CHAPTER 5 Cost-Volume-Profit ASSIGNMENT CLASSIFICATION TABLE Study Objectives
Questions
Brief Exerc Exercis ises es
1.
Disti istin nguish ish betw etween variable and fixed costs.
1, 2, 3, 6
1
1, 2, 3, 4, 5, 6
2.
Expl Explai ain n the the sign signif ific ican ance ce of the relevant range.
4, 5
2
2
3.
Expla xplain in the the con conce cep pt of of mixed costs.
6, 7, 8
1, 3, 4, 5
1, 3, 4, 5, 6
4.
List List the the fiv five e com compo pone nent nts s of of cost-volume-profit cost-volume-profit analysis.
9
5.
Indi Indica cate te wha whatt cont contri ribu buti tion on margin is and how it can be expressed.
10, 11, 17
6, 7
8, 9, 10, 11, 1A, 2A, 3A, 12, 13 4A, 5A
1B, 2B, 3B, 4B, 5B
6.
Iden Identi tify fy the the thr three ee ways ways to determine the break-even point.
12, 13, 14
8, 9
8, 9, 10, 11, 1A, 2A, 3A, 12, 13,14, 4A, 5A 16
1B, 2B, 3B, 4B, 5B
7.
Give the the for formul mulas for for determining sales required to earn target net income.
16
10, 12
14, 15
2A, 5A
2B, 5B
8.
Defi Define ne marg margin in of safe safety ty,, and give the formulas for computing it.
15
11
16
2A, 4A, 5A
2B, 4B, 5B
Exer Exercis cises es
A Problems
B Problems
1A
1B
1A
1B
7
5-1
ASSIGNMENT CHARACTERISTICS TABLE Problem Numb Number er
Descr Descrip ipti tion on
Difficulty Level
Time Allotted (min.)
1A
Dete Determ rmin ine e var varia iabl ble e and and fixe fixed d cos costs ts,, comp comput ute e bre break ak-e -eve ven n point, prepare a CVP graph, and determine net income.
Simple
20–30
2A
Prep Prepar are e a CVP CVP inc incom ome e sta state teme ment nt,, com compu pute te brea breakk-ev even en point, contribution margin ratio, margin of safety ratio, and sales for target net income.
Moderate
30–40
3A
Comp Comput ute e bre break ak-e -eve ven n poi point nt unde underr alt alter erna nati tive ve cour course ses s of action.
Simple
20–30
4A
Comp Comput ute e bre break ak-e -eve ven n poi point nt and and mar margi gin n of of saf safet ety y rat ratio io,, and prepare CVP income statement before and after changes in business environment. environment.
Moderate
20–30
5A
Comp Comput ute e bre break ak-e -eve ven n poi point nt and and mar margi gin n of of saf safet ety y rat ratio io,, and prepare a CVP income statement before and after changes in business environment. environment.
Moderate
20–30
1B
Dete Determ rmin ine e var varia iabl ble e and and fixe fixed d cos costs ts,, comp comput ute e bre break ak-e -eve ven n point, prepare a CVP graph, and determine net income.
Simple
20–30
2B
Prep Prepar are e a CVP CVP inc incom ome e sta state teme ment nt,, com compu pute te brea breakk-ev even en point, contribution margin ratio, margin of safety ratio, and sales for target net income.
Moderate
30–40
3B
Comp Comput ute e bre break ak-e -eve ven n poi point nt unde underr alt alter erna nati tive ve cour course ses s of action.
Simple
20–30
4B
Comp Comput ute e bre break ak-e -eve ven n poi point nt and and mar margi gin n of of saf safet ety y rat ratio io,, and prepare CVP income statement before and after changes in business environment. environment.
Moderate
20–30
5B
Comp Comput ute e bre break ak-e -eve ven n poi point nt and and mar margi gin n of of saf safet ety y rat ratio io,, and and prepare a CVP income statement before and after changes in business environment.
Moderate
20–30
5-2
BLOOM’S TAXONOMY TABLE
s m e l b o r P d n a s e s i c r e x E r e t p a h C f o d n E d n a s e v i t c e j b O y d u t S , y m o n o x a T s ’ m o o l B n e e w t e b t r a h C n o i t a l e r r o C
B 5 5 P
n o i t a u l a v E
A B A A B B 3 - 3 - 4 - 5 - 4 - 5 5 5 5 5 5 5 P P P P P P
s i s e h t n y S s i s y l a n B A 3 6 A - - 1 - 1 5 5 5 5 E E P P n o i t a c i l p p A 5 5 E n 1 - 2 o 5 1 - i s E 5 5 n B E E e h e r p m 1 - 2 - 3 - 6 o 5 5 5 C Q Q Q 5 Q e g d e l w o 4 n K 5 E
e v i t c e j b O y d u t S
d n a e l b a i r a v n e e w t e b . h s t s i s u o g c n i t d s e i x D i f . 1 *
A A B B A 3 - 4 - 3 - 4 - 5 5 5 5 5 5 P P P P P
B B 4 - 5 5 5 P P
A B 5 - 5 5 5 P P
B 1 5 P 2 5 E B
2 5 E
B 2 5 P
3 - A 5 3 - 1 E 5 5 B E P
6 B B - A A 5 1 - 2 - 1 - 2 E 5 5 5 5 B P P P P
6 A A B B 1 - 1 - 2 - 1 - 2 5 5 5 5 5 E P P P P
A B 2 - 2 5 5 P P
5 - 6 5 5 E E
0 1 2 3 1 - 1 - 1 - 1 5 5 5 5 E E E E
0 1 2 3 4 1 - 1 - 1 - 1 - 1 5 5 5 5 5 E E E E E
2 4 5 1 - 1 - 1 5 5 5 E E E
4 - 5 8 - 5 5 5 E E Q B B
1 7 6 - 7 - 9 1 - 1 - 5 5 8 - 5 5 E E 5 5 Q Q B B E E
3 8 - 9 - 9 1 - 5 5 8 - 5 E E 5 5 Q B B E E
0 2 6 1 - 1 1 - 5 5 5 E E Q B B
1 5 E
4 - 5 5 5 Q Q
1 6 - 7 - 5 5 5 E Q Q B
e h t f o e c n a c i f i n . g e i s g e n a h r t t n n i a a l v p l e x e E r . 2 *
4 5 E . s t s o c d e x i m f o t p e c n o c e h t n i a l p x E . 3 *
A A 4 - 5 5 5 P P
9 5 Q
0 1 5 Q
2 4 1 - 1 5 5 Q Q
n i . g r d a e m s s n e r o i t p u x e b i e r t b n n o a c c t t a i h w w o e h t a d c n i d a n i s I
e n i m r e t e d o t s . y t a n w i e o p e r n h t e v e e h t k a y e f i r t b n e e d I h t
7 5 E
. f s o i s s l y t n a e n n a o i t p f m o o r c p e e v m i f l u e o h v t t t s s i o L c . . 4 5 * *
. 6 *
5-3
6 A 1 - 2 5 5 E P
1 5 1 1 - 5 5 E Q B
s i s y l a n u A e o l s Y a a t i r C u e o g s b a i c n h A a t l l M E A
g n n i k e i o a h t t a M z i n s n s o i o a s r g i c r c A e O D s b u e c W o e F h t d l r g o i n r W - l o l a p e x R E n o i t a c i n u m m o C
g n t i n e n i t m r e e g r t a e t d r n o r a f s e o a t l u d e m r r i o f u . e q e e h t r m e s e o v l i a c n G s i . 7 *
e v i . g t i d g n n a i e , t i v u y t t p c e f m e a o p s s r f c e o r o P f r n i s g a u r l o a u Y m m g e r n o i n f i f e n e e D h t d a o r . 8 B *
STUDY 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-VOLUMEPROFIT 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 SALES REQUIRED TO EARN TARGET NET INCOME.
8.
DEFINE MARGIN OF SAFETY, AND GIVE THE FORMULAS FOR COMPUTING IT.
5-4
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.
(S.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.
(S.O. 2) The range over which a company expects to operate during the year is called the relevant range. Within the relevant range a straight-line relationship exists for both variable and fixed costs.
Mixed Costs
6.
(S.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.
(S.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. 5-5
10.
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.
(S.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.
(S.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
÷
Contribution Margin per Unit
5-6
=
Break-even Point in Units
18.
The formula using the contribution margin is: Fixed Costs
19.
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 breakeven 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
500 400 300 200
Fixed Cost Line
100
Fixed Costs
0
200 400 600 800 1000 1200 1400 1600 1800 Units of Sales
Target Net Income
20.
(S.O. 7) Target net income is the income objective for individual product lines. The follow-ing equation is used to determine target net income sales: Required Sales = Variable Costs + Fixed Costs + Target Net Income
Margin of Safety
21.
(S.O. 8) Margin of safety is the difference between actual or expected sales and sales at the break-even 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. 5-7
LECTURE OUTLINE A.
Cost Behavior Analysis.
1. Cost behavior analysis is the study of how specific costs respond to changes in the level of business activity. 2. The activity index identifies the activity that causes changes in the behavior of costs. With an appropriate activity index, companies can classify the behavior of costs into three categories: variable, fixed, or mixed.
TEACHING TIP
Use ILLUSTRATION 5-1 to define and graphically illustrate variable and fixed cost classifications. Emphasize total cost behavior with changes in activity levels, then demonstrate unit cost behavior with activity level changes. Point out that for internal analysis of operations by management, having costs classified into variable and fixed classifications facilitates CVP analysis. 3. Variable costs are costs that vary in total directly and proportionately with changes in the activity level. A variable cost 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. a.
Because total fixed costs remain constant as activity changes, it follows that fixed costs per unit vary inversely with activity.
b.
Examples of fixed costs include property taxes, insurance, rent, supervisory salaries, and depreciation on buildings and equipment.
5-8
5. The relevant range is the range of activity over which a company expects to operate during a year. It is important in CVP analysis because the behavior of costs is assumed to be linear (straight-line) throughout the relevant range. Although the linear relationship may not be completely realistic, the linear assumption produces useful data for CVP analysis as long as the level of activity remains within the relevant range. 6. Mixed costs are costs that contain both a variable element and a fixed element. Mixed costs change in total but not proportionately with changes in the activity level. a.
For purposes of CVP analysis, mixed costs must be classified into their fixed and variable elements. One method that management may use to classify these costs is the high-low method.
TEACHING TIP
Use ILLUSTRATION 5-2 to define and graphically illustrate the mixed costs classification. Point out that for CVP analysis, the variable and fixed elements of a mixed cost should be separated using a method such as the high-low method. b.
B.
The high-low method uses the total costs incurred at the high and low levels of activity. The difference in costs between the high and low levels represents variable costs, since only the variable cost element can change as activity levels change. Fixed costs are determined by subtracting the total variable cost at either the high or low activity level from the total cost at that activity level.
Cost-Volume-Profit Analysis.
1. Cost-volume-profit (CVP) analysis is the study of the effects of changes in costs and volume on a company’s profits. CVP analysis is important in profit planning. It is useful in setting selling prices, determining product mix, and maximizing use of production facilities.
5-9
TEACHING TIP
ILLUSTRATION 5-3 lists the basic components and assumptions that underlie
CVP analysis. 2. 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.
e.
Sales mix.
3. 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.
Costs can be classified accurately as either variable or fixed.
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 (the percentage that each product represents of total sales will stay the same).
4. Contribution margin is the amount of revenue remaining after deducting variable costs. It can be expressed as a per unit amount or as a ratio.
5-10
TEACHING TIP
Use ILLUSTRATION 5-4 to demonstrate the calculation of the contribution margin on a unit basis and as a ratio. Emphasize the importance of the contribution margin in CVP analysis.
C.
a.
Contribution Margin per Unit = Unit Selling Price – Unit Variable Costs.
b.
Contribution Margin Ratio = Contribution Margin per Unit ÷ Unit Selling Price.
Break-even Analysis.
1. At the break-even point, the company will realize no income but will suffer no loss. 2. 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. 3. The break-even point can be: a.
Computed from a mathematical equation: Break-even Point in Dollars = Total Variable Costs + Total Fixed Costs. The break-even point in units can be computed by using unit selling prices and unit variable costs.
TEACHING TIP
ILLUSTRATION 5-5 provides an example of break-even analysis calculated by
the equation approach. The break-even point can be stated in terms of units or sales dollars. 5-11
b.
Computed by using contribution margin: Break-even Point in Units = Fixed Costs ÷ Contribution Margin per Unit. Break-even Point in Dollars = Fixed Costs ÷ Contribution Margin Ratio.
TEACHING TIP
ILLUSTRATION 5-6 provides an example of computing the break-even point in
dollars and units using the contribution margin approach. c.
Derived from a CVP graph at the intersection of the total-cost line and the total-sales line.
TEACHING TIP
ILLUSTRATION 5-7 provides an example of determining the break-even point in
dollars and units by using a CVP graph. Point out that the equation approach (Illustration 5-5), the contribution margin technique (Illustration 5-6), and the CVP graph all provide the same answer and are alternative approaches to CVP analysis. 4. The income objective set by management is called target net income. To meet target net income, required sales must be determined. a.
Mathematical equation: Required Sales = Variable Costs + Fixed Costs + Target Net Income. Required sales may be expressed in either sales units or sales dollars.
b.
Contribution margin technique: Fixed Costs + Target Net Income ÷ Contribution Margin Ratio = Required Sales in Dollars.
c.
Graphic presentation: In the profit area of the CVP graph, the distance between the sales line and the total cost line at any point equals net income. A company can find required sales by analyzing the differences between the two lines until the desired net income is found. 5-12
TEACHING TIP
ILLUSTRATION 5-8 provides an example of calculating target net income using
the mathematical equation approach, contribution margin technique, and the CVP graph (see Illustration 5-7 at 14,000 units of activity). 5. Margin of safety is the difference between actual or expected sales and sales at the break-even point. The margin of safety can be expressed in dollars or as a ratio. a.
Margin of Safety in Dollars = Actual (Expected) Sales – Break-even Sales.
b.
Margin of Safety Ratio = Margin of Safety in Dollars ÷ Actual (Expected) Sales.
5-13
20 MINUTE QUIZ Circle the correct answer. True/False 1.
The range over which a company is expected to operate is called the relevant range of the activity index. True
2.
A mixed cost contains both selling and administrative cost elements. True
3.
False
In a CVP income statement, contribution margin is reported in the body of the statement. True
10.
False
If the unit contribution margin is $300 and fixed costs are $240,000 then the break-even point in units would be 800 units. True
9.
False
Sales mix is the percentage that each product represents of total sales. True
8.
False
The contribution margin is the amount of revenue remaining after deducting fixed costs. True
7.
False
If revenue = $80 and variable cost = 40% of revenue, then contribution margin = $48. True
6.
False
If a salesperson incurs $2,000 of expenses in servicing two customers and $4,000 of expenses in servicing four customers, the fixed costs are $1,000. True
5.
False
Variable costs are costs that remain the same per unit at every level of activity. True
4.
False
False
Margin of safety is the difference between actual sales and contribution margin. True
False
5-14
Multiple Choice
1.
Which of the following is a false statement regarding assumptions of CVP analysis? a. Total fixed costs remain constant over the relevant range. b. Unit selling prices are constant. c. Changes in volume or level of activity increase variable costs per unit. d. All units produced are sold.
2.
Mixed costs may be separated into fixed costs and variable costs by using a. the relevant range method. b. the high-low method. c. the contribution margin method. d. all of the above.
3.
If the unit selling price is $500, the unit variable cost is $300, and the total monthly fixed costs are $300,000, then the contribution margin ratio is a. 30%. b. 40%. c. 50%. d. 60%.
4.
If activity level increases 25% and a specific cost increases from $40,000 to $50,000, this cost would be classified as a a. variable cost. b. mixed cost. c. fixed cost. d. none of the above.
5.
If total fixed costs are $900,000 and variable costs as a percentage of unit selling price are 40%, then the break-even point in dollars is a. $1,500,000. b. $360,000. c. $2,250,000. d. not determinable with the information given.
5-15
ANSWERS TO QUIZ True/False
1. 2. 3. 4. 5.
True False True False True
6. 7. 8. 9. 10.
False True True True False
Multiple Choice
1. 2. 3. 4. 5.
c. b. b. a. a.
5-16
ILLUSTRATION 5-1 COST CLASSIFICATIONS—VARIABLE AND FIXED COSTS
VARIABLE COST TOTAL COST BEHAVIOR
$ t s o C
Costs that vary in total directly and proportionately with changes in activity levels. Activity
UNIT COST BEHAVIOR: Variable cost per unit remains constant for all activity levels. FIXED COST TOTAL COST BEHAVIOR
$ t s o C
Costs that remain the same in total regardless of changes in activity levels.
Activity UNIT COST BEHAVIOR: Fixed cost per unit varies inversely with changes in activity levels. Note: Cost behavior assumptions are valid only in the relevant range.
5-17
ILLUSTRATION 5-2 COST CLASSIFICATION—MIXED COSTS
MIXED COST TOTAL COST BEHAVIOR
$ t s o C
Costs that contain both variable and fixed elements, and increase in total but not proportionately with changes in activity levels. Activity
EXAMPLE High Change in activity level
5,000 hours Low
Jan. Feb. Mar. Apr. May June
Machine Hours 5,000 8,000 4,000 6,000 3,000 6,500
Power Costs $ 800 1,100 700 $500 900 600 950
Change in costs
1. Determine variable cost per unit:
Change in Total Cost $500
÷
High – Low Activity Levels 5,000
2. Determine fixed cost: Total cost Less: Variable cost 8,000 × $.10 = 3,000 × $.10 = Total fixed cost
=
Variable Cost per Unit $.10 per hour
Activity Level High Low $1,100 $600 800 $ 300
300 $300
Power costs are $300 per month plus $.10 per hour. 5-18
ILLUSTRATION 5-3 BASIC COMPONENTS AND ASSUMPTIONS THAT UNDERLIE CVP ANALYSIS INTERRELATIONSHIPS AMONG THE BASIC COMPONENTS
1. Volume or level of activity. 2.
Unit selling prices.
3.
Variable cost per unit.
4.
Total fixed costs.
5.
Sales mix.
ASSUMPTIONS FOR CVP ANALYSIS
1. The behavior of both costs and revenues is linear throughout the relevant range of the activity index. 2. All costs can be classified accurately as either variable or fixed. 3. Changes in activity are the only factors that affect costs. 4. All units produced are sold. 5. When more than one type of product is sold, the sales mix will remain constant.
5-19
ILLUSTRATION 5-4 CONTRIBUTION MARGIN CONTRIBUTION MARGIN: REVENUE REMAINING AFTER DEDUCTING VARIABLE COSTS
Example: Selling price Variable costs Contribution margin
Per Unit
%
$25 15 $10
100% 60% 40%
CONTRIBUTION MARGIN PER UNIT
Unit Selling Price
–
$25
Unit Variable Costs
=
$15
Contribution Margin Per Unit $10
CONTRIBUTION MARGIN RATIO
Contribution Margin Per Unit $10
÷
Unit Selling Price $25
5-20
=
Contribution Margin Ratio 40%
ILLUSTRATION 5-5 BREAK-EVEN ANALYSIS—EQUATION APPROACH
EXAMPLE:
Per Unit % $25 100% 15 60% $10 40% $100,000
Selling price Variable costs Contribution margin Fixed costs
Break-even point in dollars: Let X = sales dollars at break-even point X = .60 X + $100,000 .40 X = $100,000 X = $250,000 Break-even point in units: Let X = number of units to sell to break-even $25 X = $15 X + $100,000 $10 X = $100,000 X = 10,000 units Proof:
Sales Variable costs Contribution margin Fixed costs Net income
$250,000 (10,000 units × $25) 150,000 (10,000 units × $15) 100,000 (10,000 units × $10) 100,000 $ 0
5-21
ILLUSTRATION 5-6 BREAK-EVEN ANALYSIS—CONTRIBUTION MARGIN TECHNIQUE
EXAMPLE:
Per Unit % $25 100% 15 60% $10 40% $100,000
Selling price Variable costs Contribution margin Fixed costs
Break-even point in dollars:
Fixed Costs
÷
Contribution Margin Ratio
$100,000
=
Break-even Point in Dollars
.40
$250,000
Contribution Margin per Unit
Break-even Point in Units
Break-even point in units:
Fixed Costs $100,000
÷
$10
5-22
=
10,000 units
ILLUSTRATION 5-7 CVP GRAPH
Sales Line
450 400
Profit Area
350 300
Break-even Point
) 0 0 250 0 ( s r a l l o 200 D
150 100
Loss Area
Variable Costs Fixed Cost Line
Fixed Costs
50 0
Total Cost Line
2,000
6,000
10,000 14,000 Units of Sales
5-23
18,000
ILLUSTRATION 5-8 TARGET NET INCOME
EXAMPLE: Target net income — $40,000 Per Unit % Selling price $25 100% Variable costs 15 60% Contribution margin $10 40% Fixed costs $100,000 EQUATION APPROACH Required sales in units: Let X = unit sales for target net income of $40,000 $25 X = $15 X + $100,000 + $40,000 $10 X = $140,000 X = 14,000 units Required sales in dollars: Let X = sales dollars for target net income of $40,000 X = .60 X + $100,000 + $40,000 .40 X = $140,000 X = $350,000 CONTRIBUTION MARGIN TECHNIQUE Required sales in units:
Fixed Costs + Target Income
÷
Contribution Margin per Unit
$140,000
=
Required Sales in Units
$10
14,000 units
Contribution Margin Ratio
Required Sales in Dollars
Required sales in dollars:
Fixed Costs + Target Income $140,000
÷
.40 5-24
=
$350,000
