Part II
Management Accounting
Decision-Making Tools
Chapter 7
•
Cost-Volume-Profit Analysis
Chapter 8
•
Comprehensive Business Budgeting
Chapter 9
•
Incremental Analysis and Decision-making Costs
Chapter 10 •
Incremental Analysis and Cost-Volume-profit Analysis:
Special Applications
Chapter 11 •
Economic Order Quantity Models
Chapter 12 •
Capital Budgeting Decisions Tools
Chapter 13 •
Pricing Decision Analysis
Management Accounting
Cost-Volume-Profit Analysis
The success of a business as measured in terms of profit depends upon
adequate sales; that is; the volume of sales must be sufficient to cover all costs
and allow a satisfactory margin for net income. When the proportion of fixed costs
in a business becomes large in relation to total costs, then volume becomes an
extremely important factor in achieving profitability. For example, a business with
only variable costs would be able to report net income at any level of sales as long
as price exceeds the variable cost rate. However, a business with only fixed costs
cannot show a profit until the contribution from sales is equal to the amount of fixed
expenses. Therefore, a minimum level of sales is absolutely essential in a business
that incurs fixed expenses.
Because changes in volume can have a profound impact on the profits of a
business, cost-volume-profit analysis has been developed as a management tool to
enable analysis of the following variables:
1. Price
2. Quantity
3. Variable costs
4. Fixed costs
The focal point of cost-volume-profit analysis is on the effect that changes in
volume have on fixed and variable costs. Volume may be regarded as either units
sold or the dollar amount of sales. Typically, the theory of cost-volume-profit analysis
is explained in terms of units. However, using units as the measure of volume for
computing break even point or target income point requires that the business sell
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114 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
only a single product. Since all businesses from a practical viewpoint sell multiple
products, the real world use of cost-volume-profit analysis requires that volume be
measured in terms of sales dollars.
Cost-volume-profit analysis may be used as (1) a tool for profit planning and
decision-making and (2) as a tool for evaluating the profitability of proposed business
ventures. In this chapter, the discussion of profit analysis shall be limited to its use as
a current period profit and decision-making tool.
Nature of Cost-Volume-Profit Analysis
In chapter 5, the subject of cost behavior was discussed. The point was made that
the costs of a business could be classified as either fixed or variable. Mathematically,
it was stated:
TC = V(Q) + F
TC - total costs
V - variable cost rate
Q - quantity
Revenue or sales may be defined as:
(1)
S = P(Q)
S - sales
P - price
Income may be defined as:
(2)
R
E
I
I
-
-
-
= R - E
revenue
expense
income
(3)
When equations (1) and (2) are substituted into equation (3), equation (3) becomes
I = P(Q) - V(Q) - F
(4)
Equation (4) is recognized in this chapter as the foundation of cost-volumeprofit analysis. Quantity (Q) is generally treated as the independent variable; that is,
income is regarded as a function of quantity (Q). The variable cost rate (V) and fixed
expenses (F) are assumed to be constants. However, for certain analytical purposes,
the values of V and F may be assigned different values in order to determine the
effect of the changes in these values on net income.
Equation 4, it should be noted, may be used as a tool of analysis only for a single
product business. For firms that have more than one product, another equation which
emphasizes sales as volume in dollars must be used:
I = S - v(S) - F
(5)
S - sales in dollars
v - variable cost percentage
In a multiple product business, it is necessary to express variable cost as a
percentage of sales. This percentage will be discussed in detail in a later section of
this chapter.
Management Accounting
Cost-volume-profit Analysis for a Single Product Business
Frequently, it is necessary to ask the question: how many units must be sold in
order to attain a given level of net income? Equation (4) may be used to answer this
question; however, in order to do so it is necessary to solve for quantity, Q.
I = Q(P - V) - F
I + F =
Q(P - V )
I+F
Q = –––––
P-V
(6)
Equation (6) may be used to determine the quantity of sales required to attain
any desired level of income. For example, assume that the Acme Company’s selling
price is $10 and its variable cost rate is $8. Also, assume that it has fixed expenses of
$5,000. Suppose that management desires to earn $8,000 for the period. How many
units must the company sell in order to attain the desired net income?
Answer: This question may be answered simply by substituting these given revenue and cost values into equation 6:
I + F $8,000 + $5,000 $13,000
Q = –––– = ––––––––––––– = –––––––
P - V
$10 - $8
2
= 6,500 units
Therefore, the Acme Company must sell 6,500 units to earn $8,000. The validity
of this answer can be demonstrated as follows:
Sales (6,500 x $10)
$65,000
Expenses:
Variable (6,500 x $8)
$52,000
Fixed
5,000
_______
Total expenses
$57,000
_______
Net income
$ 8,000
–––––––
–––––––
In management accounting literature, considerable emphasis is given to the
concept of a break even point. While it is an interesting academic exercise to compute
break even point, it should be stressed that a company does not set a goal to break
even. The primary object of management in using cost-volume-profit analysis is to
determine target income point and not break even point.
Nevertheless, assuming for some reason that it is considered desirable to know
the break even point of a business, the break even point is calculated exactly in the
same way as target income point. Equation (6) may be used to compute break even
point. Break even point is simply the quantity of sales that achieves zero net income.
It is that level of sales where total sales equals total expenses.
Using the same data from the example above, break even point may be computed
as follows:
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116 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
I + F
0 + 5,000
5,000
Q = ––––– = –––––––– = –––––
P - V
10 - 8
2
= 2,500 units
The correctness of this answer may be demonstrated as follows:
Sales (2,500 x $10)
$25,000
Expenses:
Variable (8 x 2,500)
$20,000
Fixed
5,000
––––––– 25,000
–––––––
Net income
$       0
–––––––
Cost-volume-profit Analysis for a Multiple Product Business
A company with more than one product cannot use equations (4) or (6) as illustrated
and discussed above. It is not possible to logically add different quantities of product.
The saying that “you can’t add apples and oranges” applies here. However, it is
possible to meaningfully add the dollar value of oranges to the dollar value of apples.
In a multiple product business, it is necessary to use the dollar value of sales as the
measure of volume.
Equation 5, as previously indicated, is the basis of cost-volume-profit analysis for
a multiple product business.
I = S - v(S) - F
S - sales in dollars
v - variable cost percentage
The expression v(S) represents total variable expenses. It may be calculated by
simply dividing total variable expenses or cost by total sales:
Where:
TVE
v = ––––
S
(7)
v
- variable cost percentage
TVE - total variable expenses
S
- sales ($)
The variable, v, requires an explanation. As used in the above equation, it is the
variable cost percentage; that is, it represents the percentage that total variable cost
bears to total sales. The variable cost percentage is assumed to be constant at all
levels of activity. For example, assume that v = 70%. Total variable costs would vary
with sales as illustrated:
Q
v
TVC
––––––––
–– ––––––––
$  10,000
.7
$   7,000
$100,000
.7
$  70,000
$200,000
.7
$140,000
$400,000
.7
$280,000
Management Accounting
In order for the variable cost percentage to hold constant in a multiple product
business, it is necessary for the sales mix ratio to remain the same. The sales mix
ratio is discussed later in this chapter.
As in the case of a single product firm, it is desirable to ask the question: how
many units must be sold in order to attain a desired income level? Equation 5 may
be used to answer this question; however, it is first necessary to solve for S (sales)
as follows:
I = S -
v(S) - F
S(1 - v) - F = I
S(1 - v) = I + F
I+F
S = ––––––
1-v
(8)
This equation may be used to compute the dollar level of sales required to attain
a desired level of income. For example, assume that the Barton Company’s variable
cost percentage is 80% and its fixed cost is $10,000. Furthermore, assume that
management has set a profit goal of $50,000. What must the dollar volume of sales
be in order to attain the $50,000 income objective?
Answer:
I + F 50,000 + 10,000
S = –––––– = –––––––––––––– =
1 - v
1 - .8
60,000
––––––
.2
= $300,000
The correctness of this answer can be demonstrated as follows:
Sales
Expenses:
Variable ($300,000 x .8)
Fixed $300,000
$240,000
10,000
– ––––––– Net income
250,000
– –––––––
$ 50,000
– –––––––
The Contribution Margin Concept
The study and use of cost-volume-profit analysis requires understanding the
concept of contribution margin. The study of this unique concept contributes greatly
to an understanding of the importance of changes in volume. In an aggregate sense,
contribution margin is simply total sales less total variable costs. From a decisionmaking tool perspective, it is also necessary to understand the concept mathematically.
Variation of this concept include:
Single product business:
Total contribution margin
Contribution margin rate (per unit of product)
Multiple product business
Total contribution margin
Contribution margin percentage
- P(Q) - V(Q) or Q(P - V)
- ( P - V)
- S - v(S) or S(1 - v)
- ( 1 - v)
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118 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
The contribution margin rate (per unit) and the contribution margin percentage
are often called the contribution margin ratio. A ratio may be expressed on a unit
basis or a percentage basis.
The concept of contribution margin provides a rather unique way of interpreting
the activity of a business. At the start of the operating period, a business with fixed
expenses would show a loss. At zero sales, the loss would be equal to total fixed
expenses. As each unit of product is sold, the loss is gradually reduced by the
contribution margin of each unit sold. No profit can be reported until total contribution
equals total fixed expenses. After break even point, each unit sold contributes to net
income an amount equal to the contribution margin per unit of product.
Total Contribution Margin - As previously defined, total contribution margin is
total sales less total variable costs. Mathematically, in terms of the profit equation
for a single product business, total contribution margin is equal to P(Q) - V(Q). It
is important to understand that the term “contribution” means a contribution first to
fixed expenses. As previously mentioned, there can be no profit in a business until
total contribution equals total fixed expenses. When this occurs, the business has
reached break even point. Break even point is that quantity of sales that causes total
contribution margin to be exactly equal to total fixed expenses.
Contribution Margin Per Unit of Product - The use of cost-volume-profit analysis
as a decision-making tool also requires understanding of the concept of contribution
margin per unit of product. The contribution margin rate is simply price less the
variable cost rate. Mathematically, the contribution margin rate is P - V.
The use of the contribution margin rate is obvious in equation 6:
I + F
Q = –––––––
P - V
The denominator in this equation, P - V, is the contribution margin rate and, I +
F, is the total contribution desired. An important question is: how much contribution is
required in any business? The answer is that the contribution required must be enough
to pay fixed expenses and then be sufficient to allow the firm to attain the desired
level of income. Consequently, I + F, represents the total required contribution.
Illustration
The Acme Company’s accountant provided the following cost-volume-profit
data:
P - $10.00
V - $8.00
F - $5,000
I
- $25,000
The company’s contribution margin rate is $2 ($10 - $8). Each sale contributes
$2. If the company sells 1,000 units, then the total contribution would be $2,000. The
company obviously needs an additional $3,000 of contribution to reach break even
point. When sales reach 2,500 the total contribution is $5,000 which is equal to fixed
expenses. Break even point has been reached. Each additional units sold after break
Management Accounting
even point contributes $2 to income. If 2,600 units are sold, net income would be
$200 ($2 x 100).
Contribution Margin Percentage - In a multiple product firm, it is necessary to talk
in terms of contribution as a percentage. Mathematically, the contribution margin
percentage rate is 1 - v. The contribution margin percentage requires that the
variable cost percentage be first computed. If the variable cost percentage is 70%,
then the contribution margin percentage would be 30% (1 - .70). The importance of
the contribution margin percentage is apparent from examining equation 8:
S =
I + F
–––––––
1 - v
The contribution margin percentage is the percentage that each dollar of sales
contributions towards fixed expenses and desired net income. The total contribution
required to attain the desire income goal can be computed by simply dividing total
desired contribution by the contribution margin percentage.
Contribution Margin Income Statement - Cost-volume-profit analysis may be
made an integral part of financial reporting. Companies who do this generally prefer
to prepare income statements in which fixed costs, variable cost, and contribution
margin are explicitly shown. For example, assume that during the year the Acme
Company had sales of $50,000 and fixed and variable costs as follows:
Fixed Expenses
Variable Expenses
Selling
Selling
Advertising
$5,000
Sales people commissions$ 5,000
Sales people salaries $3,000
Sales people travel
$ 2,000
Supplies
$ 500
Cost of goods sold
$20,000
General & Admin.
General & Admin.
Utilities
$ 500
Supplies
$ 5,000
Supplies
$ 500
Other
$ 2,000
Executive salaries
$2,000
Depreciation
$1,000
Based on the above data, the following income statement may be prepared as
shown in Figure 7.1.
Graphical Illustration of Cost-volume-profit Analysis
Because the fundamental relationships of cost-volume-profit analysis are basically
mathematical in nature, the elements of cost-volume-profit analysis can be illustrated
graphically. The general procedure is to plot the revenue and cost functions on the
same graph. In order to illustrate the cost-volume-profit graphically, the following data
has been assumed:
Price
$10
Variable cost rate
$6
Fixed expenses
$20,000
For purposes of preparing the graph, assume different levels of quantity starting
with 1,000 units and increasing activity by increments of 1,000 units. The following
calculations are helpful in plotting the graph.
| 119
120 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Figure 7.1
Acme Manufacturing Company
Income Statement, Contribution Basis
For the Year Ended, Dec. 31, ____
Sales
Variable costs:
Selling:
Cost of goods sold
$20,000
Sales people commissions
5,000
Sales people travel
2,000
$27,000
–––––––
General & Admin.
Supplies
$  5,000
Other
2,000
7,000
–––––––
––––––
Contribution Margin
Fixed Expenses:
Selling:
Advertising
$  5,000
Sales people salaries
3,000
Supplies
500
$8,500
–––––––
General & Admin.
Executive salaries
$  2,000
Utilities
500
Supplies
500
Depreciation
1,000
4,000
–––––––
––––––
Net income
Revenue (sales)
–––––––––––––––––––––––––––– Q
– ––––
1,000
2,000
3,000
4,000
5,000
P
–––– $10
$10
$10
$10
$10 Total Sales
–––––––––– $10,000
$20,000
$30,000
$40,000
$50,000
$50,000
$34,000
–––––––
$16,000
$12,500
–––––––
$ 3,500
________
________
Total Variable Costs
– ––––––––––––––––––––––––––––––
Q
– ––––
1,000
2,000
3,000
4,000
5,000
V
–––
$6
$6
$6
$6
$6
Total Variable Costs
–––––––––––––––––––
$ 6,000
$12,000
$18,000
$24,000
$30,000
The procedure for preparing the cost-volume-chart is as follows:
(1) Plot the data for total fixed costs (See Figure 7.2a)
(2) Plot the data for total variable expenses (See Figure 7.2b)
(3) Plot the data for total sales (See Figure 7.2c)
Management Accounting
Figure 7. 2
2a
2b
Fixed Cost
Total Fixed and Variable Cost
60000
50000
40000
Cost $
Cost $
40000
20000
30000
20000
10000
0
2000
4000
6000
Volume
0
8000
0
2000
4000
6000
8000
Volume (Quantity)
2c
Cost-Volume-Profit Chart
70000
Sales/Cost ($)
60000
50000
40000
30000
20000
10000
0
0
2000
4000
6000
8000
Volume (Quantity)
Figure 7.2c represents the completed cost-volume-profit graph. The graph
represents an excellent visual means of presenting the basic concepts and cost
behavior relationships inherent in cost-volume-profit analysis. An enlarged version of
Figure 7.2c is presented is Figure 7.3. Notice that the Acme Company’s break even
point can easily be seen to be 5,000 units. Assume that the Acme Company desires
to attain an income level of $7,000. The level of sales that will result in this amount of
income is $67,500. The graph can be easily used to shown net income and net loss
as has been done in Figure 7.3a.
In addition, the concept of contribution margin can be visually represented in
Figure 7.3. Notice that in Figure 7.3 that variable cost has been plotted before fixed
cost. Note that in Figure 7.3B, the total contribution margin area is indicated by an
arrow. By definition total contribution margin is simply total sales less total variable
expenses, and this is exactly what is shown in Figure 7.3B. Also, notice that at break
even point, the total contribution margin is equal to fixed costs, as illustrated by chart
7.3B. The break even point may be defined in several ways. One definition defines
break even point as that level of sales where total contribution margin is equal to
total fixed expenses as illustrated in 7.3B. Another definition defines break even point
as that level of sales where sales = total expenses (Figure 7.3A). Obviously, in both
definitions, net income is zero at break even point.
| 121
122 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Figure 7.3 • Graphical Illustration of Contribution Margin
(000)
(000)
80
80
70
70
60
60
Net Income
50
Net Loss
40
50
40
30
30
20
20
10
10
0
A
2,500
Contribution
margin
5,000
Volume (units)
6,750
Contribution margin =
fixed expenses
0
B
2,500
5,000
6,750
Volume (units)
Basic Assumptions of Cost-volume-profit Analysis
In the next section, illustrations will be given on how cost-volume-profit analysis
may be used as a profit planning and decision-making tool. However, effective use of
cost-volume-profit analysis for planning purposes requires understanding of certain
basic assumptions. Unless the following assumptions are substantially met, any
attempt to use cost-volume-profit analysis in a real world situation may prove to be
inaccurate and misleading.
Cost-volume-profit analysis assumptions may be summarized as follows:
1.
Within a relevant range of volume, the variables price, quantity,
fixed costs, and variable costs are subject to managerial control.
2.
Price and the variable cost rate are constant within the relevant
range of activity.
This assumption simply means that variable costs and revenues are
assumed to vary linearly with changes in volume. State differently,
changes in volume have no effect on price, the variable cost rate,
and fixed costs.
3.
In a multiple product company, the sales mix ratio remains constant
with changes in total sales.
Management Accounting
4.
In a company that uses absorption costing, unless sales equals
production, there exists no unique break even point. When direct
costing is used, no problems arise when production varies from
sales. In direct costing, fixed manufacturing overhead is treated
as a period charge. Direct costing and absorption are discussed in
some depth in chapter 6.
Cost-Volume-Profit Analysis: A Decision-making Analysis Tool
Previous discussion of C-V-P was based on the assumption that price, the variable
cost rate, and fixed costs remain constant with increases or decreases in quantity.
Changes in quantity do not cause changes in the other variables. However, price,
the variable cost rate, and fixed costs can change for reasons other than changes in
volume. Management can at any time decide to increase or decrease price. Suppliers
at any time can increase or decrease the cost per unit of materials. Many, if not most,
variable costs and expenses can be changed by management simply by making the
decision to do so.
Since price, variable costs, and fixed costs can be increased or decreased at the
will of management, the cost-volume-profit equations can be used to perform whatif analysis. In broad terms, six basic questions may be asked regarding changes in
revenues and costs:
Price
What is the effect on break even point and target income point of an increase
in price?
What is the effect on break even point and target income point of a decrease in
price?
Variable cost rate
What is the effect on break even point and target income point of an increase in
the variable cost rate?
What is the effect on break even point and target income point of a decrease in
the variable cost rate?
Fixed Expenses
What is the effect on break even point and target income point of an increase in
fixed costs?
What is the effect on break even point and target income point of a decrease in
fixed costs?
An effective way to answers these questions is to use a P/V graph. A P/V graph
shows the relationship of net income to volume (sales dollars or units). A P/V graph
is shown in Figure 7.4. In this graph, volume is the independent variable and net
income the dependent variable. To illustrate how a P/V graph is constructed, assume
the following:
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124 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Figure 7.4
P/V Chart
$10
$8
$5,000
6000
5000
Net Income $
Price (P)
Variable cost rate (V)
Fixed Costs (F)
Based on this data, the table below
may be prepared.
Q
P(Q)
V(Q)
F
NI
––––––––––––––––––––––––––––––––––––––––
1,000
10,000
8,000
5,000
(3,000)
2,000
20,000
16,000
5,000
(1,000)
3,000
30,000
24,000
5,000
1,000
4,000
40,000
32,000
5,000
3,000
5,000
50,000
40,000
5,000
5,000
4000
3000
2000
1000
0
2000
-1000
4000
6000
Q
-2000
-3000
-4000
Volume (units)
Net Income
Figure 7.5 • Changes in Net Income Line
Net Income
Net Income
Q
Q
Increase in Price
Decrease in Price
A
B
C
Decrease in Variable Cost
D
$
Net Income
Net Income
Q
Q
Increase in Variable Cost
$
$
Net Income
$
$
Q
Increase in Fixed Cost
E
Net Income
$
Q
Decrease in Fixed Cost
F
In Figure 7.5 is illustrated the effect on break even point and net income of changes
in price, variable cost, and fixed expenses. In chart A, an increase in price shifts the
line upwards and to the left. The result is a decrease in break even point. In Chart B,
a decrease in price has the opposite effect. Break even point has increased in chart
C. The increase in variable expenses caused the income line to shift downwards and
to the right. The opposite is true of a decrease in the variable expense rate. Break
even point has decreased. An increase in fixed expenses will cause the income line
to shift to the left and upwards. The result is a decease in break even point. The
Management Accounting
opposite is true for an increase in fixed expenses. Whether a given change is good
or bad for fixed expenses such as advertising can not be stated. For example, an
increase in advertising might cause an increase in sales with a resulting increase in
net income.
The P/V graph can effectively be used to illustrate changes in price, the variable
cost rate, and fixed costs. A change in one of these variables will cause a shift or
movement in the net income line.
Changes in Price - An increase in price will most likely result in a decrease
in sales. However, a decrease in sales does not necessarily mean a decrease in
net income. Regarding the units that are sold, the contribution margin is greater.
Consequently, less units of sales are required to attain a profit goal. Given an increase
in price, management will probably want to ask the question: how many units of sales
can be lost and the same net income earned?
This question can be answered by using the following equation:
I + F
Q = –––––––
Figure 7.6 • P/V Chart
P - V
The procedure is simply to
$
P/V Chart
compute Q, or quantity, at the new
P=$12.00
10000
price and then subtract this quantity
from the quantity of sales before
7500
the price change.
Illustration
Last year, at a sales volume of 5,000
units, the Ace Manufacturing Company’s
income statement show the following:
Sales (5,000 x $10)
Expenses
Variable ($8 x 5000)
Fixed
Net income
$50,000
40,000
5,000
������
45,000
������
$  5,000
–––––––
–––––––
P=$10.00
5000
2500
0
1,250
2,500
3,750
5,000
units
-2500
-5000
-7500
Management is considering increasing price to $12 per unit. At the new price, the
quantity necessary to earn the same income would be:
Q =
5,000 + 5,000
––––––––––––– =
12 - 8
10,000
–––––––
4
=
2,500
At the new price, only 2,500 units need to be sold to earn $5,000. The company
can lose one half of its sales without suffering any loss in income. The effect of the
change in price on break even point and net income at different levels of sales is
shown in Figure 7.5A. Note that in Figure 7.6, the income function shifts upward and
to the left. BEP point is now 1,250 units and the income previously earned at 5,000
units can now be earned at 2,500 units.
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126 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Multiple Product Business and Sales Mix
The break even point and target income point for a multiple product business
can be computed using equation 8. This equation requires that variable cost be
expressed as a percentage of sales. A number of questions arise unique to multiple
product business. One of these problems pertains to the fact that the sale of multiple
products give rise to a sales mix ratio. The term sales mix refers to the ratio of the
units sold for each product. If product A is sold at the rate of 10,000 units per year and
product B at the rate of 20,000 per year, then the sales mix ratio is 1:2.
There are two methods for computing the variable cost percentage in a multiple
product business. The first method was previously discussed and presented as
equation 7
TVE
v = –––––
S
The second method involves using the sales mix ratio and knowing the variable
cost rates of each product: Mathematically, this method may be defined as follows:
∑ ViQi
v = ––––––––
∑ PiQi
Where:
(9)
i = 1, n
v
Vi
Qi
Pi
-
-
-
-
aggregate percentage variable cost
variable cost rate of product i
quantity of product i
price of product i
To illustrate, assume the following:
Price
Variable cost
Quantity
Fixed cost
Product A
$12.00
$ 8.00
1,000
$300
Product B
$  8.00
$  2.00
400
$1,000
Based on the above information, the variable cost percentage may be calculated
as follows:
∑PiQi = 12(1,000) + 8(400) = 12,000 + 3,200 = 15,200
∑ViQi ) = 8(1,000) + 2(400) = 8,000 + 800 = 8,800
∑ ViQi
8,800
v = –––––
= ––––––
∑ PiQi 15,200
= .5789
Changes in the Sales Mix Ratio
A number of questions arise concerning changes in the sales mix ratio:
1. Does a change in the sales mix ratio have an affect on the variable
cost percentage?
2. Can a separate break even point be computed for each product?
Management Accounting
3. Is the most profitable product the product with largest contribution
margin?
4. Should the product that generates the highest volume of sales dollars
also be the product that is promoted the most?
5. Is it possible for sales to increase and costs per unit to remain the
same and yet for net income to decrease?
Effect of a Change in the Sales Mix Ratio on the Variable Cost Percentage
Computing a break even point in a multiple product business is based on the
assumption that the sales mix remains the same. In the above example, the sales
mix ratio was 2.5 to 1. Based on this ratio, the break even point is:
1,300
1,300
BEP = ––––––––––– = ––––––– =
1 - .5789
.4211
3,087
Suppose, in fact, the ratio become the opposite; that is 1:2.5. The variable cost
percentage then becomes.
8.00(400) + 2.00(1000)
v = –––––––––––––––––––– =
12.00(400) + 8.00(1000)
5,200
––––––––– =
12,800
.40625
The break even point is now:
1,300
BEP = –––––––– =
1 - .40625
1,300
–––––––––
.59375
= 2,189
If a significant change is the sale mix ratio occurs, then the previous computation
of the break even point based on the original sales mix is unreliable.
Computing Break even Point for each Product - It is still possible to compute a
break even point for each product separately; however, now care must be taken to
not include common fixed costs in the total fixed costs for each product. Common
fixed costs are those costs that occur whether or not the particular product is sold.
For example, salaries to top management are most likely to be common in nature.
Assuming there are no common costs in the fixed costs of products A and B, then the
individual product break even points may be computed as follows:
Product A
Product B
300 300
1,000 1,000
BEP = ––––– = –––– = 900
BEP = –––––– = ––––– = 1,333
1 - .67 .33
1 - .25
.75
Contribution Margin Rate Differences - It is highly unlikely that the contribution
margin rate of each product will be the same. The question is: will the product with the
largest contribution margin rate be the most profitable? The answer is no. Net income
also depends on the quantity sold. Because the contribution rate is the greatest, this
is no guarantee that this product will even be profitable. Using the same data as
previously, net income for products A and B may be computed as shown in Figure
7.7:
As can clearly be seen, product B which has a greater contribution margin rate
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128 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Figure 7.7 • Effect of Different Contribution Margin Rates
Product A
Income Statement
Sales ($12 x 1,000)
Variable expenses ($8 x 1000)
Contribution margin
Fixed Expenses
Net income
$12,000
8,000
–––––––
4,000
1,000
–––––––
$ 3,000
–––––––
–––––––
Product B
Income Statement
Sales ($8 x 400)
Variable expenses ($2 x 400)
Contribution margin
Fixed Expenses
Net income
$3,200
800
––––––
2,400
300
––––––
$2,100
–––––––
–––––––
($6.00 versus $4.00 for product A) is not the most profitable product. While product
A does have the greater sales volume in dollars this does not mean that the product
with the highest sales volume will be the most profitable. Profitability also depends on
the contribution margin rate and the amount of fixed expenses.
Increasing Sales, Constant Costs, and Decreasing Net Income - One of the
unusual phenomenons in a business is that sales can be increasing and costs can
be constant yet the business is experiencing a decrease in net income. This situation
can happen when there is a substantial shift in the sales mix from the product with
the greatest contribution margin rate to the products with a lower contribution margin
rate.
To illustrate, assume that all costs remain the same in our example except that
the sales mix becomes 1,100 to 300. Based on this mix, net income for each product
may be computed as seen in Figure 7.8:
Figure 7.8 • Effect of a Change in Sales Mix Ratio
Product A
Product B
Income Statement
Income Statement
Sales ($12 x 1,100)
Variable expenses ($8 x 1100)
Contribution margin
Fixed Expenses
Net income
$13,200
8,800
–––––––
4,400
1,000
–––––––
$  3,400
–––––––
–––––––
Sales ($8 x 300)
Variable expenses ($2 x 300)
Contribution margin
Fixed Expenses
Net income
$2,400
600
––––––
1,800
300
––––––
$1,500
–––––––
–––––––
Management Accounting
Combined income then is:
Income Statement
Sales
Variable expenses
Contribution margin
Fixed Expenses
Net income
$15,600
9,400
––––––––
6,200
1,300
––––––––
$  4,900
––––––––
Previously, combined sales was $15,200 ($12,000 + $3,200). Now combined
sales is $15,600 ($13,200 + $2,400); however net income is now $4,900 ($3,400
+ $1,500) whereas it was previously $5,100 ($3,000 + $2,100). Even though sales
increased by $400, net income has decreased by $200. This decrease in net income
happened despite that fact that price, the variable cost rates, and fixed costs remained
the same.
A multiple product business requires close monitoring of the profitability of each
product. General rules for managing and promoting each product based on price,
variable cost rates and fixed cost are difficult to formulate. The computation of break
even or target income point does not tell management which product will be become
the most profitable. However, the effect of changes or shifts in the sales mix can
easily be calculated.
The best approach to evaluating multiple products is to prepare segmental income
statements. This management accounting tool is discussed in depth in chapter 15.
A product that is not making a significant contribution to fixed expenses should
be a candidate for discontinuance. If after all attempts to increase the segmental
contribution have failed, the only course of action is to discontinue the product.
Adding and discontinuing products is a constant and ongoing process. The role of
the management accounting and the use of the appropriate management accounting
tools becomes extremely important in a multiple product business.
Computing Target Income Point After Taxes
In order to compute a target income point, it is necessary to specify the desired
level of income. However, the concept of net income is somewhat ambiguous. Net
income can be before taxes or after taxes. Up to this point in this chapter, it has been
assumed that the desired level of net income is net income before taxes, although
this assumption was never explicitly made.
Net income after income taxes in many instances is more useful in making
decisions. For example, a dividend policy is easier to formulate based on net income
after taxes. Also, in planning cash flow, net income after taxes is more useful. However,
net income before tax and after tax are obviously not independent of each other. In
order to specify net income after tax as the goal in computing target income point, it
is still necessary to know net income before tax. To illustrate, assume that the goal is
| 129
130 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
to earn $120,000 after tax and that the tax rate is 40%. The equation for converting
after tax income to before tax income is:
NI bt = NI at / (1 - T)
Where:
NI bt - net income before tax
NI at - net income after tax
T
- tax rate
If the desired net income after tax is $120,000 and the tax rate is 40%, then net
income before tax is:
Ni bt = $120,000 / ( 1 - .4) = $120,000 / .6 = $200,000
If price is $100, V is $70,00, and fixed expenses $400,000, then we can compute
target income point using a slightly modified version of equation 6.
Q =
I+F
–––––
P-V
(6)
NI AT / (1 - T) + F
Q = ––––––––––––––––––
P - V
Based on this equation, then target income point maybe be computed as
follows:
120,000 /( 1 - .4) + 400,000 200,000 + 400,000
Q = –––––––––––––––––––––– = ––––––––––––––––– =
100 - 70
30
600,000
–––––––– = 20,000
30
The correctness of this computation can be demonstrated as follows:
Sales
$2,000,000
Variable expenses
1,400,000
––––––––––
Contribution margin
$   600,000
Fixed expenses
$   400,000
––––––––––
Net income before taxes
$   200,000
Tax expense
80,000
––––––––––
Net income after taxes
$   120,000
––––––––––
Management Accounting
Summary
Cost-volume-profit analysis is a powerful analytical tool. It can be effectively used
in many different kinds of decisions. Cost-volume-profit analysis is based on the
theory of cost behavior and as such it is imperative that the management accounting
and also management have a good understanding of cost behavior. Because
cost-volume-profit analysis is based on a number of critical assumptions, it is also
important to recognize when the use of this tool is valid and when it is not. If the data
used in cost-volume-profit analysis extends too far beyond the relevant range, the
results obtained can be inaccurate and misleading. Nevertheless, as long as the
assumptions on which cost-volume-profit analysis is based hold true, then the tool
can provide very useful information concerning decisions to be made and the evaluation of results already obtained.
Q. 7.1
Define the following terms:
a.
b.
c.
d.
e.
f.
g.
h.
Q. 7.2
Fixed cost
Variable cost
Semi-variable cost
Step cost
Average fixed cost
Average variable cost
Relevant range
Contribution margin
i. Contribution margin rate
j. Variable cost rate
k. Break even point
l. Target income point
m. Contribution margin income
statement
n. Sales mix
o. Net income before tax
Define the following mathematically.
a.
b.
c.
d.
Sales
Total variable cost
Total fixed cost
Net income
Q. 7.3
What are the two basic equations from which formulas for break even
point or target income point may be derived?
Q. 7.4
Explain how cost-volume-profit analysis may be used as a tool for
decision-making. (Give several examples.)
Q. 7.5
What are the basic assumptions that underlie cost-volume-profit
analysis?
Q. 7.6
What equation may be used to answer the question: how many units
must be sold in order to attain a desired level of net income?
Q. 7.7
What equation may be used to answer the question: how many
dollars of sales are required in order to attain a desired level of
net income?
Draw a graph illustrating break even point. On this chart, show total
sales, total variable cost, and total fixed costs. Shade in the areas of net
loss and net income.
| 131
132 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Q. 7.8
Define the following mathematical expressions:
a.
b.
c.
d.
P(Q) - V(Q)
P-V
1-v
Q(P - V )
Q. 7.9
If total contribution margin is $100,000 and fixed expenses is $80,000,
then the difference ($100,000- $80,000 = $20,000) is called?
Q. 7.10
When total fixed expenses equals total contribution margin, then this
point is called?
Q. 7.11
What effect do the following changes have on break even point:
a.
b.
c.
d.
e.
f.
Increase in price
Decrease in price
Increase in the variable cost rate
Decrease in the variable cost rate
Increase in fixed expenses
Decrease in fixed expenses
Q. 7.12
What assumption must be made in order to use cost-volume-profit
analysis in a multiple product business?
Q. 7.13
What effect does a change in the sales mix ratio have on the variable
cost percentage?
Q. 7.14
Assume a business has three products. What equation may be use to
compute the variable cost percentage?
Q. 7.15
Draw a chart that illustrates the use of this equation:
I = P(Q) - V(Q) - F
Note: ( use only one line to prepare this chart)
Explain how this chart shows break even point.
Q. 7.16
Given that price, the variable cost rates, and fixed costs have not
changed, explain how net income can decrease even though total sales
has increased.
Management Accounting
Exercise 7.1 • Contribution Margin Income Statement
The management accountant has done an analysis of costs and has arrived at
the following cost-volume-profit analysis data based on general ledger information for
the year ended December 31, 20xx.
Sales
$100,000
Variable expenses
Selling
$ 20,000
General and administrative
$ 10,000
Cost of goods sold
$ 50,000
Fixed
Selling
$ 5,000
General and administrative
$ 2,000
Cost of goods sold
$ 10,000
Units sold 1,000
Desired level of income
$ 50,000
Required:
1. Prepare a contribution margin income statement.
2. Determine the units that must be sold to attain the desired level of net income.
Exercise 7.2 • Preparing a Break even Graph
Based on the following information, prepare a break even chart.
Price $ 80.00
Variable cost rate
$ 60.00
Fixed expenses
$50,000
Desired net income
$80,000
Exercise 7.3 • Contribution Margin Income Statement
Sales
Expenses
Net income
Income Statement
(Sales - 10,000 units)
$200,000
$150,000
––––––––
$ 50,000
––––––––
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134 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
It has been determined that of the $150,000 of expenses, $100,000 were fixed.
The desired company net income is $150,000.
Required:
1. Based on the above information, prepare a contribution margin income
statement.
2.
Answer the following:
a. Contribution margin per unit of product – ––––––––––––––––––––
b. Variable cost rate
– ––––––––––––––––––––
c. Total desired contribution
– ––––––––––––––––––––
d. Break even point
– ––––––––––––––––––––
e. Target income point
– ––––––––––––––––––––
– ––––––––––––––––––––
Exercise 7.4 • Cost-Volume-Profit Relationships
Cost-Volume-Profit Chart
$
I
E
K
M
J
L
C
N
G
A
D
B
F
H
Q
Based on the above cost-volume-profit chart, identify the following line segments:
Line Segments
– –––––––––––––––
1 A - B
––––––––––––––––––––––––––––––––––––––––––
2 C - D
––––––––––––––––––––––––––––––––––––––––––
3 E - F
––––––––––––––––––––––––––––––––––––––––––
4 G - H
––––––––––––––––––––––––––––––––––––––––––
5 I - J
––––––––––––––––––––––––––––––––––––––––––
6 K - L
––––––––––––––––––––––––––––––––––––––––––
7 M - N
––––––––––––––––––––––––––––––––––––––––––
Management Accounting
Exercise 7.5 • Computing New Target Income Point
The owner of the Brown Retail Company believes that current sales volume is less
than potential because of inadequate advertising. He has tentatively decided to
increase his advertising budget by $2,000. Last year’s income statement was as
follows:
Sales (1,000 units @ $20.00)
$20,000
Variable expenses
$10,000
–––––––
Contribution margin
$10,000
Fixed expenses
$ 6,000
–––––––
Net income
$ 4,000
–––––––
Advertising, if increased, will change from $2,000 to $4,000. The maximum market
potential is probably between 1,300 and 1,400 units of product.
Required: Evaluate this proposed increase in advertising. To offset the increase in
advertising, by how much must sales increase in units.
Exercise 7.6 • Computing Break even point and Target Income Point
The following information from the records of the Ajax Manufacturing Company has
been provided to you:
Sales price:
Product A
Product B
Product C
$ 60.00
$ 40.00
$100.00
Variable costs:
Product A
Product B
Product C
$ 45.00
$ 30.00
$ 40.00
Units sold:
Product A
Product B
Product C
$ 1,000
$ 2,000
$ 3,000
Fixed costs for each product was determined as follows:
Product A
Product B
Product C
$40,000
$30,000
$80,000
Common fixed costs of the business are $200,000.
| 135
136 | CHAPTER SEVEN • Cost-Volume-Profit Analysis
Required:
1.
2.
3.
4.
5.
Compute the variable cost percentage for each product.
Compute the contribution margin percentage for each product.
Compute the break even point of each product.
Compute the break even point of the business as a whole.
Explain how it is possible for each product to break even yet the business
as a whole is operating at a loss.
6. Suppose the sales mix ratio rather than 1:2:3 becomes 3:1:2. How would
this change in the sales mix ratio affect the variable cost percentage?
Exercise 7.7 • Computing Target Income Point After Taxes
The Acme Manufacturing Company income statement for the year ended was as
follows:
Sales (10,000 units)
$200,000
Variable expenses 120,000
_ _______
Contribution margin
$ 80,000
Fixed expenses 60,000
_ _______
Net income
$ 20,000
Tax expense
8,000
_ _______
Net income after taxes
$ 12,000
_ _______
Required:
The company would like to have an after tax income of $50,000. What level of sales
is required to attain this level of after tax net income?