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Complete Part I: Time Value of Money worksheet by defining the time value of money. Include a real-world example that illustrates the concept. Answer the questions:
·
Why is time such an important factor in financial matters?
· How might you use the principles of the time value of money to your financial benefit?
Complete Part II by calculating the present value, internal rate of return, and payback period depicted in the worksheet.
Post assignment as an attachment. Chapters included (IF NEEDED)
Time Value of Money
HCA/270 Version 3
1
Associate Level Material
Time Value of Money
Resource: Ch. 12, 12-A, & 12-C of Health Care Finance
Part I: Complete the following table by inserting your responses to the questions. Cite any sources you use.
|
Define the time value of money. |
|
Provide a real-world example for the time value of money. |
|
Why is time such an important factor in financial matters? |
|
How would you use the time value of money to your financial benefit? |
Part II: Complete the following table by calculating the ratios.
Present Value
|
Amount |
Compounding period |
Rate of interest |
Present value |
|
|
$100,000 |
Annual |
6% for 10 years |
||
|
$70,000 |
4% for 15 years |
Internal Rate of Return
|
Initial cost of investment |
Periods of useful life |
Estimated annual net cash inflow generated |
Look-up table value |
|
$75,000 |
10 |
$10,190 |
|
|
$56,000 |
6 |
$12,115 |
Payback Period: Assume there are no income taxes for both scenarios.
|
Purchase price of equipment |
Period of useful life |
Annual revenue generated per year |
Operating costs associated with revenue |
Depreciation expense per year |
Payback period result |
|
$550,000 |
10 years |
$32,000 |
$55,000 |
||
|
$350,000 |
$80,500 |
$36,000 |
$35,000 |
P A R T
Too l s t o A n a l y z e
& Understand
Financial
Operations
III
59
Cost Behavior and
B re a k – E v e n
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 co
st
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:
60 CHAPTER 7 Cost Behavior and Break-Even Analysis
0
1000
2000
3000
4000
5000
0 10 20 30 40 50 60
Number of Residents
To
ta
l M
o
n
th
ly
F
ix
e
d
C
o
st
Figure 7–1 Fixed Costs—Jones Group Home.
0
1000
2000
3000
4000
0 10 20 30 40 50 60
Number of Residents
To
ta
l M
o
n
th
ly
V
a
ri
a
b
le
C
o
st
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
0
3000
6000
9000
12000
0 10 20 30 40 50 60
Number of Residents
To
ta
l S
e
m
iv
a
ri
a
b
le
C
o
st
Figure 7–3 Semivariable Cost—Jones Group Home.
62 CHAPTER 7 Cost Behavior and Break-Even Analysis
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-
0
100
200
300
400
0 10 20 30 40 50 60
Number of Residents
F
ix
e
d
C
o
st
p
e
r
R
e
si
d
e
n
t
Fixed Cost per Resident
0
1000
2000
3000
4000
5000
0 10 20 30 40 50 60
Number of Residents
To
ta
l M
o
n
th
ly
F
ix
e
d
C
o
st
Total Monthly Fixed Cost
Figure 7–4 Two Views of Fixed Costs.
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
0 10 20 30 40 50 60
Number of Residents
V
a
ri
a
b
le
C
o
st
p
e
r
R
e
si
d
e
n
t
Variable Cost per Resident
0
10000
20000
30000
40000
0 10 20 30 40 50 60
Number of Residents
To
ta
l M
o
n
th
ly
V
a
ri
a
b
le
C
o
st
Total Monthly Variable Cost
0
200
400
600
800
Figure 7–5 Two Views of Variable Costs.
64 CHAPTER 7 Cost Behavior and Break-Even Analysis
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 �
$2.80 per meal
Table 7–4 Employee Cafeteria Number of Meals
and Cost by Month
No. of Employee
Month Meals Cafeteria Cost
($)
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 4,7
50
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.
0
100
200
300
400
$500
0 1000 2000 3000 4000 5000
Variable Cost
Line
Fixed Cost
Line
Break-Even
Point
Revenue
Line
Net
Operating
Income
Net
Loss
F
ix
e
d
C
o
s
ts
V
a
ri
a
b
le
C
o
s
ts
Number of Visits
R
e
ve
n
u
e
(
in
t
h
o
u
sa
n
d
s)
70 CHAPTER 7 Cost Behavior and Break-Even Analysis
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
+100
+90
+80
+70
+60
+50
+40
+30
+20
+10
0
–10
–20
–30
–40
–50
–60
–70
–80
–90
–100
–
110
–120
–130
–140
–
150
+100
+90
+80
+70
+60
+50
+40
+30
+20
+10
0
–10
–20
–30
–40
–50
–60
–70
–80
–90
–100
–110
–120
–130
–140
–150
N
e
t
L
o
s
s
(u
n
d
e
r
b
re
a
k-
e
ve
n
)
N
e
t
In
c
o
m
e
(o
ve
r
b
re
a
k-
e
ve
n
)
Net
Income
Net Loss
(due to
unrecovered
fixed costs)
Safety
Cushion
(before
break-even)
0 100 200 300 400 500 600 700
Revenue (in thousands of dollars)
Fixed Costs
Recovered
Projected
Revenues
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
400
350
300
250
200
150
100
50
0
$0 $1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000
Contribution Margin per Case
C
a
se
V
o
lu
m
e
112
113
121
106
114
127
107
108
110
105
104 103
111
116
124
120
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
195
185
175
165
155
145
135
125
115
105
95
85
20,000 30,000 40,000 50,000
Volume
(Number of Meals)
C
o
st
T
h
o
u
sa
n
d
s
Figure 7–9 Employee Cafeteria Scatter Graph.
$5,250
$5,000
$4,750
$4,500
$4,250
$4,000
$3,750
$3,500
$3,250
$3,000
500 600 700 800 900 1000 1100
Volume
(Samples)
C
o
st
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?
123
The Time Value
o f M o n e y 12
C H A P T E R
PURPOSE
The purpose of these computations is to evaluate the use
of money. The manager has many options as to where re-
sources of the organization should be spent.1 These cal-
culations provide guides to assist in evaluating the
alternatives.
UNADJUSTED RATE OF RETURN
The unadjusted rate of return is a relatively unsophisti-
cated return-on-investment method, and the answer is
only an estimate, containing no precision. The computa-
tion of the unadjusted rate of return is as follows:
Average Annual Net Income
� Rate of Return
Original Investment Amount
OR
Average Annual Net Income
� Rate of Return
Average Investment Amount
The original investment amount is a matter of record.
The average investment amount is arrived at by taking
the total unrecovered asset cost at the beginning of esti-
mated useful life plus the unrecovered asset cost at the
end of estimated useful life and dividing by two. This
method has the advantage of accommodating whatever
depreciation method has been chosen by the organiza-
tion. This method is sometimes called the accountant’s
method because information necessary for the computa-
tion is obtained from the financial statements.
After completing this chapter,
you should be able to
1. Compute an unadjusted rate of
return.
2. Understand how to use a
present-value table.
3. Compute an internal rate of
return.
4. Understand the payback period
theory.
P r o g r e s s N o t e s
124 CHAPTER 12 The Time Value of Money
PRESENT-VALUE ANALYSIS
The concept of present-value analysis is based on the time value of money. Inherent in this
concept is the fact that the value of a dollar today is more than the value of a dollar in the
future: thus the “present value” terminology. Furthermore, the further in the future the re-
ceipt of your dollar occurs, the less it is worth. Think of a dollar bill dwindling in size more
and more as its receipt stretches further and further into the future. This is the concept of
present-value analysis.
We learned about compound interest in math class. We learned that
$500 invested at the beginning of year 1
.05 earns interest (assumed) at a rate of 5% for one year,
$525 and we have a compound amount at the end of year 1 amounting to $525,
.05 which earns interest (assumed) at the rate of 5% for another year,
$551 and we have a compound amount at the end of year 2 amounting to $551
(rounded), and so on.
Using this concept, it is possible to restate the present values of $1 to be paid out or re-
ceived at the end of each of these years. It is possible to use equations, but that is not neces-
sary because we have present value tables (also called “look-up tables,” because one can
“look-up” the answer). A present value table is included at the end of this chapter in
Appendix 12-A. All of the figures on the present value table represent the value of a dollar.
The interest rate available on this version of the table is on the horizontal columns and
ranges from 1% to 50%. The number of years in the period is on the vertical; in this version
of the table, the number of years ranges from 1 to 30. To look up a present value, find the
column for the proper interest. Then find the line for the proper number of years. Then
trace down the interest column and across the number-of-years line item. The point where
the two lines meet is the number (or factor) that represents the value of $1 according to
your assumptions. For example, find the year 10 by reading down the left-hand column la-
beled “Year.” Then read across that line until you find the column labeled “10%.” The point
where the two lines meet is found to be 0.3855. The present value of $1 under these as-
sumptions (10 year/10%) is about 38.5 cents (shown as 0.3855 on the table).
Besides using the look-up table, you can also compute this factor on a business analyst
calculator. A reference to business analyst calculators is contained in Appendix B at the
back of this book. Besides using either the look-up table or the business calculator, you can
use a function on your computer spreadsheet to produce the factor. The important point is
this: no matter which method you use, you should get the same answer.
Now that you have the present value of $1, by whichever method, it is simple to find the
present value of any other number. You merely multiply the other number by the factor you
found on the table—or in the calculator or the computer. Say, for example, you want to find
the present value of $8,000 under the assumption used above (10 years/10%). You simply
multiply $8,000 by the factor of 0.3855 you found in the table. The present value of $8,000
is $3,084 (or $8,000 times 0.3855).
A compound interest table is also included at the end of this chapter in Appendix 12-B,
along with a table showing the present value of an annuity of $1.00 in Appendix 12-C, so
that you have the tools for computation at your disposal.
INTERNAL RATE OF RETURN
The internal rate of return (IRR) is another return on investment method. It uses a dis-
counted cash flow technique. The internal rate of return is the rate of interest that dis-
counts future net inflows (from the proposed investment) down to the amount invested.
The return for a particular investment can therefore be known. The IRR recognizes the el-
ements contained in the previous two methods discussed, but it goes further. It also recog-
nizes the time pattern in which the earnings occur. This means more precision in the
computation because IRR calculates from period to period, whereas the other two methods
rely on an average investment.
The IRR computation is not very complicated. The computation requires two assump-
tions and three steps to compute. Assumption 1: find the initial cost of the investment. As-
sumption 2: find the estimated annual net cash inflow the investment will generate.
Assumption 3: find the useful life of the asset (generally expressed in number of years,
known as periods for this computation). Step 1: Divide the initial cost of the investment (as-
sumption 1) by the estimated annual net cash inflow it will generate (assumption 2). The
answer is a ratio. Step 2: Now use the look-up table. Find the number of periods (assump-
tion 3). Step 3: Look across the line for the number of periods and find the column that
approximates the ratio computed in Step 1. That column contains the interest rate repre-
senting the rate of return.
How is IRR used? It can take the rate of return obtained and restate it. The restated fig-
ure represents the maximum rate of interest that can be paid for capital over the entire
span of the investment without incurring a loss. (You can think of that restated figure as a
kind of break-even point for investment purposes.) The fact that a rate of return can be
computed is the benefit of using an IRR method.
PAYBACK PERIOD
The payback period is the length of time required for the cash coming in from an invest-
ment to equal the amount of cash originally spent when the investment was acquired. In
other words, if we invested $1,000, under a particular set of assumptions, how long would it
take to get our $1,000 back? The payback period concept is used extensively in evaluating
whether to invest in plant and/or equipment. In that case, the question can be restated as
follows: If we invested $1,200,000 in a magnetic resonance imaging machine, under a par-
ticular set of assumptions, how long would it take to get the hospital’s $1,200,000 back?
The assumptions are key to the computation of the payback period. In the case of equip-
ment, volume of usage is a critical assumption and is sometimes very difficult to predict.
Therefore, it is prudent to run more than one payback period computation based on differ-
ent circumstances. Generally a “best case” and a “worst case” run are made.
The computation itself is simple, although it has multiple steps. The trick is to break it
into segments.
For example, Doctor Green is considering the purchase of a machine for his office
laboratory. It will cost $300,000. He wants to find the payback period for this piece of equip-
ment. To begin, Dr. Green needs to make the following assumptions: Assumption 1: Pur-
chase price of the equipment. Assumption 2: Useful life of the equipment. Assumption 3:
Payback Period
125
126 CHAPTER 12 The Time Value of Money
Revenue the machine will generate per year. Assumption 4: Direct operating costs associ-
ated with earning the revenue. Assumption 5: Depreciation expense per year (computed as
purchase price per assumption 1 divided by useful life per assumption 2).
Dr. Green’s five assumptions are as follows:
1. Purchase price of equipment � $300,000
2. Useful life of the equipment � 10 years
3. Revenue the machine will generate per year � $10,000 after taxes
4. Direct operating costs associated with earning the revenue � $150,000
5. Depreciation expense per year � $30,000
Now that the assumptions are in place, the payback period computation can be made. It
is in three steps, as follows:
Step 1: Find the machine’s expected net income after taxes:
Revenue (assumption #3) $200,000
Less
Direct operating costs
(assumption 4) $150,000
Depreciation
(assumption 5) 30,000
180,000
Net income before taxes $20,000
Less income taxes of 50% 10,000
Net income after taxes $10,000
Step 2: Find the net annual cash inflow after taxes the machine is expected to generate (in
other words, convert the net income to a cash basis):
Net income after taxes $10,000
Add back depreciation (a noncash expenditure) 30,000
Annual net cash inflow after taxes $40,000
Step 3: Compute the payback period:
Investment: $300,000 Machine Cost*
� 7.5 year
Net Annual $40,000**
Cash Flow
after Taxes:
*assumption 1 above
**per step 2 above
The machine will pay back its investment under these assumptions in 7.5 years.
Payback period computations are very common when equipment purchases are being
evaluated. The evaluation process itself is the final subject we consider in this chapter.
Payback Period
EVALUATIONS
Evaluating the use of resources in healthcare organizations is an important task. There are
never enough resources to go around, and it is important to use an objective process to eval-
uate which investments will be made by the organization. A uniform use of a chosen
method of evaluating return on investment and/or payback period makes the evaluation
process more manageable.
It is important to choose a method that is understood by the managers who will be using
it. It is equally important to choose a method that can be readily calculated. If a multiple-
page worksheet has to be constructed to set up the assumptions for a modestly priced piece
of equipment, the evaluation method is probably too complex. This comment actually
touches on the cost-benefit of performing the evaluation.
Sometimes a computer program is chosen that performs a uniform computation of in-
vestment returns and payback periods. Such a program is a suitable choice if the managers
who use it understand the printouts it produces. Understanding both input and output is
key for the managers. In summary, evaluations should be objective, the process should not
be too cumbersome, and the responsible managers should understand how the computa-
tion was achieved.
INFORMATION CHECKPOINT
What Is Needed? Information sufficient to perform these calculations.
Where Is It Found? In the files of your supervisor; also in the office of the finan-
cial analyst; probably also in the strategic planning of-
fice.
How Is It Used? To measure the time value of money
KEY TERMS
Internal Rate of Return
Payback Period
Present Value Analysis
Time Value of Money
Unadjusted Rate of Return
DISCUSSION QUESTIONS
1. Can you compute an unadjusted rate of return now? Would you use it? Why?
2. Are you able to use the present-value look-up table now? Would you prefer a com-
puter to compute it?
Discussion Questions 127
128 CHAPTER 12 The Time Value of Money
3. Have you seen the payback period concept used in your workplace? If not, do you
think it ought to be used? What are your reasons?
4. Have you had a chance to participate in an evaluation of an equipment purchase at
your workplace? If so, would you have done it differently if you had supervised the
evaluation? Why?
129
Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091
2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264
3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513
4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830
5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209
6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645
7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132
8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665
9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241
10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855
11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505
12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186
13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2987
14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633
15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394
16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176
17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978
18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799
19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317. 0.1945 0.1635
20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486
21 0.8114 0.6598 0.5375 0.4388 0.3589 0.2942 0.2415 0.1987 0.1637 0.1351
22 0.8034 0.6468 0.5219 0.4220 0.3418 0.2775 0.2257 0.1839 0.1502 0.1228
23 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.2109 0.1703 0.1378 0.1117
24 0.7876 0.6217 0.4919 0.3901 0.3101 0.2470 0.1971 0.1577 0.1264 0.1015
25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923
26 0.7720 0.5976 0.4637 0.3607 0.2812 0.2198 0.1722 0.1352 0.1064 0.0839
27 0.7644 0.5859 0.4502 0.3468 0.2678 0.2074 0.1609 0.1252 0.0976 0.0763
28 0.7568 0.5744 0.4371 0.3335 0.2552 0.1956 0.1504 0.1159 0.0895 0.0693
29 0.7493 0.5631 0.4243 0.3207 0.2429 0.1846 0.1406 0.1073 0.0822 0.0630
30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.1314 0.0994 0.0754 0.0573
P resent Value Table
(The Present Value of $1.00) 12-A
A P P E N D I X
130 CHAPTER 12 The Time Value of Money
Year 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333
2 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944
3 0.7312 0.7118 0.6913 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787
4 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823
5 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4190 0.4019
6 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.3349
7 0.4817 0.4523 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.2791
8 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.2487 0.2326
9 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.2255 0.2090 0.1938
10 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.1911 0.1756 0.1615
11 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346
12 0.2858 0.2567 0.2307 0.2076 0.1869 0.1685 0.1520 0.1372 0.1240 0.1122
13 0.2575 0.2292 0.2042 0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935
14 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0985 0.0876 0.0779
15 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649
16 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541
17 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451
18 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376
19 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313
20 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261
21 0.1117 0.0926 0.0768 0.0638 0.0531 0.0443 0.0370 0.0309 0.0259 0.0217
22 0.1007 0.0826 0.0680 0.0560 0.0462 0.0382 0.0316 0.0262 0.0218 0.0181
23 0.0907 0.0738 0.0601 0.0491 0.0402 0.0329 0.0270 0.0222 0.0183 0.0151
24 0.0817 0.0659 0.0532 0.0431 0.0349 0.0284 0.0231 0.0188 0.0154 0.0126
25 0.0736 0.0588 0.0471 0.0378 0.0304 0.0245 0.0197 0.0160 0.0129 0.0105
26 0.0663 0.0525 0.0417 0.0331 0.0264 0.0211 0.0169 0.0135 0.0109 0.0087
27 0.0597 0.0469 0.0369 0.0291 0.0230 0.0182 0.0144 0.0115 0.0091 0.0073
28 0.0538 0.0419 0.0326 0.0255 0.0200 0.0157 0.0123 0.0097 0.0077 0.0061
29 0.0485 0.0374 0.0289 0.0224 0.0174 0.0135 0.0105 0.0082 0.0064 0.0051
30 0.0437 0.0334 0.0256 0.0196 0.0151 0.0116 0.0090 0.0070 0.0054 0.0042
131
Year 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100
2 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210
3 1.030 1.061 1.093 1.125 1.156 1.191 1.225 1.260 1.295 1.331
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611
6 1.062 1.120 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949
8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144
9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594
11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853
12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138
13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452
14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797
15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177
16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595
17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054
18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560
19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116
20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.728
25 1.282 1.641 2.094 2.666 3.386 4.292 5.427 6.848 8.632 10.835
30 1.348 1.811 2.427 3.243 4.322 5.743 7.612 10.063 13.268 17.449
Compound
Interest Table
Compound Interest of $1.00
(The Future Amount of $1.00)
12-B
A P P E N D I X
132 CHAPTER 12 The Time Value of Money
Year 12% 14% 16% 18% 20% 24% 28% 32% 40% 50%
1 1.120 1.140 1.160 1.180 1.200 1.240 1.280 1.320 1.400 1.500
2 1.254 1.300 1.346 1.392 1.440 1.538 1.638 1.742 1.960 2.250
3 1.405 1.482 1.561 1.643 1.728 1.907 2.067 2.300 2.744 3.375
4 1.574 1.689 1.811 1.939 2.074 2.364 2.684 3.036 3.842 5.062
5 1.762 1.925 2.100 2.288 2.488 2.932 3.436 4.007 5.378 7.594
6 1.974 2.195 2.436 2.700 2.986 3.635 4.398 5.290 7.530 11.391
7 2.211 2.502 2.826 3.185 3.583 4.508 5.629 6.983 10.541 17.086
8 2.476 2.853 3.278 3.759 4.300 5.590 7.206 9.217 14.758 25.629
9 2.773 3.252 3.803 4.435 5.160 6.931 9.223 12.166 20.661 38.443
10 3.106 3.707 4.411 5.234 6.192 8.594 11.806 16.060 28.925 57.665
11 3.479 4.226 5.117 6.176 7.430 10.657 15.112 21.199 40.496 86.498
12 3.896 4.818 5.936 7.288 8.916 13.215 19.343 27.983 56.694 129.746
13 4.363 5.492 6.886 8.599 10.699 16.386 24.759 36.937 79.372 194.619
14 4.887 6.261 7.988 10.147 12.839 20.319 31.691 48.757 111.120 291.929
15 5.474 7.138 9.266 11.074 15.407 25.196 40.565 64.350 155.568 437.894
16 6.130 8.137 10.748 14.129 18.488 31.243 51.923 84.954 217.795 656.840
17 6.866 9.276 12.468 16.672 22.186 38.741 66.461 112.140 304.914 985.260
18 7.690 10.575 14.463 19.673 26.623 48.039 85.071 148.020 426.879 1477.900
19 8.613 12.056 16.777 23.214 31.948 59.568 108.890 195.390 597.630 2216.800
20 9.646 13.743 19.461 27.393 38.338 73.864 139.380 257.920 836.683 3325.300
25 17.000 26.462 40.874 62.669 95.396 216.542 478.900 1033.600 4499.880 25251.000
30 29.960 50.950 85.850 143.371 237.376 634.820 1645.500 4142.100 24201.432 191750.000
133
Periods 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Periods
1 .980 .962 .943 .926 .909 .893 .877 .862 .848 .833 1
2 1.942 1.886 1.833 1.783 1.736 1.690 1.647 1.605 1.566 1.528 2
3 2.884 2.775 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.107 3
4 3.808 3.630 3.465 3.312 3.170 3.037 2.914 2.798 2.690 2.589 4
5 4.713 4.452 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 5
6 5.601 5.242 4.917 4.623 4.355 4.111 3.889 3.685 3.498 3.326 6
7 6.472 6.002 5.582 5.206 4.868 4.564 4.288 4.039 3.812 3.605 7
8 7.325 6.733 6.210 5.747 5.335 4.968 4.639 4.344 4.078 3.837 8
9 8.162 7.435 6.802 6.247 5.759 5.328 4.946 4.607 4.303 4.031 9
10 8.983 8.111 7.360 6.710 6.145 5.650 5.216 4.833 4.494 4.193 10
15 12.849 11.118 9.712 8.560 7.606 6.811 6.142 5.576 5.092 4.676 15
20 16.351 13.590 11.470 9.818 8.514 7.469 6.623 5.929 5.353 4.870 20
25 19.523 15.622 12.783 10.675 9.077 7.843 6.873 6.097 5.467 4.948 25
P resent Value of an
Annuity of $1.00 12-C
A P P E N D I X
151
Using
Comparative Data 14
C H A P T E R
OVERVIEW
Comparative data can become an important tool for the
manager. It is important, however, to fully understand
the requirements and the uses of such data.
COMPARABILITY REQUIREMENTS
True comparability needs to meet three criteria: consis-
tency, verification, and unit measurement. Each is dis-
cussed in this section.
Consistency
Three equally important elements of consistency should
be considered as follows.
Time Periods
Time periods should be consistent. For example, a ten-
month period should not be compared to a twelve-
month period. Instead, the ten-month period should be
annualized, as described within this chapter.
Consistent Methodology
The same methods should be used across time periods.
For example, Chapter 8 discusses the use of two inven-
tory methods: first-in, first-out (FIFO) versus last-in, last-
out (LIFO). The same inventory method—one or the
other—should always be used consistently for both the
beginning of the year and for the end of the year.
After completing this chapter,
you should be able to
1. Understand the three criteria
for true comparability.
2. Understand the four uses of
comparative data.
3. Annualize partial-year
expenses.
4. Apply inflation factors.
5. Understand basic currency
measures.
P r o g r e s s N o t e s
152 CHAPTER 14 Using Comparative Data
Inflation Factors
Finally, if multiple years are being compared, should inflation be taken into account? The
proper application of an inflation factor is also described within this chapter.
Verification
Basically, can these data be verified? Is it reasonable? If an objective, qualified person re-
viewed the data, would he or she arrive at the same conclusion and/or results? You may
have to do a few tests to determine if the data can in fact be verified. If so, you should retain
your back-up data, because it is the evidence that supports your conclusions about
verification.
Monetary Unit Measurement
In regard to comparative data, we should ask: “Is all the information being prepared or
under review measured by the same monetary unit?” In the United States, we would expect
all the data to be expressed in dollars and not in some other currency such as euros (used
in much of Europe) or pounds (used in Britain and the United Kingdom). Most of the
manager’s data will automatically meet this requirement. However, currency conversions
are an important part of reporting financial results for companies that have global opera-
tions, and consistency in applying such conversions can be a significant factor in expressing
financial results.
A MANAGER’S VIEW OF COMPARATIVE DATA
It is important for the manager to always be aware of whether the data he or she is receiving
(or preparing) are appropriate for comparison. It is equally important for the manager to
perform a comprehensive review, as described below.
The Manager’s Responsibility
Whether you as a manager must either review or prepare required data, your responsibility
is to recall and apply the elements of consistency. Why? Because such data will typically be
used for decision making. If such data are not comparable, then relying upon them can re-
sult in poor decisions, with financial consequences in the future. The actual mechanics of
making a comparative review are equally important. The deconstruction of a comparative
budget review follows.
Comparative Budget Review
The manager needs to know how to effectively review comparative data. To do so, the man-
ager needs to understand, for example, how a budget report format is constructed. In gen-
eral, the usual operating expense budget that is under review will have a column for actual
expenditures, a column for budgeted expenditures, and a column for the difference be-
tween the two. Usually, the actual expense column and the budget column will both have a
vertical analysis of percentages (as discussed in the preceding chapter). Each different line
item will have a horizontal analysis (also discussed in the preceding chapter) that measures
the amount of the difference against the budget.
Table 14-1, entitled “Comparative Analysis of Budget versus Actual” illustrates the oper-
ating expense budget configuration just described. Notice that the “Difference” column
has both positive and negative numbers in it (the negative numbers being set off with
parentheses). Thus, the positive numbers indicate budget overage, such as the dietary line,
which had an actual expense of $405,000 against a budget figure of $400,000, resulting in a
$5,000 difference. The next line is maintenance. This department did not exceed its
budget, so the difference is in parentheses; the maintenance budget amounted to
$290,000, and actual expenses were only $270,000, so the $20,000 difference is in paren-
theses. In this case, parentheses are good (under budget) and no parentheses is bad (over
budget).
USES OF COMPARATIVE DATA
Four common uses of comparisons that the manager will find helpful are discussed in this
section.
Compare Current Expenses to Current Budget
Managers are most likely to be responsible for comparing the current expenses of their de-
partment, division, unit, or program to their current budget. Of the four types of compar-
isons discussed in this section, this is the one most commonly in use.
The preceding “Comparative Budget Review” used Table 14-1 to illustrate a comparison
of actual expenses versus budgeted expenses. This format reflects both dollars and per-
centages, as is most common. Table 14-1 shows the grand totals for each department
Uses of Comparative Data 153
Table 14–1 Comparative Analysis of Budget versus Actual
Hospital 1
Year 2 Actual Year 2 Budget Difference
$ % $ % $ %
General Services expense
Dietary $405,000 45 $400,000 46 $5,000 12.5
Maintenance 270,000 30 290,000 33 (20,000) (6.9)
Laundry 45,000 5 50,000 6 (5,000) (10.0)
Housekeeping 180,000 20 130,000 15 50,000 38.5
General Service expense $900,000 100 $870,000 100 $30,000 3.5
154 CHAPTER 14 Using Comparative Data
(Dietary, Maintenance, etc.) contained in General Services expense for this hospital. There
is, of course, a detailed budget for each of these departments that adds up to the totals
shown on Table 14-1. Thus, for example, all the detailed expenses of the Laundry depart-
ment (labor, supplies, etc.) are contained in a supporting detailed budget whose total ac-
tual expenses amount to $45,000 and whose total budgeted expenses amount to $50,000.
The department manager will be responsible for analyzing and managing the detailed
budgets of his or her own department. A manager at a higher level in the organization—
the chief financial officer (CFO), perhaps—will be responsible for making a comparative
analysis of the overall operations of the organization. This comparative analysis at a higher
level will condense each department’s details into a departmental grand total, as shown in
Table 14-1, for convenience and clarity in review.
The CFO may also convert this comparative data into charts or graphs in order to “tell
the story” in a more visual manner. For example, the total General Service expense in Table
14-1 can be readily converted into a graph. Thus Figure 14-1 “A Comparison of Hospital
One’s Budgeted and Actual Expenses” illustrates such a graph.
Compare Current Actual Expenses to Prior Periods in Own Organization
Trend analysis, as explained in the preceding chapter, allows comparison of current actual
expenses to expenses incurred in prior periods of the same organization. For example,
Table 13-4 entitled “Trend Analysis for Expenses” showed total general services expenses of
$800,000 for year 1 and $900,000 for year 2. The CFO could easily convert this information
into a graph, as shown in Figure 14-2 “A Comparison of Hospital One’s Expenses Over
820000
840000
860000
880000
900000
920000
Year 2
Budgeted
Expenses
870000
Year 2
Actual Expenses
900000
800000
Figure 14–1 A Comparison of Hospital One’s Budgeted and Actual Expenses.
Time.” (This information might be even more valuable for decision-making input if the
CFO used five years instead of the two years that are shown here.)
Compare to Other Organizations
Common sizing, as explained in the preceding chapter, allows comparison of your organi-
zation to other similar organizations. To illustrate, refer to Table 13-1, entitled “Common
Sizing Liability Information.” Here we see the liabilities of three hospitals that are the same
size expressed in both dollars and in percentages. Therefore, our CFO can convert the per-
centages into an informative graph, as shown in Figure 14-3 “A Comparison of Three One-
Hundred Bed Hospitals’ Long-Term Debt.”
Be warned that the basis for some comparisons will be neither useful nor valid. For ex-
ample, see Figure 14-4, “A Comparison of Three Hospitals’ Expenses.” Here we have a
graph of the grand totals from Table 13-2, entitled “Common Sizing Expense Information.”
The percentages shown for the General Services departments of each hospital have been
common sized to percentages, as is perfectly correct. However, Figure 14-4 attempts to com-
pare the total General Services expense (the total of all four departments as shown) in dol-
lars. As we can see here, hospital 1 and hospital 3 are both 100 beds, while hospital 2 is 400
beds. Obviously a 400-bed hospital will incur much more expense than a 100-bed hospital,
so this graph cannot possibly show a valid comparison among the three organizations.
Instead, the CFO should find a standard measure that can be used as a valid basis for
comparison. In this case, he or she can choose size (number of beds) for this purpose. The
Uses of Comparative Data 155
800000
600000
1000000
Year 1
$800,000
Year 2
$900,000
Figure 14–2 A Comparison of Hospital One’s Expenses Over Time.
156 CHAPTER 14 Using Comparative Data
resulting graph is shown in Figure 14-5, entitled “A Comparison of Three Hospitals’ Ex-
penses per Bed.” As you can see, hospital 1’s cost per bed is $8,000, computed as follows.
The total expense in Table 13-1 of $800,000 for hospital 1 is divided by 100 beds (its size) to
arrive at the $8,000 expense per bed shown on the graph in Figure 14-5. Hospital 2
2
0%
40%
60%
80%
0%
100%
Hospital 1
(100 beds)
80%
Hospital 2
(100 beds)
75%
Hospital 3
(100 beds)
20%
Figure 14–3 A Comparison of Three One-Hundred Bed Hospitals’ Long-Term Debt.
$1,000,000
$500,000
$1,500,000
$2,000,000
$2,500,000
$3,000,000
$0
$3,500,000
Hospital 1
(100 beds)
$800,000
Hospital 2
(400 beds)
$3,000,000
Hospital 3
(100 beds)
$900,000
Figure 14–4 A Comparison of Three Hospitals’ Total Expenses.
($3,000,000 total expense divided by 400 beds to equal $7,500 per bed) and hospital 3
($900,000 total expense divided by 100 beds to equal $9,000 per bed) have the same com-
putations performed on their equivalent figures.
In actual fact, another step in this computation should be performed in order to make the
comparisons completely valid. A per-bed computation implies inpatient expenses incurred,
since beds are occupied by admitted inpatients. (Outpatients, on the other hand, use a dif-
ferent mix of services.) Therefore, a more accurate comparison would adjust the overall total
expense using one subtotal for inpatients and another subtotal for outpatients. Let us assume,
for purposes of illustration, that the CFO of hospital 1 has determined that 70% of General
Services expense can be attributed to inpatients and that the remaining 30% can be attrib-
uted to outpatients. Let us further assume that hospital 1’s General Services expense of
$800,000 as shown, is indeed a hospital-wide expense. The CFO would then multiply $800,000
by 70% to arrive at $420,000, representing the inpatient portion of General Services expense.
Compare to Industry Standards
In the example just given in the paragraph above, the CFO has computed his or her own
hospital’s percentage of inpatient versus outpatient utilization of General Services expense.
But this CFO may not have any way to know these equivalent percentages for hospitals 2
and 3. If this is the case, computing the per-bed expense using overall expense, as shown in
Figure 14-5, may be the only way to show a three-hospital comparison.
The CFO, however, can use the 70% inpatient and 30% outpatient expense breakdown
for another type of comparison. It should be possible to find industry standards that break
Uses of Comparative Data 157
$6,500
$7,000
$7,500
$8,000
$8,500
$9,000
$6,000
$9,500
Hospital 1
(100 beds)
$8,000
Hospital 2
(400 beds)
$7,500
Hospital 3
(100 beds)
$9,000
Figure 14–5 A Comparison of Three Hospitals’ Expenses per Bed.
158 CHAPTER 14 Using Comparative Data
out inpatient versus outpatient expense percentages. The use of industry standards is of
particular use for decision making because it positions the particular organization within a
large grouping of facilities that provide a similar set of services.
Healthcare organizations are particularly well suited to use industry standards because
both the federal and state governments release a wealth of public information and statistics
regarding the provision of health care. Figure 14-6, entitled “A Comparison of Hospital
One’s GS Inpatient Expenses with Industry Standards,” illustrates the CFO’s graph using
such a standard. (The figures shown are for illustration only and do not reflect an actual
standard.)
MAKING DATA COMPARABLE
This section discusses annualizing partial-year expenses, along with using inflation factors,
standardized measures, and currency measures. The manager needs to know how to make
data comparable as a basis for properly preparing and/or reviewing budgets and reports.
Annualizing
Because comparability requires consistency, the manager needs to know how to annualize
partial-year expenses. Table 14-2, entitled “Annualizing Operating Room Partial-Year Ex-
penses,” sets out the actual 10-month expenses for the operating room. But these expenses
are going to be compared against a 12-month budget. What to do? The actual 10-month ex-
penses are converted, or annualized, to a 12-month basis, as shown in the second column of
Table 14-2.
55%
60%
65%
70%
50%
75%
GS Inpatient Expense %
Hospital 1
70%
GS Inpatient Expense %
Industry Standard
60%
Figure 14–6 A Comparison of Hospital One’s GS Inpatient Expenses with Industry Standards.
These computations were performed on a
computer spreadsheet; however, the calcula-
tion is as follows. Using the first line as an ex-
ample, $50,431 is 10-months worth of
expenses; therefore, one month’s expense is
one tenth of $50,431 or $5,043. To annualize
for 12-months worth of expenses, the 10-
month total of $50,431 is increased by two
more months at $5,043 apiece (50,431 plus
5,043 for month eleven, plus another 5,043
for month twelve, equals 60,517, the annual-
ized twelve-month figure for the year).
Inflation Factors
Inflation means “an increase in the vol-
ume of money and credit relative to avail-
able goods and services resulting in a con-
tinuing rise in the general price level.”1 An
inflation factor is used to compute the effect
of inflation.
Table 13-4, entitled “Trend Analysis for
Expenses” and presented in a prior chapter,
compared hospital 1’s General Services ex-
penses for Year 1 ($800,000) versus Year 2
($900,000). We can assume that these
amounts reflect actual dollars expended in
each year. But let us also now assume that in-
flation caused these expenses to rise by 5
percent in Year 2. If the Chief Financial
Officer (CFO) decides to take such inflation
into account, a government source will be
available to provide the appropriate infla-
tion rate. (The 5 percent in our example is
for illustration only and does not reflect an
actual rate.)
The inflation factor for this example is
expressed as a factor of 1.05 (1.00 plus 5%
[expressed as .05] equals 1.05). The CFO
might apply the inflation factor to year 1 in
order to give it a spending power basis
equivalent to that of year 2. (Applying an in-
flation factor for a two-year comparison is
not usually the case, but let us assume the
CFO has a good reason for doing so in this
Making Data Comparable 159
Table 14–2 Annualizing Operating Room Partial-
Year Expenses
Expenses
Actual Annualized
Account 10 Month 12 Month
Social Security 50,431 60,517
Pension 17,229 20,675
Health Insurance 7,018 8,422
Child Care 3,803 4,564
Patient Accounting 129,463 155,356
Admitting 91,878 110,254
Medical Records 76,432 91,718
Dietary 22,938 27,526
Medical Waste 1,981 2,377
Sterile Procedures 65,600 78,720
Laundry 33,911 40,693
Depreciation—
Equipment 72,815 87,378
Depreciation—
Building 34,481 41,377
Amortization—
Interest (4,849) (5,819)
Insurance 3,513 4,216
Administration 48,305 57,966
Medical Staff 1,435 1,722
Community
Relations 41,511 49,813
Materials
Management 53,811 64,573
Human Resources 25,888 31,066
Nursing
Administration 68,726 82,471
Data Processing 14,846 17,815
Fiscal 14,750 17,700
Telephone 2,366 2,839
Utilities 22,005 26,406
Plant 64,664 77,597
Environmental
Services 27,395 32,874
Safety 1,680 2,016
Quality
Management 8,347 10,016
Medical Staff 7,870 9,444
Continuous Quality
Improvement 4,079 4,895
EE Health 474 569
Total Allocated 1,014,796 1,217,756
All Other Expenses 1,009,673 1,211,608
Total Expense 2,024,469 2,429,364
Source: Adapted from J.J. Baker, Activity-Based Costing and
Activity-Based Management for Health Care, p. 190, © 1998,
Aspen Publishers, Inc.
160 CHAPTER 14 Using Comparative Data
case.) The computation would thus be $800,000 year 1 expense times the 1.05 inflation fac-
tor equals an inflation-adjusted year 1 expense figure of $840,000.
However, if the CFO wants to apply an inflation factor to a whole series of years, he or she
must account for the cumulative effect over time. An example appears in Table l4-3, enti-
tled “Applying a Cumulative Inflation Factor.” We assume a base of $500,000 and an annual
inflation rate of 10 percent. The inflation factor for the first year is 10 percent, converted to
1.10, just as in the previous example, and $500,000 multiplied by 1.10 equals $550,000 in
nominal dollars.
Beyond the first year, however, we must determine the cumulative inflation factor. For
this purpose we turn to the Compound Interest Table. It shows “The Future Amount of
$1.00,” and appears in Appendix 12-B. “The Future Amount of $1.00” table has years down
the left side (vertical) and percentages across the top (horizontal). We find the 10 percent
column and read down it for years one, two, three, and so on.
As shown in Table 14-3.2, the factor for year 2 is 1.210; for year 3 is 1.331, etc. We carry
those factors to column C of Table 14-3.1. Now we multiply the $500,000 in column B times
the factor for each year to arrive at the cumulative inflated amount in column D. Thus
$500,000 times the year 2 factor of 1.210 equals $605,000 and so on.
Table 14–3 Applying a Cumulative Inflation Factor
Table 14–3.1
SOURCE OF FACTOR IN COLUMN C ABOVE:
From the Compound Interest Look-Up Table
“The Future Amount of $1.00” (Appendix 12-B)
Year Factors as shown at 10%
1 1.100
2 1.210
3 1.331
4 1.464
Table 14–3.2
(A) (B) (C) (D)
Real Cumulative Nominal
Year Dollars Inflation Factor* Dollars**
1 $500,000 (1.10)1 � 1.100 $550,000
2 500,000 (1.10) 2 � 1.210 605,000
3 500,000 (1.10) 3 � 1.331 665,500
4 500,000 (1.10)4 � 1.464 732,050
*Assume an annual inflation rate of 10%. Thus 1.00 � 0.10 � the 1.10 factor in Column C.
**Column D “Nominal Dollars” equals Column B times Column C.
Currency Measures
Monetary unit measurement, and the related currency measures and currency conversions
are typically beyond most manager’s responsibilities. Nevertheless, it is important for the
manager to understand that consistency in applying such measures and conversions will be
a significant factor in expressing financial results of companies that have global operations.
Therefore, for comparative purposes we must determine if all the information being pre-
pared or under review is measured by the same monetary unit. A few foreign currency ex-
amples are illustrated in Exhibit 14-1. Currencies are typically converted for financial
reporting purposes using the U.S.-dollar foreign exchange rates as of a certain date.
Exchange rates may be expressed in two ways: “in U.S. dollars” or “per U.S. dollars.”
For example, assume the euro is trading at 1.3333 in U.S. dollars and at .7500 per U.S.
dollars. That means if you were spending your U.S. dollar in, say, France (part of the
“euro area”), it would take a third as much (1.33) in your dollars to buy products priced
in euros. If your French friend, on the other hand, was spending euros for products
priced in U.S. dollars, he or she could buy one quarter as much for his or her money (be-
cause the U.S. dollar would be worth only three quarters [.7500] of the euro at that par-
ticular exchange rate).
Standardized Measures
A final word about standardized measures. Standardized measures aid comparability. They
especially assist in performance measurement. Types of standardized measures include the
typical hospital per-bed measure along with work load measures.
There is, of course, a whole array of uses for standardized measures. Managed care plans,
for example, may use a standard set of measures that are applied to every physician who
contracts with the plan. Each physician then receives a report from the plan that illustrates
his or her performance.
Finally, electronic medical records (as discussed in Chapters 19 and 20) depend upon
standardized input. The input into various fields is standardized (and thus made compara-
ble) by the very nature of the electronic system design.
Making Data Comparable 161
Exhibit 14–1 Foreign Currency Examples
Country (or Area) Currency
Canada Canadian dollar
China Yuan
Euro Area Euro
Japan Yen
Mexico Peso
United Kingdom Pound
162 CHAPTER 14 Using Comparative Data
INFORMATION CHECKPOINT
What Is Needed? Example of a detailed comparative budget review (com-
paring budget to actual).
Where Is It Found? With the supervisor responsible for the budget.
How Is It Used? To find whether data are stated in comparable terms be-
tween actual amounts and budget amounts.
KEY TERMS
Annualize
Inflation Factor
Monetary Unit
DISCUSSION QUESTIONS
1. Do you believe your organization uses a flexible or static budget? Why do you
think so?
2. If you reviewed a budget at your workplace, do you think the major increases and de-
creases could be explained? If so, why? If not, why not?
3. Have you ever in the course of your work reviewed a report that had been annual-
ized? If so, did you agree with how it appeared to be annualized?
4. Were you also able to see the assumptions used to annualize? If so, were you able to
recalculate the results using the same assumptions?
5. Have you ever in the course of your work reviewed a financial report that applied in-
flation factors? If so, were you able to see the assumptions used to apply the factors? If
not, why not? Please describe.
