LEARNING OBJECTIVES
1.
DISTINGUISH BETWEEN VARIABLE AND FIXED COSTS.
2.
EXPLAIN THE SIGNIFICANCE OF THE RELEVANT RANGE.
3.
EXPLAIN THE CONCEPT OF MIXED COSTS.
4.
LIST THE FIVE COMPONENTS OF COST-VOLUME-PROFIT
ANALYSIS.
5.
INDICATE WHAT CONTRIBUTION MARGIN IS AND HOW IT
CAN BE EXPRESSED.
6.
IDENTIFY THE THREE WAYS TO DETERMINE THE
BREAK-EVEN POINT.
7.
GIVE THE FORMULAS FOR DETERMINING
REQUIRED TO EARN TARGET NET INCOME.
8.
DEFINE MARGIN OF SAFETY, AND GIVE THE FORMULAS
FOR COMPUTING IT.
SALES
CHAPTER REVIEW
Cost Behavior Analysis
1.
Cost behavior analysis is the study of how specific costs respond to changes in the level of business
activity. A knowledge of cost behavior helps management plan operations and decide between
alternative courses of action.
2.
The activity index identifies the activity that causes changes in the behavior of costs; examples include
direct labor hours, sales dollars, and units of output. Once an appropriate activity index is chosen, costs
can be classified as variable, fixed or mixed.
Variable and Fixed Costs
3.
(L.O. 1) Variable costs are costs that vary in total directly and proportionately with changes in the
activity level. Examples of variable costs include direct materials and direct labor, cost of goods sold,
sales commissions, and freight-out. A variable cost may also be defined as a cost that remains the
same per unit at every level of activity.
4.
Fixed costs are costs that remain the same in total regardless of changes in the activity level. Examples
include property taxes, insurance, rent, supervisory salaries, and depreciation. Fixed costs per unit vary
inversely with activity; as volume increases, unit cost declines and vice versa.
Relevant Range
5.
(L.O. 2) The range over which a company expects to operate during the year is called the relevant
range. Although a linear (straight-line) relationship for costs may not be realistic, the linear
assumption produces useful data for CVP analysis as long as the level of activity remains within
the relevant range.
Mixed Costs
6.
(L.O. 3) Mixed costs are costs that contain both a variable element and a fixed element; they increase
in total as the activity level increases, but not proportionately. For purposes of CVP analysis, mixed costs
must be classified into their fixed and variable elements.
7.
The high-low method uses the total costs incurred at the high and low levels of activity. The difference
in costs represents variable costs, since only the variable cost element can change as activity levels
change.
8.
The steps in computing fixed and variable costs under the high-low method are:
a. Determine variable cost per unit from the following formula:
Change in
Total Costs
b.
÷
High minus Low
Activity Level
=
Variable Cost
per Unit
Determine the fixed cost by subtracting the total variable cost at either the high or the low activity
level from the total cost at that activity level.
Cost-Volume-Profit Analysis
9.
10.
(L.O. 4) Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on
a company’s profits. It is a critical factor in such management decisions as profit planning, setting selling
prices, determining product mix, and maximizing use of production facilities.
CVP analysis considers the interrelationships among the following components: (a) volume or level of
activity, (b) unit selling prices, (c) variable cost per unit, (d) total fixed costs, and (e) sales mix.
Basic CVP Components
11.
The following assumptions underlie each CVP analysis:
a. The behavior of both costs and revenues is linear throughout the relevant range of the activity index.
b. All costs can be classified as either variable or fixed with reasonable accuracy.
c. Changes in activity are the only factors that affect costs.
d. All units produced are sold.
e. When more than one type of product is sold, the sales mix will remain constant. That is, the
percentage that each product represents of total sales will stay the same.
Contribution Margin
12.
(L.O. 5) Contribution margin is the amount of revenue remaining after deducting variable costs. The
formula for contribution margin per unit is:
Unit Selling
Price
13.
Unit Variable
–
=
Costs
Contribution
Margin per Unit
Contribution margin per unit indicates the amount available to cover fixed costs and contribute to income.
The formula for the contribution margin ratio is:
Contribution
Margin Per Unit
÷
Unit Selling
=
Price
Contribution
Margin Ratio
The ratio indicates the portion of each sales dollar that is available to apply to fixed costs and to
contribute to income.
Break-Even Analysis
14.
(L.O. 6) The break-even point is the level of activity at which total revenue equals total costs (both fixed
and variable). Knowledge of the break-even point is useful to management when it decides whether to
introduce new product lines, change sales prices on established products, or enter new market areas.
15.
A common equation used for CVP analysis is as follows:
Sales - Variable Costs - Fixed Costs = Net Income
16.
Under the contribution margin technique, the break-even point can be computed by using either the
contribution margin per unit or the contribution margin ratio.
17.
The formula, using unit contribution margin, is:
Fixed
Costs
18.
Margin per Unit
=
Break-even
Point in Units
The formula using the contribution margin is:
Fixed
Costs
19.
Contribution
÷
÷
Contribution
Margin Ratio
=
Break-even
Point in Dollars
A chart (or graph) can also be used as an effective means to determine and illustrate the break-even
point. A cost-volume-profit (CVP) graph is as follows:
Dollars (000)
Sales Line
900
Total Cost Line
800
700
600
Break-even Point
Variable Costs
500
400
300
Fixed Cost Line
200
100
0
Fixed Costs
200 400 600 800 1000 1200 1400 1600 1800
Units of Sales
Target Net Income
20.
(L.O. 7) Target net income is the income objective for individual product lines. The following equation is
used to determine target net income sales:
Required Sales - Variable Costs - Fixed Costs = Target Net Income
21.
Using the contribution margin technique, we can compute in either units or dollars the sales required to
meet a target net income. To compute the sales required in units the following formula is used:
(Fixed Costs + Target Net Income) ÷ Contribution Margin per Unit = Required Sales in Units
To compute the sales required in dollars, the contribution margin ratio is used rather than the contribution
margin per unit, as follows:
(Fixed Costs + Target Net Income) ÷ Contribution Margin Ratio = Required Sales in Dollars
Margin of Safety
22.
(L.O. 8) Margin of safety is the difference between actual or expected sales and sales at the breakeven point.
a.
The formula for stating the margin of safety in dollars is:
Actual (Expected)
Sales
b.
–
Break-even
Sales
=
Margin of Safety
in Dollars
The formula for determining the margin of safety ratio is:
Margin of Safety
in Dollars
÷
Actual (Expected)
Sales
=
Margin of
Safety Ratio
The higher the dollars or the percentage, the greater the margin of safety.
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 5-1
Indirect labor is a variable cost because it increases in total directly and
proportionately with the change in the activity level.
Supervisory salaries is a fixed cost because it remains the same in total regardless of
changes in the activity level.
Maintenance is a mixed cost because it increases in total but not proportionately with
changes in the activity level.
BRIEF EXERCISE 5-2
VARIABLE COST
Relevant Range
FIXED COST
Relevant Range
$10,000
$10,000
8,000
8,000
6,000
6,000
4,000
4,000
2,000
2,000
0
20
40
60
80 100
Activity Level
0
20
40
60
80 100
Activity Level
BRIEF EXERCISE 5-3
$60,000
Total Cost Line
COST
45,000
Variable Cost Element
30,000
15,000
Fixed Cost Element
0
500
1,000
1,500
2,000
2,500
Direct Labor Hours
BRIEF EXERCISE 5-4
High
Low
Difference
$15,000 – $13,500 =
$1,500
8,500 –
7,500 =
1,000
$1,500 ÷ 1,000 = $1.50—Variable cost per mile.
Total cost
Less: Variable costs
8,500 X $1.50
7,500 X $1.50
Total fixed costs
High
$15,000
Low
$13,500
12,750
$ 2,250
11,250
$ 2,250
The mixed cost is $2,250 plus $1.50 per mile.
BRIEF EXERCISE 5-5
High
Low
Difference
$66,100 – $32,000 = $34,100
40,000 – 18,000 =
22,000
$34,100 ÷ 22,000
Total cost
Less: Variable costs
40,000 X $1.55
18,000 X $1.55
Total fixed costs
= $1.55 per unit.
Activity Level
High
Low
$66,100
$32,000
62,000
000,000
$ 4,100
27,900
$ 4,100
BRIEF EXERCISE 5-6
1.
(a)
(b)
$288 = ($640 – $352)
45% ($288 ÷ $640)
2.
(c)
(d)
$207 = ($300 – $93)
31% ($93 ÷ $300)
3.
(e)
(f)
$1,300 = ($325 ÷ 25%)
$975 ($1,300 – $325)
BRIEF EXERCISE 5-7
RADIAL INC.
CVP Income Statement
For the Quarter Ended March 31, 2014
Sales ..................................................................................
Variable costs ($920,000 + $70,000 + $86,000) ................
Contribution margin .........................................................
Fixed costs ($440,000 + $45,000 + $98,000) ....................
Net income ........................................................................
BRIEF EXERCISE 5-8
(a)
$520Q – $286Q – $163,800 = $0
$2,400,000
1,076,000
1,324,000
583,000
$ 741,000
$234Q = $163,800
Q = 700 units
(b) Contribution margin per unit $234, or ($520 – $286)
X = $163,800 ÷ $234
X = 700 units
BRIEF EXERCISE 5-9
Contribution margin ratio = [($300,000 – $180,000) ÷ $300,000] = 40%
Required sales in dollars = $170,000 ÷ 40% = $425,000
BRIEF EXERCISE 5-10
If variable costs are 70% of sales, the contribution margin ratio is ($1 – $0.70) ÷ $1 =
.30.
Required sales in dollars = ($195,000 + $75,000) ÷ .30 = $900,000
BRIEF EXERCISE 5-11
Margin of safety = $1,000,000 – $840,000 = $160,000
Margin of safety ratio = $160,000 ÷ $1,000,000 = 16%
BRIEF EXERCISE 5-12
Contribution margin per unit $1.60 is ($6.00 – $4.40)
Required sales in units = ($480,000 + $1,500,000) ÷ $1.60 = 1,237,500.