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Cost-Volume-Profit

Analysis

L 11

Chapter 20

20-1 Copyright 2014 Pearson Education, Inc. Publishing as Prentice Hall

Learning Objectives

1. Determine how changes in

volume affect costs

2. Calculate operating income

using contribution margin and

contribution margin ratio

3. Use cost-volume-profit (CVP)

analysis for profit planning


Learning Objective 1

Determine how

changes in volume

affect costs


Types of costs

Variable costs

Fixed costs

Mixed costs

Copyright 2014 Pearson Education, Inc. Publishing as Prentice Hall 20-4

Variable Costs Batteries in Tablets

Number of

Tablets Produced

Variable Cost

per Tablet

Total

Variable Cost

0 tablets $55 $ 0

25 tablets 55 1,375

50 tablets 55 2,750

75 tablets 55 4,125

100 tablets 55 5,500


Total Variable Costs


Total Fixed Costs


Fixed Costs

Total

Fixed Costs

Number of

Tablets Produced

Fixed Cost

per Tablet

$12,000 25 tablets $480

12,000 50 tablets 240

12,000 75 tablets 160

12,000 100 tablets 120


Characteristics of

Variable and Fixed Costs


Mixed Costs Cell Phone

$100 per month plus $0.10 for each minute of use

Number of

Minutes Used

Total Fixed

Cost

Total Variable

Cost

Total Cost

100 minutes $100 $10 $110

200 minutes 100 20 120

300 minutes 100 30 130

400 minutes 100 40 140

500 minutes 100 50 150


Mixed Costs


Manufacturing Equipment

Maintenance Costs

Number of

Tablets Produced

Total

Maintenance

Cost

1st Quarter 360 tablets $1,720

2nd Quarter 415 tablets 1,830

3rd Quarter 480 tablets 1,960

4th Quarter 240 tablets 1,480


Highest Volume

Lowest Volume

High-Low Method

Step 1

Step 1: Identify the highest and lowest levels of

activity, and calculate the variable cost per unit.

Variable cost per unit = Change in total cost / Change in volume of activity

= (Highest cost Lowest cost) / (Highest volume Lowest volume)


High-Low Method

Step 1

Step 1: Identify the highest and lowest levels of

activity, and calculate the variable cost per unit.

Variable cost per unit = Change in total cost / Change in volume of activity

= (Highest cost Lowest cost) / (Highest volume Lowest volume)

= ($1,960 $1,480) / (480 tablets 240 tablets)

= $480 / 240 tablets

= $2 per tablet


High-Low Method

Step 2

Step 2: Calculate the total fixed cost.

Total fixed cost = Total mixed cost Total variable cost

= Total mixed cost (Variable cost per unit Number of units)


High-Low Method

Step 2

Step 2: Calculate the total fixed cost.

Total fixed cost = Total mixed cost Total variable cost

= Total mixed cost (Variable cost per unit Number of units)

= $1,960 ($2 per tablet 480 tablets)

= $1,960 $960

= $1,000


High-Low Method

Step 3

Step 3: Create and use an equation to show the

behavior of a mixed cost.

Total mixed cost = (Variable cost per unit Number of units) + Total fixed cost


High-Low Method

Step 3

Step 3: Create and use an equation to show the

behavior of a mixed cost.

Total mixed cost = (Variable cost per unit Number of units) + Total fixed cost

Total manufacturing maintenance cost = ($2 per tablet Number of tablets) + $1,000


Estimated manufacturing equipment

maintenance cost at 400 tablets



Estimated manufacturing equipment

maintenance cost at 400 tablets


= ($2 per tablet 400 tablets) + $1,000

= $1,800


Relevant Range


Following is a list of costs for a furniture

manufacturer that specializes in wood tables.

Classify each cost as variable, fixed, or mixed

relative to tables produced and sold.

1. Wood used to build tables






1. Wood used to build tables

Variable






2. Depreciation on saws and other

manufacturing equipment






2. Depreciation on saws and other

manufacturing equipment

Fixed






3. Compensation for sales representatives paid

on a salary plus commission basis






3. Compensation for sales representatives paid

on a salary plus commission basis

Mixed






4. Supervisors salary






4. Supervisors salary

Fixed






5. Wages of production workers






5. Wages of production workers

Variable



Calculate operating

income using

contribution margin

and contribution

margin ratio


Contribution Margin

If Smart Touch Learning sells 200 tablets for $500

each that incur variable costs of $275 each, then

the contribution margin is:

Contribution margin = Net sales revenue Variable costs


Contribution Margin



the contribution margin is:

Contribution margin = Net sales revenue Variable costs

= ($500 per tablet 200 tablets) ($275 per tablet 200 tablets)

= $100,000 $55,000

= $45,000


Unit Contribution Margin



the unit contribution margin is:

Unit contribution margin = Net sales revenue per unit Variable costs per unit


Unit Contribution Margin



the unit contribution margin is:

Unit contribution margin = Net sales revenue per unit Variable costs per unit

= $500 per tablet $275 per tablet

= $225 per tablet


Contribution Margin Ratio



the contribution margin ratio is:

Contribution margin ratio = Contribution margin / Net sales revenue


Contribution Margin Ratio



the contribution margin ratio is:

Contribution margin ratio = Contribution margin / Net sales revenue

= $45,000 / $100,000

= 45%

= $225 per tablet / $500 per tablet

= 45%


Traditional Income

Statement Format

Net sales revenue

Cost of goods sold

= Gross profit

Selling and administrative expenses

= Operating income


Period costs (some variable, some fixed)

Product cost (some variable, some fixed)

Contribution Margin

Income Statement Format

Net sales revenue

Variable costs

= Contribution margin

Fixed Costs

= Operating income


Some product, some period

Some product, some period

A furniture manufacturer specializes in wood

tables. The tables sell for $100 and incur $40 in

variable costs. The company has $6,000 in fixed

costs per month.

6. Prepare a contribution margin income statement

for one month if the company sells 200 tables.

7. What is the total contribution margin for the month

when the company sells 200 tables?


6. Sales revenue (200 tables $100 per table) $ 20,000

Variable costs (200 tables $40 per table) 8,000

Contribution margin (200 tables $60 per table) 12,000

Fixed costs 6,000

Operating income $ 6,000

7. Contribution margin = $12,000





costs per month.

8. What is the unit contribution margin?

9. What is the contribution margin ratio?





costs per month.


Unit contribution margin = $100 per table $40 per table = $60 per table






costs per month.


Unit contribution margin = $100 per table $40 per table = $60 per table


Contribution margin ratio = $60 per table / $100 per table = 60%



Use cost-volume-profit

(CVP) analysis for

profit planning


Cost-Volume-Profit Analysis

Assumes the Following:

The price per unit does not change as volume changes.

Managers can classify each cost as variable, fixed, or mixed.

The only factor that affects total costs is change in volume, which increases variable and mixed

costs.

Fixed costs do not change.

There are no changes in inventory levels.


Target ProfitThree Approaches

Equation approach

Contribution margin approach

Contribution margin ratio approach


Equation Approach

Net sales revenue Total costs = Operating income


Equation Approach

Net sales revenue Total costs = Operating income

Net sales revenue Variable costs Fixed costs = Operating income


Equation Approach

Smart Touch Learning sells tablets for $500 each, variable costs are $275 each, and fixed costs are $12,000 per month. If the company desires to earn $6,000 in profits each month, how many tablets must it sell?

Net sales revenue Variable costs Fixed costs = Target profit


Equation Approach



($500 per unit Units sold) ($275 per unit Units sold) - $12,000 = $ 6,000

[($500 $275 per unit) Units sold] - $12,000 = $ 6,000

$225 per unit Units sold = $12,000 + $6,000

$225 per unit Units sold = $18,000

Units sold = $18,000 / $225 per unit

Units sold = 80 units


Equation Approach Check Your Calculation



Equation Approach Check Your Calculation


($500 per unit 80 units) ($275 per unit 80 units) $12,000 = $6,000

$40,000 -- $22,000 $12,000 = $6,000


Contribution Margin Approach


Required sales in units = Fixed costs + Target profit

Contribution margin per unit






= $12,000 + $6,000

$225 per unit

= 80 units


Contribution Margin ApproachCheck Your Calculation

Net sales revenue

Variable costs

= Contribution margin

Fixed costs

= Operating income


Contribution Margin ApproachCheck Your Calculation

Net sales revenue ($500 per unit 80 units) $ 40,000

Variable costs ($275 per unit 80 units) 22,000

= Contribution margin ($225 per unit 80 units) 18,000

Fixed costs 12,000

= Operating income $ 6,000


Contribution Margin Ratio Approach


Required sales in dollars = Fixed costs + Target profit

Contribution margin ratio






= $12,000 + $6,000

45%

= $40,000


Breakeven Point Calculations

for Smart Touch Learning



for Smart Touch Learning Exhibit 21-6 Breakeven Point Calculations for Smart Touch Learning

Equation approach

Net sales revenue Variable costs Fixed Costs = Target Profit

($500 per unit Units sold) ($275 per unit Units sold) $12,000 = $ 0

[($500$275 per unit) Units sold] $12,000 = $ 0

$225 per unit Units sold = $ 12,000

Units sold = $ 12,000/$225 per unit

Units sold = 54 units*



*Actual result of 53.3333 rounded up to the next full unit as it is not possible to sell partial tablets.




Equation approach








Required sales in units = Fixed Costs + Target profit


= $12,000 + $0

$225 per unit

= 54 units*






Equation approach








Required sales in units = Fixed Costs + Target profit


= $12,000 + $0

$225 per unit

= 54 units*


Required sales in dollars = Fixed Costs + Target profit


= $12,000 + $0

45%

= $26,667**


**Actual result of $26,666.6667 rounded up to next full dollar.


Cost-Volume-Profit Graph




variable costs. The company has $6,000 in

fixed costs per month. The company desires to

earn an operating profit of $12,000 per month.


10. Calculate the required sales in units to earn the

target profit using the equation method.



target profit using the equation method.


($100 per unit Units sold) ($40 per unit Units sold) $6,000 = $12,000

[($100 $40 per unit) Units sold] $6,000 = $12,000

$60 per unit Units sold = $ 6,000 + $12,000

$60 per unit Units sold = $18,000

Units sold = $18,000 / $60 per unit

Units sold = 300 units



target profit using the contribution margin

method.



target profit using the contribution margin

method.

Required sales in units = Fixed costs + Target profit Contribution margin per unit

= $6,000 + $12,000

$100 per unit $40 per unit

= 300 units


12. Calculate the required sales in dollars to earn

the target profit using the contribution margin

ratio method.


12. Calculate the required sales in dollars to earn

the target profit using the contribution margin

ratio method.

Contribution margin ratio = $60 per table / $100 per table = 60%



= $6,000 + $12,000

60%

= $30,000


13. Calculate the required sales in units to

breakeven using the contribution margin

method.


13. Calculate the required sales in units to

breakeven using the contribution margin

method.



= $6,000 + $0


= 100 units


Change in the Selling PriceContribution Margin Approach

Smart Touch Learning believes it must cut the selling price to $475 per tablet. Variable costs remain at $275 per tablet. Fixed costs stay at $12,000. How many tablets must be sold to break even?




Change in the Selling PriceContribution Margin Approach

Smart Touch Learning believes it must cut the selling price to $475 per tablet. Variable costs remain at $275 per tablet. Fixed costs stay at $12,000. How many tablets must be sold to break even?



= $12,000 + $0


= 60 units


Change in the Variable CostsContribution Margin Approach

Smart Touch Learnings selling price remains at $500 per tablet. Variable costs increase to $285 per tablet. Fixed costs stay at $12,000. How many tablets must be sold to break even?




Change in the Variable CostsContribution Margin Approach

Smart Touch Learnings selling price remains at $500 per tablet. Variable costs increase to $285 per tablet. Fixed costs stay at $12,000. How many tablets must be sold to break even?



= $12,000 + $0


= 56 units*

* Rounded up to next full unit


Change in the Fixed CostsContribution Margin Approach

Smart Touch Learnings selling price remains at $500 per tablet. Variable costs stay at $275 per tablet. Fixed costs increase to $15,000. How many tablets must be sold to break even?




Change in the Fixed CostsContribution Margin Approach

Smart Touch Learnings selling price remains at $500 per tablet. Variable costs stay at $275 per tablet. Fixed costs increase to $15,000. How many tablets must be sold to break even?



= $15,000 + $0


= 67 units*

* Rounded up to the next full unit


Effects of Changes in Selling Price,

Variable Costs, and Fixed Costs

Exhibit 20-8 Effects of Changes in Selling Price, Variable Costs,

and Fixed Costs

Cause Effect Result

Change Contribution Margin per Unit Breakeven point

Selling price per unit increases Increases Decreases

Selling price per unit decreases Decreases Increases

Variable cost per unit increases Decreases Increases

Variable cost per unit decreases Increases Decreases

Total fixed cost increases No effect Increases

Total fixed cost decreases No effect Decreases
