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Individual Fixed Costs, Variable Costs, and Break-Even Point |
Resource: Ch. 10 in Financial Management Complete Exercises 10.1 & 10.2 on pp. 146–47. Post your final answers as a Microsoft® Word attachment |
C H A P T E R
10 Differential Cost Analysis
This chapter deals with the use of differential cost analysis in financial manage-
ment decision making situations. The basic premise of differential cost analysis is
that different costs are treated differently in different financial management deci-
sion situations. Hence the name differential costs.
Two major applications of differential cost analysis are presented. The first
application is called break-even analysis. In break-even analysis, differential cost
analysis is used to answer the question, How much service must a human service
program provide during a fiscal year in order to recover its total costs? The second
application can be called decrease/discontinue decisions. In these types of financial
management decisions, differential cost analysis answers the question, What will
be the effect on fixed and variable costs of a decision to reduce or discontinue a
human service program?
Some Concepts and Definitions
Before proceeding to the discussion of the applications of differential cost analysis,
some basic concepts and definitions need to be introduced including fixed costs,
variable costs, step costs, maximum efficiency, and surplus capacity.
Fixed Costs and
Variable Costs
In Chapter 8 the concepts of direct and indirect costs were introduced as part of the
discussion of cost analysis. As was noted in Chapter 8, the full cost, or total cost, of
a human service program is the sum of its direct costs and indirect costs. In differ-
ential cost analysis, the full cost, or total cost, of a human service program is the
sum of its fixed costs and variable costs. Items of cost in the budget of a human ser-
vice program can also be classified as either fixed costs or variable costs. It is the
classification of costs as fixed and variable and the analysis of how these costs
behave, or differ, in various financial management decision situations that consti-
tutes the essence of differential cost analysis.
A fixed cost is any item of cost that does not vary with the amount of service
provided. Hence the name fixed cost. The salary of a cook in a congregate meals
132
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
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program is an example of a fixed cost. Figure 10.1 provides a graphic representa-
tion of why a cook’s salary is a fixed cost. The y-axis of the graph in the figure is the
cook’s monthly salary; the x-axis is meals per day. A meal is a commonly accepted
output (or unit of service) measure for a congregate meals program because it pro-
vides a readily understandable measure of service volume. As Figure 10.1 demon-
strates, the cook’s monthly salary ($2,500) does not vary depending on how many
meals per day the program provides. The line that expresses the relationship
between the cook’s monthly salary and meals per day is flat, meaning that no rela-
tionship exists. The congregate meals program can provide 25 meals per day, 10
0
meals per day, 150 meals per day, or any other number of meals per day between 0
and 150 and the cook’s monthly salary remains fixed at $2,500. The salaries of staff
working in human service programs are generally treated as fixed costs because
they do not vary depending on the amount of service provided. Other types of
costs that are generally considered to be fixed costs include rent, telephone, insur-
ance, and any other cost that is not affected, or does not vary, depending on how
much service a human service program provides.
A variable cost is any item of cost that varies with the amount of service pro-
vided. Hence the name variable cost. Food in a congregate meals program is an
example of a variable cost. Figure 10.2 is a graphic representation of the relation-
ship between the monthly food costs ( y-axis) and the number of meals per day (x-
axis). As the number of meals per day increases, so does the cost of food. Providing
100 meals per day requires more food and thus higher food costs than providing 25
meals per day. Types of costs that are generally treated as variable costs include
Differential Cost Analysis 133
FIGURE 10.1 A Graphic Display of a Cook’s Salary
as a Fixed Cost
$
3,000
$
2,
500
$
2,000
$1,500
$
1,000
$500
250 50 75 100 125 150
x -axis (Meals per Day
)
y
-a
xi
s
(C
o
o
k’
s
M
o
n
th
ly
S
a
la
ry
)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
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supplies in a homemaker or home health aid program (the more service that is pro-
vided, the more supplies that are used), gasoline in a specialized transportation
program (the more trips that are provided, the more gasoline that is used), and any
other item of cost in any other human service program that varies depending on
how much service is provided.
Step Costs
A third type of cost sometimes encountered in differential cost analysis is called a
step cost. A step cost is a fixed cost that remains fixed up to some point at which it
then increases in a stepwise fashion. Hence the name step costs. The concept of a
step cost is perhaps best explained by the use of an example. Let’s assume that the
cook in the congregate meals program is capable of preparing and serving up to
150 meals per day by himself. If the congregate meals program decides to provide
more than 150 meals per day, a second cook will need to be hired. At 150 meals per
day, the congregate meals program’s fixed costs for cooks would jump, or step up,
in a nonincremental fashion to a new level. This phenomenon is graphically illus-
trated in Figure 10.3. The cook’s monthly salary ($2,500) remains fixed until the
meals per day reaches 150. The exact amount of the new fixed costs will depend on
the status (full-time or part-time) of the new cook as well as the salary. If the con-
gregate meals program hires a second full-time cook at the same salary as the first
cook, then monthly fixed costs for cooks would jump, or step up, from $2,500 per
month to $5,000 per month.
134 C H A P T E R 1 0
FIGURE 10.2 A Graphic Display of Food Costs as a
Variable Cost
$
5,000
$2,500
$2,000
$3,500
$3,000
$
4,500
$
4,000
$1,500
$1,000
$500
250 50 75 100 125 150
x -axis (Meals per Day)
y
-a
xi
s
(C
o
o
k’
s
M
o
n
th
ly
S
a
la
ry
)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
Maximum Efficiency and Surplus Capacity
In the preceding congregate meals example, 150 meals per day is the maximum
number that one cook can prepare and serve. At 150 meals per day, one cook is
assumed to be working at maximum efficiency. If the congregate meals program
served only 50 meals a day, the cook would not be maximally efficient, because an
additional 100 meals per day could still be prepared and served without the con-
gregate meals program incurring any additional fixed costs for cooks. At 50 meals
per day, the congregate meals program has surplus capacity of 100 meals per day.
Surplus capacity is the difference between the current service capability of a staff
person, facility, or human service program and the point of maximum efficiency.
With the introduction of these concepts and definitions, the discussion can
now proceed to the first application of differential cost analysis.
Break-Even Analysis
The purpose of break-even analysis is to determine how much service a human
service program must provide during a fiscal year in order to generate revenues
sufficient to cover expenses. Thinking back to Chapter 7 dealing with budgets and
budgeting systems, one might well ask, Isn’t this type of financial information
readily available from a human service agency’s line-item, performance, and pro-
gram budgets? Well, not exactly. Budgets deal with estimation and monitoring of
Differential Cost Analysis 135
FIGURE 10.3 A Graphic Display of a New Cook’s
Salary as a Step Cost
$6,000
$2,500
$2,000
$3,500
$3,000
$4,500
$4,000
$5,500
$5,000
$1,500
$1,000
$500
250 50 75 100 125 100 150 175 250200
x -axis (Meals per Day)
y
-a
xi
s
(M
o
n
th
ly
S
a
la
ry
)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
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revenues and expenses during a fiscal year. Break-even analysis is used during the
planning and budgeting processes to estimate fixed costs and variable costs and to
determine the amount of service a human service program must provide in order
to reach the break-even point (BEP) given different price levels. Break-even analy-
sis is also used during the fiscal year to monitor actual service levels, actual fixed
costs, and actual variable costs as well as to periodically recompute the BEP.
In break-even analysis, and for purposes of computing the break-even point,
all expenses are divided into two categories (fixed costs and variable costs). Break-
even analysis determines the point during the fiscal year at which a human service
program will recover its fixed costs. The BEP is computed using the formula
shown in Figure 10.4.
The following two case examples demonstrate the use of break-even analy-
sis and the BEP formula. The first case example, the New River Community Coun-
cil, demonstrates the use of break-even analysis at the beginning of the fiscal year
as part of the planning and budgeting processes. The second case example, the
Westchester Home-Delivered Meals Program, demonstrates the use of break-even
analysis during the fiscal year to monitor service delivery, actual fixed costs,
actual variable costs, and the BEP.
New River Community Council Case Example
The New River Community Council (NRCC) is a 501(c)(3) private nonprofit orga-
nization that engages in human services planning and advocacy and also provides
financial and programmatic technical assistance to other local human service agen-
cies. The NRCC is planning to publish a newsletter that will keep local human ser-
vice agencies informed about state and community funding (contract and grant)
opportunities. Within the program structure of the NRCC, the newsletter will be
treated as a program and as both an expense center and a revenue center. As part
of the planning and budgeting processes, NRCC wants to determine the program’s
fixed costs, variable costs, and BEP. NRCC plans to hire a part-time (ten hours per
week) social work student to be the newsletter coordinator in charge of compiling
the contract and grant information and preparing, printing, and mailing the
newsletter. The salary of the newsletter coordinator (a fixed cost) will be $5,000 for
the year. The newsletter coordinator’s salary is a fixed cost because it does not vary
depending on the number of newsletters produced. The unit cost of printing and
136 C H A P T E R 1 0
FIGURE 10.4 The Break-Even Point (BEP) Formula
PX = A + BX
where P = Unit cost or price of the service
X = Amount of service to be provided (an unknown)
A = Fixed costs
B = Variable costs
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
mailing six bimonthly issues of the newsletter (the variable costs) is estimated at $4
per subscriber per year. The printing and mailing costs are variable costs because
they will vary depending on how many newsletters are printed and mailed. In
order to simplify this first case example, agency indirect (overhead) costs are
excluded.
The tentative price of the newsletter is set at $12 per year. The executive direc-
tor of NRCC uses this information and the BEP formula to compute the BEP (Table
10.1). Given the fixed costs ($5,000) and the variable costs ($4) involved and the
tentative subscription price of $12, the BEP is computed at 625 subscribers.
After some discussion, the executive director of NRCC decides that the BEP is
outside the feasible range. The feasible range is the number of potential break-even
points that represent viable solutions. Feasible range issues are most frequently
encountered with step costs, but they can be relevant to any type of break-even
analysis. The executive director believes that a BEP of 625 is outside the feasible
range because it is unreasonable to expect that the newsletter will be able to attract
this number of subscribers the first year. The executive director decides to recom-
pute the newsletter program’s BEP using higher subscription rates. Table 10.2
shows the revised BEPs based on annual subscription rates of $15 (Part A) and $20
(Part B), respectively. If the subscription rate is increased to $15, the BEP will be low-
ered to 454 subscribers. If the subscription rate is increased to $20, the BEP will be
lowered to 313 subscribers.
The executive director decides that 454 subscribers is a feasible target (a
potential BEP that is within the feasible range) for the newsletter’s first year; con-
sequently, the newsletter price is set at $15. Charging $15 for the newsletter repre-
sents only a small increase ($3) in price, but results in significantly reducing the
Differential Cost Analysis 137
TABLE 10.1 Computing the Break-Even Point for the New River Community Council
Newsletter Program
PX = A + BX
12X = 5,000 + 4X
(Subtract 4X from each side.)
8X = 5,000
(Divide each side by 8.)
X = 625 (BEP)
The proof of this solution is as follows:
Revenues
Expenses
$12(625) = $7,500 Fixed costs = $5,000 (coordinator’s salary)
Variable costs = 2,500 (variable costs)*
$7,500
*625 members @ $4.00 = $2,500
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
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number (–171) of subscribers needed to reach the BEP. Collectively, Tables 10.1 and
10.2 also demonstrate how price and the BEP are inversely related. The higher the
price, the lower the BEP. The lower the price, the higher the BEP.
Taking a more detailed look at Part A of Table 10.2, we can analyze exactly
what the BEP formula really does. In the formula PX = A + BX, when 4X (the vari-
able costs) is subtracted from both sides of the equation, the amount ($4) of the sell-
ing price ($15) that is needed to cover variable costs is removed from the
equation. What is left (11X) is the amount ($11) of the selling price ($15) that is
available to cover the program’s fixed costs ($5,000). This amount ($11) is referred
to as the unit contribution rate. The BEP formula then divides the fixed costs ($5,000)
by the unit contribution rate ($11) with the resulting BEP being 454.
At this point in the discussion of break-even analysis, mention should be
made of profitability analysis and marginal pricing.
Profitability Analysis and Marginal Pricing
How much profit will NRCC earn if 454 people subscribe to the newsletter? The
answer is none. At the BEP, a human service program will earn revenues sufficient
to cover its fixed and variable costs, but nothing more. How much profit will
NRCC earn if 455 people subscribe to the newsletter? As Table 10.3 demonstrates,
the answer is $11. Regardless of when during the fiscal year the BEP (454) is
reached, total program fixed costs for the entire fiscal year will be covered. At the
BEP, the variable cost, also called the marginal cost, of producing one more news-
138 C H A P T E R 1 0
TABLE 10.2 Revised Break-Even Points for the New River
Community Council Newsletter Program
Part A. Newsletter Subscription Price of $15
PX = A + BX
15X = 5,000 + 4X
(Subtract 4X from each side.)
11X = 5,000
(Divide each side by 11.)
X = 454 (BEP)
Part B. Newsletter Subscription Price of $20
PX = A + BX
20X = 5,000 + 4X
(Subtract 4X from each side.)
16X = 5,000
(Divide each side by 16.)
X = 313 (BEP)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
letter is only $4. Thus, between 454 newsletters and the point at which the newslet-
ter coordinator will be working at maximum efficiency and will need some staff
assistance, the newsletter program can earn a profit of $11 on each new subscrip-
tion. Given that it only costs $4 to produce each additional newsletter, when the
BEP (454) is reached, the NRCC might consider offering a special trial subscription
rate (50 percent off) to entice more individuals to subscribe. For example, if the
NRCC were to offer a special 50 percent discounted subscription rate of $7.50, it
would still earn a profit of $3.50 on each new subscription.
Pricing a product or service based on the marginal costs of production is
referred to as marginal pricing. The concept of marginal pricing is one of the reasons
that many government agencies prefer to contract with private nonprofit organi-
zations to provide some types of human service programs rather than providing
them directly. Take the case of child day care services. If a government human ser-
vice agency were to directly operate a child day cay facility, its costs would include
both fixed costs and variable costs. But if an already existing child day care facility
operated by a private nonprofit organization has surplus capacity, then the gov-
ernment human service agency might be able to purchase a portion or all of the
surplus capacity on a marginal cost basis. Such situations are win–win for both
parties. The government human service agency does not have to pay the full cost
of care (fixed costs plus variable costs), whereas the private nonprofit agency can
sell its surplus capacity (for variable costs plus perhaps a small profit), thereby
generating additional revenues.
Westchester Home-Delivered
Meals (WHDM) Program
The Westchester Home-Delivered Meals (WHDM) program provides one hot
nutritious meal five days per week to elderly clients residing in their own homes.
During the planning and budgeting processes, the program director estimates that
total program costs for the fiscal year will be $260,000 consisting of $95,000 in fixed
costs (a cook’s salary, equipment rental, and agency indirect or overhead costs) and
$165,000 in variable costs (food, supplies, and disposable food containers, paper
cups, and so on plus delivery costs). Note that in this case example, agency indirect
costs are included.
Differential Cost Analysis 139
TABLE 10.3 New River Community Council
Profitability Analysis with 455 Newsletter Subscribers
Selling price = $15.00
Variable costs = – 4.00
$11.00 (profit)
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The program director estimates that the home-delivered meals program can
provide about 45,000 meals during the fiscal year. Dividing the variable costs
($165,000) by the total estimated number (45,000) of meals to be provided, the vari-
able cost per meal is estimated at $3.66. Using the BEP formula, but solving for
price rather than BEP (Table 10.4), the program director estimates the total, or full,
cost per meal for the fiscal year will be $5.77. Based on this analysis, the executive
director enters into a “performance contract” (see Chapter 12) with the City of
Westchester to have the WHDM program provide 45,000 meals during the coming
fiscal year at a unit cost of $5.77 per meal.
Four months into the fiscal year, the program director decides to conduct a
break-even analysis in order to compare the estimated fixed costs, variable costs,
and BEP with the actual fixed costs, variable costs, and BEP year-to-date. The pro-
gram director is particularly interested in the program’s variable costs because the
prices of some foods (fresh fruits and vegetables) have declined slightly during the
first four months of the fiscal year. A decrease in food prices may mean that the
home-delivered meals program’s actual BEP will be lower than the estimated BEP.
Table 10.5 presents the home-delivered meals program’s service and cost data for
the first four months of the fiscal year.
In computing fixed costs, variable costs, and the BEP, the program director
could collect the financial information from the agency’s accounting records.
Instead, the program director decides to the use the high–low method for comput-
ing the program’s break-even point. Computing the BEP using the high–low
method can be done by hand without the aid of a computer. As its name suggests,
in the high–low method, the time periods with the highest and lowest amounts of
service provision (service volume) are selected. In Table 10.5, July is the time
period with the lowest amount of service provision (3,500 meals) and October is
the time period with the highest (4,600). Using data from the high and low time
periods, the program director computes fixed costs, variable costs, and the BEP
using the following steps:
Step 1. The difference in service volume between the high and low time periods
is computed. The resulting figure is 1,100 meals (4,600 – 3,500).
140 C H A P T E R 1 0
TABLE 10.4 Westchester Home-Delivered Meals Program
Computing Price Using the Break-Even Point Formula
PX = A + BX
P (45,000) = 95,000 + 3.66 (45,000)
P (45,000) = 95,000 + 164,700
P (45,000) = 259,700
(Divide each side by 45,000.)
P = $5.77 (price or cost per meal)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
Step 2. The difference in costs between the high and low time periods is com-
puted. The resulting figure is $4,000 ($24,500 – $20,500).
Step 3. The variable cost per meal is computed. The cost difference ($4,000) com-
puted in Step 2 is divided by the difference (1,100) in service volume computed in
Step 1. The resulting figure is $3.64. This figure is the variable cost per unit of ser-
vice (one meal). The logic here is quite simple: Since fixed costs do not vary, the
only costs that can vary between the high and low time periods are the variable
costs.
Step 4. Total variable costs are computed for the low time period. However, the
computations work the same for either the high or the low time period. In the low
time period, the service volume (the number of meals provided) is 3,500. Service
volume is multiplied by the variable costs per meal ($3.64). The resulting figure is
$12,740. This figure is the amount of variable costs for the low month.
Step 5. Total fixed costs are computed for the low time period. The total program
costs in the low month are $20,500. If the variable costs ($12,740) are subtracted
from the total costs ($20,500), the remainder ($7,760) is the amount of the fixed
costs. Again, the logic is straightforward. Since there are only two types of costs
(fixed and variable), if one knows the total costs and the variable costs, one knows
the fixed costs.
Step 6. The break-even point is computed using the BEP formula and the data
generated in Steps 1 through 5 plus one additional piece of information. The addi-
tional piece of information needed to compute the BEP is the service price. The ser-
vice price is $5.77, which is the contract price between the WHDM program and
the City of Westchester. As Table 10.6 shows, when the computations are per-
formed, the resulting BEP is 3,643 meals. This figure, however, is a monthly figure
based on monthly data so the program director must annualize the data to get the
BEP for the fiscal year:
3,643 meals per month × 12 months = 43,716 meals
Differential Cost Analysis 141
TABLE 10.5 Westchester Home-Delivered Meals Program
Service and Cost Data (July 1, 20X1–October 31, 20X1)
Month
July
August
September
October
Meals
Served
3,500
4,000
4,200
4,600
Total
Costs
$
20,500
22,600
23,350
24,500
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
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The high–low method computes the actual BEP for the home-delivered meals
program at 43,716 meals. At 43,716 meals, the home-delivered meals program will
recover its fixed costs for the fiscal year. Assuming that the WHDM program com-
pletes its 45,000 meals contract with the City of Westchester, a small profit will be
earned. For each meal provided above the break-even point (43,716), the home-
delivered meals program will incur variable costs of $3.64 per meal, but will earn
revenues of $5.77 per meal. The difference between the variable cost per meal and
the revenue per meal is $2.13 per meal. The difference between contracted meals
(45,000) and the BEP (43,716) is 1,284. The potential profit is $2,735 (1,284 meals ×
$2.13). Of course, variable costs will continue to vary during the remaining eight
months of the fiscal year, so the program director will want to continue monitoring
them and will also want to conduct additional break-even analyses during the fis-
cal year.
The preceding case examples demonstrate two principal uses of break-even
analysis: (1) to estimate a human service program’s fixed costs, variable costs, and
BEP as part of the planning and budgeting processes and (2) to monitor a human
service program’s fixed costs, variable costs, and the BEP during the fiscal year.
The discussion of differential cost analysis now shifts to decrease/discontinue
decisions.
Decrease / Discontinue Decisions
From time to time, human service administrators are unfortunately confronted
with decisions to decrease, and sometimes even to discontinue, a human service
program. In these types of financial management decision situations, differential
cost analysis is again used to determine the effect on a human service agency’s
fixed and variable costs. To demonstrate the use of differential cost analysis in
decrease/discontinue decisions, the Phoenix Specialized Transportation Services
(STS) case study introduced in Chapter 3 will again be used.
142 C H A P T E R 1 0
TABLE 10.6 Westchester Home-Delivered Meals Program
Computing the Break-Even Point
Using the High–Low Method
PX = A + BX
5.77X = 7,760 + 3.64X
(Subtract 3.64X from each side.)
2.13X = 7,760
(Divide each side by 2.13.)
X = 3,643 (monthly BEP)
3,643 × 12 = 43,716 (fiscal-year BEP)
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
The Phoenix STS operates two programs: a transportation program and an
escort program. In the just completed fiscal year 20XX, Phoenix STS had com-
bined program expenses of $515,000. The Phoenix STS has three operating
regions: Central Phoenix, East Valley, and West Valley. The Phoenix STS annually
receives a $100,000 grant from the East Valley Coalition, a business group, to sup-
port the transportation program in the East Valley. The East Valley Coalition has
just informed the program manager of Phoenix STS that this coming fiscal year
may be the last time that it will be able to provide the $100,000 grant. The program
manager decides that she needs to quickly compute the overall financial implica-
tions of a loss of $100,000 on the East Valley transportation operation, the trans-
portation program as a whole, and the Phoenix STS as a whole. The program
manger decides to conduct a differential cost analysis focusing on reducing, or
actually discontinuing, the STS program in the East Valley. The first action the
program manager takes is to review the Statement of Functional Expenses for the
last fiscal year (Table 10.7).
Differential Cost Analysis 143
TABLE 10.7 Phoenix Specialized Transportation Services
Statement of Functional Expenses
January 1, 20XX–December 31, 20XX
Salaries
Fringe benefits
Rent
Utilities
Telephone
Supplies
Vehicle
maintenance
Vehicle
depreciation
Escort
reimbursement
Other
Total expenses
Transportation
Program
$195,000
31,200
15,000
2,700
3,000
2,500
26,000
4
8,000
0
20,500
$343,900
Escort
Program
$20,000
3,200
2,000
300
1,000
500
0
0
5,000
2,100
$34,100
Total
Program
215,000
34,400
17,000
3,000
4,000
3,000
26,000
48,000
5,000
22,600
$378,000
Management
and General
$62,000
9,900
3,000
1,000
2,000
1,000
0
0
0
11,500
$90,400
Fund-
Raising
32,000
5,100
2,000
500
2,000
1,000
0
0
0
4,000
$46,600
Total
Expenses
309,000
49,400
22,000
4,500
8,000
5,000
26,000
48,000
5,000
38,100
$515,000
Note: This table also appears as Table 3.4 in Chapter 3.
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Working from the financial information in Table 10.7, the program manager
first computes the financial expense data for only the transportation program,
excluding the escort program. Then, the program manager further separates the
financial data by the three regions served by Phoenix STS. The resulting financial
data are presented in Table 10.8. As Table 10.8 illustrates, during the past fiscal
year, the East Valley operations had total expenses of $93,380.
Next, the program manager determines those line-item expenses of the East
Valley operations that constitute fixed costs and those that constitute variable costs
(Table 10.9). The $93,380 in expenses incurred in providing transportation services
to the East Valley in the past fiscal year totaled $60,040 in variable costs and
$33,340
in fixed costs. If the Phoenix STS discontinues its East Valley operations, $60,040 in
variable costs would no longer be incurred, but the $33,340 in fixed costs (indirect,
or overhead, costs) would still continue to be incurred. This latter point needs clar-
ification. Agency indirect or overhead costs (e.g., the agency executive director’s
salary, rent, and utilities for the agency’s offices) will not suddenly go away. Such
costs will still be incurred. Perhaps over time some cutbacks or cost reductions can
be made, but for purposes of differential cost analysis, indirect costs are usually
treated as fixed costs.
The loss of the $100,000 grant would mean that Phoenix STS would not only
have to discontinue providing all service in the East Valley, but it would also have
to either (a) reduce its fixed costs by $33,340 or (b) find alternative sources of rev-
enue in the same amount. Based on this analysis, the program manager concludes
that Phoenix STS is confronted with a financial crisis. The program manager briefs
144 C H A P T E R 1 0
TABLE 10.8 Phoenix STS Transportation Expenses
for Fiscal Year 20XX by Region
Expense Categories
Salaries
Fringe benefits
Rent
Utilities
Telephone
Supplies
Vehicle maintenance
Vehicle depreciation
Other
Management and general
Fund-raising
Totals
West Valley
$39,000
6,240
3,000
540
600
500
5,200
9,600
4,100
16,200
8,400
$93,380
Central
Phoenix
$117,000
18,720
9,000
1,620
1,800
1,500
15,600
28,800
12,300
48,600
25,200
$280,140
East
Valley
$39,000
6,240
3,000
540
600
500
5,200
9,600
4,100
16,200
8,400
$93,380
Totals
$195,000
31,200
15,000
2,700
3,000
2,500
26,000
48,000
20,500
81,000
42,000
$466,900
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
the executive director on the results of her analysis. The executive director calls an
emergency meeting of the agency’s board of directors.
The Phoenix STS case example demonstrates several points. First, when the
service levels of human service programs are reduced, variable costs are also
reduced. Second, when a human service program is discontinued altogether, the
program’s variable costs are eliminated altogether. Third, when the service levels
of a human service program are reduced, or when a human service program is dis-
continued altogether, the program’s fixed costs may or may not be reduced.
Fourth, at least some portion of a program’s fixed costs will consist of agency indi-
rect costs that generally will not be reduced. Fifth, the loss of revenue associated
with the reduction of a human service program’s service levels, or with the dis-
continuance of a human service program altogether, affects not just the program
but the overall agency as well.
Summary
This chapter has introduced the concepts of fixed costs, variable costs, and differ-
ential cost analysis. Two examples of differential cost analysis were demonstrated
(break-even analysis and decrease/discontinue decisions) using three human ser-
vice case examples. As a general rule, differential cost analysis is an appropriate
financial management tool for use by human service administrators in alternative
choice situations. The consideration of fixed and variable costs is also an important
consideration in pricing, the topic of the next chapter.
TABLE 10.9 Phoenix STS East Valley Transportation Expenses
for Fiscal Year 20XX by Fixed and Variable Costs
Expense Categories
Salaries
Fringe benefits
Rent
Utilities
Telephone
Supplies
Vehicle maintenance
Vehicle depreciation
Other
Management and general
Fund-raising
Totals
Total Expenses
$39,000
6,240
3,000
540
600
500
5,200
9,600
4,100
16,200
8,400
$93,380
Fixed Costs
$ 3,000
540
600
500
4,100
16,200
8,400
$33,340
Variable Costs
$39,000
6,240
5,200
9,600
$60,040
Differential Cost Analysis 145
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E X E R C I S E S
Exercise 10.1
During the sixth month of the fiscal year, the program director of the Westchester
Home-Delivered Meals (WHDM) program decides to again recompute fixed costs,
variable costs, and the BEP using the high–low method. Here are the number of
meals served and the total costs of the program for each of the first six months:
Month Meals Served Total Costs
July 3,500 $20,500
August 4,000 22,600
September 4,200 23,350
October 4,600 24,500
November 4,700 25,000
December 4,900 26,000
Recompute fixed costs, variable costs, and the BEP. What are the variable
costs? What are the fixed costs? How many meals will the WHDM program need
to provide during the fiscal year to reach the BEP? How much profit will the pro-
gram earn if it completes its 45,000-meal contract with the City of Westchester?
Exercise 10.2
It has been two years since the New River Community Council (NRCC) started its
newsletter dealing with state and community funding opportunities for human ser-
vice agencies. The current number of subscribers to the newsletter is 525. During the
second year, the NRCC hired a new part-time newsletter coordinator (social work
student). The NRCC has raised the salary of the part-time newsletter coordinator to
$6,000 per year and has also hired another part-time student as an assistant for ten
hours a week. The assistant is to be paid $75 per week or $3,900 per year. Together
the newsletter coordinator and the part-time assistant believe they can handle up to
650 newsletter subscribers. Beyond this number, the newsletter program will
require still more staff resources. In order to help cover the cost of the new part-time
assistant, the executive director has also decided to increase the annual subscription
price of the newsletter to $20. Additionally, the variable costs of preparing, printing,
and mailing six bimonthly issues of the newsletter have risen to $4.50.
Recompute the BEP for the newsletter program. What is the new BEP? Is the
new BEP a feasible solution? Why or why not? Will any slack capacity exist? If so,
how much? If not, why not?
Exercise 10.3
The Mountain View Senior Adult Program (MVSAP) is interested in starting a vis-
iting nurse program. The program would use licensed practical nurses to make
146 C H A P T E R 1 0
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
home visits once a week to full-pay clients in the community. The MVSAP will
treat the visiting nurse program as a profit center. If the visiting nurse program is
successful and profitable, the profits will be used to expand the program to partial-
pay and no-pay clients during the second year of operation. The executive director
is not sure how best to implement the program. She has two major alternatives.
The first alternative is to hire a small number of nurses and make them full-time
employees. The second alternative is to contract with several nurses who would be
interested in working part-time. To help in thinking through this financial man-
agement decision situation, the executive director decides to compute a series of
BEPs based on contracting for the service and based on hiring one, two, and three
full-time nurses.
The executive director makes the following assumptions about the new visit-
ing nurse program:
■ The price of the service will be set at $65 per visit.
■ One full-time nurse position can provide a maximum of 120 one-hour visits
per month.
■ If the service is contracted, the agency plans to pay the contract nurses at the
rate of $45 per visit including the cost of supplies.
■ If the agency hires the nurses, the monthly salary will be $4,000 and the
agency plans on spending an average of $10 per client per visit for supplies.
■ Regardless of the method of service delivery (direct or contract) and regard-
less of the number of nurses hired, the agency plans to charge (allocate)
$4,000 per month in indirect costs to the visiting nurse program.
Compute four annualized BEPs assuming the following: (1) the service is
contracted, (2) one full-time nurse is hired, (3) two full-time nurses are hired, and
(4) three full-time nurses are hired. What are the four BEPs? Why do these BEPs
differ? Are all of these BEPs feasible solutions? If you were the executive director of
the Mountain View Senior Adult Program, what method of service delivery (direct
or contract) would you use? Why?
Exercise 10.4
Two years have passed since the Phoenix STS program faced the loss of funding
for its East Valley operations. During the two years, Phoenix STS has attempted to
broaden the funding base of the entire program, but with particular emphasis on
the East Valley service area. The program manager has just received an end of the
accompanying fiscal year financial report showing revenues and expenses for the
three transportation service areas. The report shows that overall the transporta-
tion program made a profit (had an excess of revenues over expenses) for the fis-
cal year. But for its East Valley operations, the transportation program had a loss.
Based upon the financial report, the program manager decides to recommend
discontinuing transportation services in the East Valley service area. Is this a good
financial management decision? Why? Why not?
Differential Cost Analysis 147
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Phoenix STS Transportation Services
Fiscal Year 20X1
Revenue and Expense Report by Region
148 C H A P T E R 1 0
Revenues
Expenses
1. Management
and general
2. Fund-raising
3. Program
Profit (or loss)
West
Valley
$110,000
20,000
10,000
75,000
$ 5,000
Central
Phoenix
$370,000
60,000
32,000
250,000
$ 28,000
East
Valley
$90,000
20,000
10,000
75,000
($15,000)
Total
$570,000
100,000
52,000
400,000
$ 18,000
Financial Management for Human Service Administrators, by Lawrence L. Martin. Copyright © 2001 by Allyn and Bacon, a Pearson Education Company.
ISBN
: 0-536 -12114-1
