5,000 Less: variable portion [1,000 samples � $3.20 @] (3,200) Fixed portion of cost $1,800

b. At the lowest level Total cost $4,200

Analyzing Mixed Costs 67

Table 7–5 Number of Drug Samples and Cost for November

Rep. No. of Samples Cost

J. Smith 1,000 5,000 A. Jones 900 4,300 B. Baker 850 4,600 G. Black 975 4,500 T. Potter 875 4,750 D. Conner 750 4,200

68 CHAPTER 7 Cost Behavior and Break-Even Analysis

Less: variable portion [750 samples � $3.20 @] (2,400) Fixed portion of cost $1,800

c. Proof totals: $1,800 fixed portion at both levels

The high–low method is an approximation that is based on the relationship between the highest and the lowest levels, and the computation assumes a straight-line relationship. The advantage of this method is its convenience in the computation method.

CONTRIBUTION MARGIN, COST-VOLUME-PROFIT, AND PROFIT-VOLUME RATIOS

The manager should know how to analyze the relationship of cost, volume, and profit. This important information assists the manager in properly understanding and control- ling operations. The first step in such analysis is the computation of the contribution margin.

Contribution Margin

The contribution margin is calculated in this way:

% of Revenue

Revenues (net) $500,000 100% Less: variable cost (350,000) 70% Contribution margin $150,000 30% Less: fixed cost (120,000) Operating income $30,000

The contribution margin of $150,000 or 30 percent, in this example, represents variable cost deducted from net revenues. The answer represents the contribution margin, so called because it contributes to fixed costs and to profits.

The importance of dividing costs into fixed and variable becomes apparent now, for a contribution margin computation demands either fixed or variable cost classifications; no mixed costs are recognized in this calculation.

Cost-Volume-Profit (CVP) Ratio or Break Even

The break-even point is the point when the contribution margin (i.e., net revenues less variable costs) equals the fixed costs. When operations exceed this break-even point, an excess of revenues over expenses (income) is realized. But if operations does not reach the break-even point, there will be an excess of expenses over revenues, and a loss will be realized.

The manager must recognize there are two ways of expressing the break-even point: ei- ther by an amount per unit or as a percentage of net revenues. If the contribution margin

is expressed as a percentage of net revenues, it is often called the profit-volume (PV) ratio. A PV ratio example follows this cost-volume-profit (CVP) computation.

The CVP example is given in Figure 7-6. The data points for the chart come from the contribution margin as already computed:

% of Revenue

Revenues (net) $500,000 100% Less: variable cost (350,000) 70% Contribution margin $150,000 30% Less: fixed cost (120,000) Operating income $30,000

Three lines were first drawn to create the chart. They were total fixed costs of $120,000, total revenue of $500,000, and variable costs of $350,000. (All three are labeled on the chart.) The break-even point appears at the point where the total cost line intersects the revenue line. Because this point is indeed the break-even point, the organization will have no profit and no loss but will break even. The wedge shape to the left of the break-even point is potential net loss, whereas the narrower wedge to the right is potential net income (both are labeled on the chart).

Contribution Margin, Cost-Volume-Profit, and Profit-Volume Ratios 69

Figure 7–6 Cost-Volume-Profit (CVP) Chart for a Wellness Clinic. Courtesy of Resource Group, Ltd., Dallas, Texas.

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CVP charts allow a visual illustration of the relationships that is very effective for the manager.

Profit-Volume (PV) Ratio

Remember that the second method of expressing the break-even point is as a percentage of net revenues and that if the contribution margin is expressed as a percentage of net rev- enues, it is called the profit-volume (PV) ratio. Figure 7-7 illustrates the method. The basic data points used for the chart were as follows:

Revenue per visit $100.00) 100% Less variable cost per visit (70.00) 70% Contribution margin per visit $ 30.00 30% Fixed costs per period $120,000

$30.00 contribution margin per visit divided by $100 price per visit � 30% PV Ratio

On our chart, the profit pattern is illustrated by a line drawn from the beginning level of fixed costs to be recovered ($120,000 in our case). Another line has been drawn straight across the chart at the break-even point. When the diagonal line begins at $120,000, its in- tersection with the break-even or zero line is at $400,000 in revenue (see left-hand dotted line on chart). We can prove out the $120,000 versus $400,000 relationship as follows. Each dollar of revenue reduces the potential of loss by $0.30 (or 30% � $1.00). Fixed costs are fully recovered at a revenue level of $400,000, proved out as $120,000 divided by .30 = $400,000. This can be written as follows:

.30R � $120,000 R � $400,000 [120,000 divided by .30 = 400,000]

The PV chart is very effective in planning meetings because only two lines are necessary to show the effect of changes in volume. Both PV and CVP are useful when working with the effects of changes in break-even points and revenue volume assumptions.

Contribution margins are also useful for showing profitability in other ways. An example appears in Figure 7-8, which shows the profitability of various DRGs, using contribution margins as the measure of profitability. Case volume (the number of cases of each DRG) is on the vertical axis of the matrix, and the dollar amount of contribution margin is on the horizontal axis of the matrix.3

Scatter Graph Method

In performing a mixed-cost analysis, the manager is attempting to find the mixed cost’s av- erage rate of variability. The scatter graph method is more accurate than the high–low method previously described. It uses a graph to plot all points of data, rather than the high- est and lowest figures used by the high–low method. Generally, cost will be on the vertical

Contribution Margin, Cost-Volume-Profit, and Profit-Volume Ratios 71

Break-Even Point

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Figure 7–7 Profit-Volume (PV) Chart for a Wellness Clinic. Courtesy of Resource Group, Ltd., Dallas, Texas.

axis of the graph, and volume will be on the horizontal axis. All points are plotted, each point being placed where cost and volume intersect for that line item. A regression line is then fitted to the plotted points. The regression line basically represents the average—or a line of averages. The average total fixed cost is found at the point where the regression line intersects with the cost axis.

Two examples are examined. They match the high–low examples previously calculated. Figure 7-9 presents the cafeteria data. The costs for cafeteria meals have been plotted on the graph, and the regression line has been fitted to the plotted data points. The regression line strikes the cost axis at a certain point; that amount represents the fixed cost portion of the mixed cost. The balance (or the total less the fixed cost portion) represents the variable portion.

The second example also matches the high–low example previously calculated. Figure 7-10 presents the drug sample data. The costs for drug samples have been plotted on the graph, and the regression line has been fitted to the plotted data points. The regression line again strikes the cost axis at the point representing the fixed-cost portion of the mixed cost. The balance (the total less the fixed cost portion) represents the variable portion. Further discussions of this method can be found in Examples and Exercises at the back of this book.

The examples presented here have regression lines fitted visually. However, computer pro- grams are available that will place the regression line through statistical analysis as a function

72 CHAPTER 7 Cost Behavior and Break-Even Analysis

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Figure 7–8 Profitability Matrix for Various DRGs, Using Contribution Margins. Source: Adapted from S. Upda, Activity-Based Costing for Hospitals, Health Care Management Review, Vol. 21, No. 3, p. 85, © 1996, Aspen Publishers, Inc.

Contribution Margin, Cost-Volume-Profit, and Profit-Volume Ratios 73

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Figure 7–9 Employee Cafeteria Scatter Graph.

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Figure 7–10 Drug Sample Scatter Graph for November.

of the program. This method is called the least-squares method. Least squares means that the sum of the squares of the deviations from plotted points to regression line is smaller than would occur from any other way the line could be fitted to the data: in other words, it is the best fit. This method is, of course, more accurate than fitting the regression line visually.

74 CHAPTER 7 Cost Behavior and Break-Even Analysis

INFORMATION CHECKPOINT

What Is Needed? Revenues, variable cost, and fixed cost for a unit, division, DRG, etc.

Where Is It Found? In operating reports. How Is It Used? Use the multiple-step calculations in this chapter to com-

pute the CPV or the PV ratio; use to plan and control operations.

KEY TERMS

Break-Even Analysis Cost-Profit-Volume Contribution Margin Fixed Cost Mixed Cost Profit-Volume Ratio Semifixed Cost Semivariable Cost Variable Cost

DISCUSSION QUESTIONS

1. Have you seen reports in your workplace that set out the contribution margin? 2. Do you believe that contribution margins can help you manage in your present work?

In the future? How? 3. Have you encountered break-even analysis in your work? 4. If so, how was it used (or presented)? 5. How do you think you would use break-even analysis? 6. Do you believe your organization could use these analysis tools more often than is

now happening? What do you believe the benefits would be?