The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin CHAPTER 3 Analysis of Cost, Volume, and Pricing to Increase Profitability

The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin

CHAPTER 3

Analysis of Cost, Volume, and

Pricing to Increase

Profitability


3-2

Learning Objective

LO1LO1

To use the contribution margin per unit

approach to calculate the sales volume

required to break even or earn a target profit


3-3

Determining the Contribution Margin per Unit

Bright Day produces one product called Delatine. Delatine is a nonprescription herb mixture. The

contribution margin per bottle of Delatine is:

Sales revenue per bottle 36$ Variable cost per bottle 24 Contribution margin per bottle 12$


3-4

Determining the Break-even Point

Bright Day uses a cost-plus-pricing strategy; it sets prices at cost plus a markup of 50% of cost. Delatine costs $24 per bottle to manufacture, so

a bottle sells for $36 ($24 + [50% × $24]).

Sales revenue per bottle 36$ Variable cost per bottle 24 Contribution margin per bottle 12$

The company’s first concern is if it can sell The company’s first concern is if it can sell enough bottles of Delatine to cover its fixed costs enough bottles of Delatine to cover its fixed costs

and make a profit!and make a profit!


3-5


The break-even point is the point where total total revenue equals total costsrevenue equals total costs (both variable and

fixed). For Bright Day, the cost of advertising is estimated to be $60,000. Advertising costs are

the fixed costs of the company. We use the following formula to determine the break-even

point in units.

The break-even point is the point where total total revenue equals total costsrevenue equals total costs (both variable and

fixed). For Bright Day, the cost of advertising is estimated to be $60,000. Advertising costs are

the fixed costs of the company. We use the following formula to determine the break-even

point in units.

Break-evenBreak-evenvolume in unitsvolume in units==

Fixed costsFixed costsContribution margin per Contribution margin per

unitunit

= $60,000$12

= 5,000 units5,000 units


3-6


For Delatine, the break-even point in sales dollars is $180,000 (5,000 bottles × $36 selling price).


3-7


Once all fixed costs have been covered (5,000 bottles sold), net income will increase by $12 per $12 per

unit contribution margin.unit contribution margin.

What will be the increase in net income if units sold What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?increase from 5,000 units to 5,600 units?

What will be the increase in net income if units sold What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?increase from 5,000 units to 5,600 units?

$12$12

4,998 4,999 5,000 5,001 5,002 Revenue @ $36 179,928$ 179,964$ 180,000$ 180,036$ 180,072$ Variable Expenses @ $24 (119,952) (119,976) (120,000) (120,024) (120,048) Contribution Margin @$12 59,976 59,988 60,000 60,012 60,024 Fixed Expenses (60,000) (60,000) (60,000) (60,000) (60,000) Net Income (24)$ (12)$ -$ 12$ 24$

Number of Units Sold


3-8


What will be the increase in net income if units What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?sold increase from 5,000 units to 5,600 units?

What will be the increase in net income if units What will be the increase in net income if units sold increase from 5,000 units to 5,600 units?sold increase from 5,000 units to 5,600 units?

New Units Sold 5,600 Previous Units Sold 5,000 Increase in Units Sold 600 Contribution Margin Per Unit 12$ Increase in Income 7,200$

Number of Units Sold5,000 5,600

Revenue @ $36 180,000$ 201,600$ Variable Expenses @ $24 (120,000) (134,400) Contribution Margin @$12 60,000 67,200 Fixed Expenses (60,000) (60,000) Net Income -$ 7,200$


3-9

Reaching a Target Profit

Bright Day’s president wants the advertising campaign to produce profits of $40,000 to the

company.Break-evenBreak-even

volume in unitsvolume in units== Fixed costs + Fixed costs + Desired Desired

profitprofit Contribution margin Contribution margin per unitper unit

=$60,000 + $40,000

$12

= 8,333.33 units8,333.33 unitswhich rounds towhich rounds to

8,334 whole units8,334 whole units


3-10

Reaching a Target Profit Level

At $36 per unit selling price, the sales dollars are equal to $300,000, as shown below:

IncomeUnits sold 8,334 Revenue @ $36 300,024$ Variable Expenses @ $24 (200,016) Contribution Margin @$12 100,008 Fixed Expenses (60,000) Net Income 40,008$


3-11

Check Yourself Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of

lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Matrix profit in the coming month of $37,500. Matrix must sell the following number of must sell the following number of lawnmowers:lawnmowers:

1.1. 3,000.3,000.

2.2. 3,500.3,500.

3.3. 4,000.4,000.

4.4. 4,500.4,500.

Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Matrix profit in the coming month of $37,500. Matrix must sell the following number of must sell the following number of lawnmowers:lawnmowers:

1.1. 3,000.3,000.

2.2. 3,500.3,500.

3.3. 4,000.4,000.

4.4. 4,500.4,500.

$225,000 + $225,000 + $37,500$37,500

$75$75

= 3,500= 3,500


3-12

Learning Objective

LO2LO2

To set selling prices by using

cost-plus, prestige, and target profit


3-13

Assessing the Pricing Strategy

Cost-Plus Pricing

Prestige Pricing

Target Pricing

Price products at variable cost plus some percentage of the

variable, normally 50%.

Price products with a premium because the product is new or has a prestigious name brand.

Price products at the market price and then control costs to

be profitable at the market price.


3-14

Assessing the Pricing Strategy

The Marketing Department at Bright Day The Marketing Department at Bright Day suggests that a price drop from $36 per bottle suggests that a price drop from $36 per bottle

to $28 per bottle will make Delatine a more to $28 per bottle will make Delatine a more attractive product to sell. The president wants attractive product to sell. The president wants to know what effect such a price drop would to know what effect such a price drop would

have on the company’s stated goal of have on the company’s stated goal of producing a $40,000 profit.producing a $40,000 profit.

You have been asked to determine the You have been asked to determine the number of bottles that must be sold to earn number of bottles that must be sold to earn

the $40,000 profit at the new $28 selling price the $40,000 profit at the new $28 selling price per bottle. See if you can provide an answer per bottle. See if you can provide an answer

to the president before going to the next to the president before going to the next screen!screen!


3-15

Effects of Changes in Sales Price

New Selling Price Per Bottle 28$ Variable Expenses Per Bottle 24 New Contribution Margin 4$

Step 1

Break-evenBreak-evenvolume in unitsvolume in units=

= Fixed costs + Fixed costs + Desired Desired profitprofit Contribution margin Contribution margin

per unitper unit

Step 2

=$60,000 + $40,000

$4

= 25,000 units25,000 units

Step3


3-16

Effects of Changes in Sales Price

The required sales volume in dollars is $700,000 (25,000 units × $28 per bottle) as shown below:



3-17

Learning Objective

LO3LO3

To use the contribution margin per unit to conduct cost-volume-profit

analysis


3-18Assessing the Effects of Changes in Variable Costs

Bright Day is considering an alternative mixture for Delatine along with new

packaging. This new product would sell for $28 per bottle and have a variable cost per

bottle of $12. The president is not in favor of the new product but wants to know how many units must be sold to produce the

desired profit of $40,000.

You have been asked to determine the units that must be sold and the total sales revenue

that will be produced!



New Selling Price Per Bottle 28$ Variable Expenses Per Bottle 12 New Contribution Margin 16$

Step 1

Break-evenBreak-evenvolume in unitsvolume in units=

= Fixed costs + Fixed costs + Desired Desired profitprofit Contribution margin Contribution margin

per unitper unit

Step 2

=$60,000 + $40,000

$16


Step3



At $28 per unit selling price, the sales dollars are equal to $175,000 as shown below:



3-21Assessing the Effects of Changes in Fixed CostsBright Day’s president has asked you to determine the required sales volume if

advertising costs were reduced to $30,000, from the planned level of $60,000.

= $30,000$30,000 + $40,000

$16

= 4,375 units4,375 unitsBreak-even

volume (units)



3-22

Learning Objective

LO4LO4

To draw and interpret a cost-

volume-profit graph


3-23

Cost-Volume-Profit Graph

Units sold - 5,000 10,000 Revenue @ $36 -$ 180,000$ 360,000$ Variable Expenses @ $24 - (120,000) (240,000) Contribution Margin @$12 - 60,000 120,000 Fixed Expenses (60,000) (60,000) (60,000) Net Income (60,000)$ -$ 60,000$

Income at Various Levels

Information to prepare a break-even Excel graph.Units sold - 5,000 10,000

Revenue - 180,000 360,000 Total Cost 60,000 180,000 300,000 Fixed Cost 60,000 60,000 60,000

We have developed income statements for zero sales, break-even sales, and ten thousand units.


3-24


Break-even Graph

-

100,000

200,000

300,000

400,000

- 5,000 10,000

Units Sold

Do

llars

Revenue

Total Cost

Fixed Cost$180,000$180,000

5,000 units5,000 units


3-25


Break-even Graph

-

100,000

200,000

300,000

400,000

- 5,000 10,000

Units Sold

Do

llars

Revenue

Total Cost

Fixed Cost


3-26

Learning Objective

LO5LO5

To calculate margin of safety


3-27

Calculating the Margin of Safety

The margin of safety measures the cushion between budgeted sales and the break-even point. It quantifies the amount by which actual sales can fall short of expectations before the company will

begin to incur losses. With a selling price of $28 per unit and variable costs of $12 per unit, and a

desired profit of $40,000, budgeted sales were:= $30,000$30,000 +

$40,000$16


volume (units)

Break-even unit sales assuming no profit would be:

= = 1,875 units1,875 units$30,000$30,000 $16

Break-evenvolume (units)


3-28

Calculating the Margin of Safety

In Units In DollarsBudgeted sales 4,375 122,500$ Break-even sales (1,875) (52,500) Margin of safety 2,500 70,000$

Margin ofsafety

=Budgeted sales – Break-even

salesBudgeted sales

Margin ofsafety

=$122,500 –

$52,500$122,500

= 57.14%57.14%


3-29

Management considers a new product, Delatinethat has a sales price of $36 and variable costs

of $24 per bottle. Fixed costs are $60,000. Break-even is 5,000 units.

Management wants to earn a $40,000 profit onDelatine. The sales volume to achieve this

profit level is 8,334 bottles sold.

Marketing advocates a target price of $28 perbottle. The sales volume required to earn a$40,000 profit increases to 25,000 bottles.


3-30

Target costing is employed to reengineer theproduct and reduces variable cost per unit to

$12. To earn the desired profit of $40,000, salesvolume decreases to 6,250 units.

Target costing is applied and fixed costs arereduced to $30,000. The sales volume to earn

the desired $40,000 profit is 4,375 units.

In view of the 57.14% margin of safety,management decides to add Delatine to its

product line.


3-31

Learning Objective

LO6LO6

To conduct sensitivity analysis for cost-volume-

profit relationships


3-32

Performing Sensitivity Analysis Using Spreadsheet Software

After reviewing the spreadsheet analysis, Bright Day’s management team is convinced it should undertake radio

advertising for Delatine.


3-33

Learning Objective

LO3LO3

To use the contribution margin per unit to conduct cost-volume-profit

analysis


3-34

Decrease in Sales Price with an Increase in Sales Volume

The marketing manager believes reducing the sales price per bottle to $25 will increase sales volume by 625 units. Previous sales volume was:

= $30,000$30,000 + $40,000

$16


volume (units)

In DollarsNew selling price 25$ Variable costs per unit (12) Contribution margin 13$

In DollarsPrevious units sold 4,375 Additional units sold 625 Expected sales volume 5,000

Anticipated changes:


3-35

Decrease in Sales Price with an Increase in Sales Volume


Current Situation


Proposed Situation

Because Because budgeted income budgeted income will fall by $5,000, will fall by $5,000,

the proposal the proposal should be should be rejected!rejected!


3-36

Increase in Fixed Costs and Increase in Sales Volume

After the previous project was rejected, the advertising manager believes that buying an additional $12,000 in

advertising can increase sales volume to 6,000 units. The contribution margin will remain at $16. Should the

company buy the additional advertising?


Current SituationIncome

Units sold 6,000 Revenue @ $28 168,000$ Variable Expenses @ $12 (72,000) Contribution Margin @$16 96,000 Fixed Expenses (42,000) Net Income 54,000$

Proposed Situation

Profit = Contribution margin Profit = Contribution margin – Fixed cost– Fixed cost

Profit = (6,000 Profit = (6,000 × $16)× $16) – $42,000 =– $42,000 = $54,000$54,000


3-37

Change in Several Variables

Management has been able to reduce variable Management has been able to reduce variable costs to $8 per bottle and decides to reduce costs to $8 per bottle and decides to reduce

the selling price per bottle to $25 (so the the selling price per bottle to $25 (so the contribution margin is now $17). Further, contribution margin is now $17). Further,

management believes that if advertising is cut management believes that if advertising is cut to $22,000, the company can still expect sales to $22,000, the company can still expect sales

volume to be 4,200 units.volume to be 4,200 units.

Should management adopt this plan?Should management adopt this plan?

Management has been able to reduce variable Management has been able to reduce variable costs to $8 per bottle and decides to reduce costs to $8 per bottle and decides to reduce

the selling price per bottle to $25 (so the the selling price per bottle to $25 (so the contribution margin is now $17). Further, contribution margin is now $17). Further,

management believes that if advertising is cut management believes that if advertising is cut to $22,000, the company can still expect sales to $22,000, the company can still expect sales

volume to be 4,200 units.volume to be 4,200 units.

Should management adopt this plan?Should management adopt this plan?


3-38

Change in Several Variables

Profit = Contribution margin Profit = Contribution margin – Fixed – Fixed costcostProfit = (4,200 Profit = (4,200 × $17)× $17) – $22,000 =– $22,000 = $49,400$49,400


Current SituationIncome

Units sold 4,200 Revenue @ $25 105,000$ Variable Expenses @ $8 (33,600) Contribution Margin @$17 71,400 Fixed Expenses (22,000) Net Income 49,400$

Proposed Situation


3-39

Learning Objective

LO7LO7

To use the contribution margin ratio and the equation method to

conduct cost-volume-profit analysis


3-40

Contribution Margin Ratio

The contribution margin ratio is the contribution margin divided by sales, computed using either total figures or per unit figures. Here is the total

dollar, per unit and contribution margin (CM) ratio for Bright Day when sales volume is 5,000

bottles.

Total Per Unit

CM Ratio

Revenue 180,000$ 36$ 100.00%Variable Expenses (120,000) 24 66.67%Contribution Margin 60,000 12$ 33.33%

Fixed Expenses (60,000) Net Income -$


3-41

Contribution Margin RatioBright Day is considering the introduction of a

new product called Multi Minerals. Here is some per unit information about Multi

Minerals:

Bright Day expects to incur $24,000 in fixed marketing costs in connection with Multi Minerals.

Let’s look at the calculation of the break-even point in units and dollars.

Sales revenue per unit 20$ 100%Variable cost per unit 12 60%Contribution margin per unit 8$ 40%


3-42


Break-even in Break-even in UnitsUnits

Break-even in Break-even in UnitsUnitsFixed costs

CM per unit

$24,000$8


Break-even in Break-even in DollarsDollars

Break-even in Break-even in DollarsDollarsFixed costs

CM ratio$24,000

40%= $60,000$60,000


3-43




Fixed costs + Desired profit

CM per unit



Fixed costs + Desired profit

CM ratioBright Day desires to earn a profit of $8,000 on Bright Day desires to earn a profit of $8,000 on

the sale of Multi Mineralsthe sale of Multi MineralsBright Day desires to earn a profit of $8,000 on Bright Day desires to earn a profit of $8,000 on

the sale of Multi Mineralsthe sale of Multi Minerals

= 4,000 units4,000 units$24,000 +

$8,000$8 $24,000 +

$8,00040%

= $80,000$80,000


3-44

The Equation Method

At the break-even point:At the break-even point:

Sales = Variable cost + Fixed Sales = Variable cost + Fixed costcost

At the break-even point:At the break-even point:

Sales = Variable cost + Fixed Sales = Variable cost + Fixed costcost

Selling price per unit Variable cost per unit× = × + Fixed cost

Number of units sold Number of units sold

We can look at the above equation like this:We can look at the above equation like this:


3-45

The Equation Method

Let’s use our information from Multi Minerals to solve the equation for the number of units sold.

20$ × Units = 12$ × Units + 24,000$ 8$ × Units =

Units =24,000$ 3,000


Units =24,000$ 3,000

If we want to consider the desired profit of $8,000 the solution would be:


Units =32,000$ 4,000


Units =32,000$ 4,000


3-46

Check Yourself Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of

lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Use the profit in the coming month of $37,500. Use the equation method to determine how many equation method to determine how many lawnmowers Matrix must sell next month:lawnmowers Matrix must sell next month:

1.1. 3,000.3,000.

2.2. 3,500.3,500.

3.3. 4,000.4,000.

4.4. 4,500.4,500.

Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of lawnmower that sells for $175 each. Variable lawnmower that sells for $175 each. Variable expenses to produce the lawnmower are $100 expenses to produce the lawnmower are $100 per unit. Total fixed costs are $225,000 per per unit. Total fixed costs are $225,000 per month, and management wants to earn a month, and management wants to earn a profit in the coming month of $37,500. Use the profit in the coming month of $37,500. Use the equation method to determine how many equation method to determine how many lawnmowers Matrix must sell next month:lawnmowers Matrix must sell next month:

1.1. 3,000.3,000.

2.2. 3,500.3,500.

3.3. 4,000.4,000.

4.4. 4,500.4,500.


Units =262,500$

3,500


Units =262,500$

3,500


3-47

End of Chapter 3

Documents

The McGraw-Hill Companies, Inc. 2008McGraw-Hill/Irwin CHAPTER 3 Analysis of Cost, Volume, and Pricing to Increase Profitability