accounting chapter 21

Cost-Volume-Profit Analysis

Chapter 21

21-1Copyright © 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

4. Use CVP analysis to perform sensitivity analysis


Learning Objectives

5. Use CVP analysis to calculate margin of safety, operating leverage, and multiproduct breakeven points

6. Distinguish between variable costing and absorption costing (Appendix 21A)

7. Compute operating income using variable costing and absorption costing (Appendix 21A)


Learning Objective 1

Determine how Determine how changes in volume changes in volume

affect costsaffect costs


Types of costs

• Variable costs

• Fixed costs

• Mixed costs

Copyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall 21-5

Variable Costs—Batteries in Tablets

Number of Tablets Produced

Variable Costper 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

TotalFixed Costs


Fixed Costper Tablet

$12,000 25 tablets $480

12,000 50 tablets 240

12,000 75 tablets 160

12,000 100 tablets 120


Characteristics ofVariable 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


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 MethodStep 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)



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



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)



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



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



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

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


Estimated manufacturing equipment maintenance cost at 400 tablets

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

= ($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. Supervisor’s salary



4. Supervisor’s salary

Fixed



5. Wages of production workers



5. Wages of production workers

Variable



Calculate operating Calculate operating income using income using

contribution margin contribution margin and contribution and contribution

margin ratiomargin 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

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

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

= $100,000 – $55,000

= $45,000


Unit Contribution Margin

If Smart Touch Learning sells 200 tablets for $500 each that incur variable costs of $275 each, then the unit contribution margin is:

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


Unit Contribution Margin

If Smart Touch Learning sells 200 tablets for $500 each that incur variable costs of $275 each, then 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

If Smart Touch Learning sells 200 tablets for $500 each that incur variable costs of $275 each, then the contribution margin ratio is:

Contribution margin ratio = Contribution margin / Net sales revenue


Contribution Margin Ratio

If Smart Touch Learning sells 200 tablets for $500 each that incur variable costs of $275 each, then 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 IncomeStatement Format

Net sales revenue

– Cost of goods sold

= Gross profit

– Selling and administrative expenses

= Operating income

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 MarginIncome Statement Format

Net sales revenue

– Variable costs

= Contribution margin

– Fixed Costs

= Operating income

Net sales revenue

– Variable costs


– 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 costs6,000

Operating income $6,000

7. Contribution margin = $12,000



8.What is the unit contribution margin?

9.What is the contribution margin ratio?




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





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 Use cost-volume-profit (CVP) analysis for (CVP) analysis for

profit planningprofit 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 Profit—Three 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

Net sales revenue − Variable costs − Fixed costs = Operating income


Equation Approach—Check Your Calculation

Net sales revenue − Variable costs − Fixed costs = Operating income

($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 profitContribution margin per unit


Contribution Margin Approach



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

= 80 units


Contribution Margin Approach—Check Your Calculation

Net sales revenue

– Variable costs


– Fixed costs

= Operating income


Contribution Margin Approach—Check 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 costs12,000

= Operating income $6,000


Contribution Margin Ratio Approach


Required sales in dollars = Fixed costs + Target profit Contribution margin ratio


Contribution Margin Ratio Approach



= $12,000 + $6,000 45%

= $40,000


Breakeven Point Calculationsfor Smart Touch Learning


Cost-Volume-Profit Graph


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. 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.


10. Calculate the required sales in units to earn the 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


11. Calculate the required sales in units to earn the target profit using the contribution margin method.


11. Calculate the required sales in units to earn the 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 per unit – $40 per unit

= 100 units



Use CVP analysis to Use CVP analysis to perform sensitivity perform sensitivity

analysisanalysis


Change in the Selling Price—Contribution 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 Price—Contribution 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$475 per unit – $275 per unit

= 60 unitsCopyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall 21-78

Change in the Variable Costs—Contribution Margin Approach

Smart Touch Learning’s 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 Costs—Contribution Margin Approach

Smart Touch Learning’s 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$500 per unit – $285 per unit

= 56 units*

* Rounded up to next full unitCopyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall 21-80

Change in the Fixed Costs—Contribution Margin Approach

Smart Touch Learning’s 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 Costs—Contribution Margin Approach

Smart Touch Learning’s 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$500 per unit – $275 per unit

= 67 units*

* Rounded up to the next full unitCopyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall 21-82

Effects of Changes in Selling Price, Variable Costs, and Fixed Costs

Exhibit 21-8 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


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. Calculate the breakeven point in units under each independent scenario.


14. Variable costs increase by $10 per unit.


14. Variable costs increase by $10 per unit.

Variable cost = $40 + $10 = $50

Contribution margin per unit = $100 − $50 = $50


= $6,000 + $0$50 per unit

= 120 units


15. Fixed costs decrease by $600.


15. Fixed costs decrease by $600.

Fixed costs =$6,000 − $600 = $5,400



= $5,400 + $0$60 per unit

= 90 units


16. Sales price increases by 10%.


16. Sales price increases by 10%.

Sales price = $100 × 1.10 = $110



= $6,000 + $0$70 per unit

= 86 units*

* Rounded up to next whole unit



Use CVP analysis to Use CVP analysis to calculate margin of calculate margin of

safety, operating safety, operating leverage, and leverage, and multiproduct multiproduct

breakeven pointsbreakeven points


Margin of Safety

Smart Touch Learning’s original breakeven point was 54 tablets. The company expects to sell 100 tablets.

Expected sales – Breakeven sales = Margin of safety in units


Margin of Safety



100 tablets – 54 tablets = 46 tablets


Margin of Safety




Margin of safety in units × Sales price per unit = Margin of safety in dollars


Margin of Safety





46 tablets × $500 per tablet = $23,000


Margin of Safety






Margin of safety in units / Expected sales in units = Margin of safety ratio


Margin of Safety






Margin of safety in units / Expected sales in units = Margin of safety ratio

46 tablets / 100 tablets = 46%


Expected ContributionMargin Income Statements


Actual ContributionMargin Income Statements


Degree of Operating Leverage

Degree of operating leverage = Contribution margin Operating income


Degree of Operating Leverage


Company A $10,000 = 2.50 $4,000

Company B $5,000 = 1.25$4,000


Degree of Operating Leverage—Predicting Change in Operating Income


Sales Mix

Cool Cat Furniture sold 6,000 cat beds and 4,000 scratching posts. Total fixed costs are $40,000. The cat bed’s unit selling price is $44, and variable cost per bed is $24. The scratching post’s unit selling price is $100 and variable cost per post is $30. What is the breakeven point?


Sales Mix

Cool Cat Furniture sold 6,000 cat beds and 4,000 scratching posts. Total fixed costs are $40,000. The cat bed’s unit selling price is $44, and variable cost per bed is $24. The scratching post’s unit selling price is $100 and variable cost per post is $30. What is the breakeven point?

Cat beds Scratching Posts Total6,0004,00010,00060% 40% 100%3 2 5


Breakeven Point with Sales Mix:Step 1


Step 1: Calculate the weighted-average contribution margin per unit.


Step 2: Calculate the breakeven point in units for the “package” of products.


Weighted-average contribution margin per unit






= $40,000 + $0 $40 per item

= 1,000 items



Step 3: Calculate the breakeven point in units for each product. Multiply the “package” breakeven point in units by each product’s proportion of the sales mix.




Breakeven sales of cat beds (1,000 items × 3/5) = 600 cat beds

Breakeven sales of scratching posts(1,000 items × 2/5) = 400 scratching posts

In sales dollars:

600 cat beds at $44 selling price each $26,400

400 scratching posts at $100 selling price each 40,000

Total sales revenue $66,400


Breakeven Point with Sales Mix:Contribution Income Statement


Sales Mix with Target Profit

How many units of each product must Cool Cat sell to earn a target profit of $20,000?


Sales Mix with Target Profit:Step 2

Step 2: Calculate the required sales in units for the “package” of products.




Sales Mix with Target Profit:Step 2

Step 2: Calculate the required sales in units for the “package” of products.



= $40,000 + $20,000 $40 per item

= 1,500 items


Target Profit with Sales Mix:Step 3

Step 3: Calculate the required sales in units for each product. Multiply the “package” required sales in units by each product’s proportion of the sales mix.


Target Profit with Sales Mix:Step 3

Step 3: Calculate the required sales in units for each product. Multiply the “package” required sales in units by each product’s proportion of the sales mix.

Required sales of cat beds (1,500 items × 3/5) = 900 cat beds

Required sales of scratching posts (1,500 items × 2/5) = 600 scratching posts


Target Profit with Sales Mix:Contribution Income Statement


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. Expected sales are 200 tables per month.


17. Calculate the margin of safety in units.


17. Calculate the margin of safety in units.

Breakeven sales in units = Fixed costs + Target profitContribution margin per unit

= $6,000 + $ 0 $60 per unit

= 100 units

Margin of safety in units = Expected sales − Breakeven sales= 200 tables − 100 tables= 100 tables


18. Determine the degree of operating leverage.


18. Determine the degree of operating leverage.

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 6,000Operating income $ 6,000


= $12,000 $6,000

= 2.00Copyright © 2014 Pearson Education, Inc. Publishing as Prentice Hall 21-122

19. The company begins manufacturing wood chairs to match the tables. Chairs sell for $50 each and have variable costs of $30. The new production process increases fixed costs to $7,000 per month. The expected sales mix is 1 table for every 4 chairs. Calculate the breakeven point.



Step 1: Calculate the weighted-average contribution margin per unit.




= $7,000 + $0$28 per item

= 250 items



Breakeven sales of tables (250 items × 1/5) = 50 tables

Breakeven sales of chairs (250 items × 4/5) = 200 chairs



Distinguish between Distinguish between variable costing and variable costing and absorption costing absorption costing

(Appendix 21A)(Appendix 21A)


Difference between Absorption Costing and Variable Costing


Smart Touch Learning—Price and Cost Summary


Comparison of Unit Cost Computations—2,000 Units Produced


20. Pierce Company had the following costs:

Units produced 500 units

Direct materials 25 per unit

Direct labor 45 per unit

Variable manufacturing overhead 15 per unit

Fixed manufacturing overhead 5,000 per year

Variable selling and administrative costs

30 per unit

Fixed selling and administrative costs 3,200 per year

Calculate the unit production cost using absorption costing and variable costing.


20.

Absorption Costing

Variable Costing

Direct materials $ 25 $ 25

Direct labor 45 45

Variable manufacturing overhead 15 15

Fixed manufacturing overhead ($5,000 / 500 units) 10

Total unit cost $ 95 $ 85



Compute operating Compute operating income using variable income using variable costing and absorption costing and absorption

costingcosting

(Appendix 21A)(Appendix 21A)


Absorption and Variable Costing:Three Scenarios

• Units produced equal units sold

• Units produced are more than units sold

• Units produced are less than units sold


Absorption and Variable Costing:Year 1: Production Equals Sales

For Year 1, Smart Touch Learning has the following history:

•No beginning balance in Finished Goods Inventory

•Produced 2,000 tablet computers during the year

•Sold 2,000 tablet computers during the year


Absorption and Variable Costing:Year 1: Production Equals Sales


Absorption and Variable Costing:Year 2: Production Exceeds Sales


•No beginning balance in Finished Goods Inventory (Year 1 ended with a zero balance; therefore, Year 2 will start with a zero balance)




Absorption and Variable Costing:Year 2: Production Exceeds Sales


Year 2: Production Costs in Absorption and Variable Costing—Production Exceeds Sales


Absorption and Variable Costing:Year 3: Production is Less Than Sales


•A beginning balance in Finished Goods Inventory of 500 units that cost $144,500 under absorption costing and $122,500 under variable costing (Year 2’s ending balances)






*Rounded to nearest cent

Absorption and Variable Costing:Year 3: Production Is Less Than Sales


Year 3: Production Costs in Absorption and Variable Costing—Production Is Less Than Sales


Absorption and Variable Costing:3-Year Summary


*Absorption costing total figures adjusted for $5 rounding error created in Year 3when fixed cost per unit was rounded.

21. Hayden Company has 50 units in Finished Goods Inventory at the beginning of the accounting period. During the accounting period, Hayden produced 150 units and sold 200 units for $150 each. All units incurred $80 in variable manufacturing costs and $20 in fixed manufacturing costs. Hayden also incurred $7,500 in Selling and Administrative Expenses, all fixed. Calculate the operating income for the year using absorption costing and variable costing.


Absorption Costing: Production cost per unit = $100

Sales Revenue (200 units × $150 per unit) $ 30,000

Cost of Goods Sold (200 units × $100 per unit) 20,000

Gross Profit 10,000

Selling and Administrative Expenses 7,500

Operating Income $ 2,500


Variable Costing: Production cost per unit = $80

Sales Revenue (200 units × $150 per unit) $ 30,000

Variable Cost (200 units × $80 per unit) 16,000

Contribution Margin 14,000

Fixed Costs

Manufacturing (150 units × $20 per unit) 3,000

Selling and Administrative 7,500

Operating Income $ 3,500


End of Chapter 21


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