Chapter Three Cost – Volume – Profit Analysis. Jeff Jamail is evaluating a business opportunity to sell cookware at trade shows. Mr. Jamail can buy the

Chapter Three

Cost – Volume – Profit Analysis

• Jeff Jamail is evaluating a business opportunity to sell cookware at trade shows. Mr. Jamail can buy the cookware at a wholesale cost of $210 per set. He plans to sell the cookware for $350 per set. He estimates fixed costs such as plane fare, booth rental cost, and lodging to be $5,600 per trade show.

• How many cookware sets must Mr. Jamail sell in order to breakeven?

Cost-Volume-Profit Relationship

There are 3 methods to analyze:

(1.) Contribution Margin per Unit(2.) Contribution Ratio(3.) Equation Method

NOTE: Each method yields the same results.

Cost-Plus Pricing Strategy

• It sets prices at cost plus a mark-up

• For example:– Product cost $20 to make– Mgmt decides to mark-up 30%– Selling Price = $20 + ($20 * 30%) = $26

Break-Even Point

Point where Total Revenue = Total Costs

Break-even Volume in Units =

Fixed Costs / Contribution Margin per Unit

Once fixed costs have been covered, net income will increase per unit contribution margin for each additional unit sold

Determining the Break-even Point

Bright Day produces one produce called Delatine. The company uses a cost-plus-pricing strategy; it sets prices at cost plus a markup of 50% of cost. Delatine cost $24 per bottle to manufacture, so a bottle sells for $36 ($24 + [50% × $24]). The contribution margin per bottle is:

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

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

make a profit!make a profit!


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


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


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


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$

Reaching a Target Profit Level

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 units

Reaching a Target Profit Level

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

IncomeUnits sold 8,333.33 Revenue @ $36 300,000$ Variable Expenses @ $24 (200,000) Contribution Margin @$12 100,000 Fixed Expenses (60,000) Net Income 40,000$

Check Yourself

Matrix, Inc. manufactures one model of Matrix, Inc. manufactures one model of lawnmower the sells for $175 each. Variable lawnmower the 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.



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

Effects of Changes in Sales Price

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 such a price drop would have on to know what such a price drop would have on

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


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


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

IncomeUnits sold 25,000 Revenue @ $28 700,000$ Variable Expenses @ $24 (600,000) Contribution Margin @$4 100,000 Fixed Expenses (60,000) Net Income 40,000$

Target Costing

1. Determine the market price at which product will sell

• This is the Target Price

2. Must develop the product at a cost that will enable company to be profitable selling the product at the target price

• This is known as TARGET COSTING

Changes in Variable Costs

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

product would sell for $28 per bottle and have a product would sell for $28 per bottle and have a variable cost per bottle of $12. The president is not variable cost per bottle of $12. The president is not in favor of the new product but wants to know how in favor of the new product but wants to know how

many units must be sold to produce the desired many units must be sold to produce the desired profit of $40,000.profit of $40,000.

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

be produced!be produced!

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

product would sell for $28 per bottle and have a product would sell for $28 per bottle and have a variable cost per bottle of $12. The president is not variable cost per bottle of $12. The president is not in favor of the new product but wants to know how in favor of the new product but wants to know how

many units must be sold to produce the desired many units must be sold to produce the desired profit of $40,000.profit of $40,000.

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

be produced!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:


Changes in Fixed Costs

Bright 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)


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)

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$

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 want 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.

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.

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:

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!

Increased in Fixed Costs and Increase in Sales Volume

After the previous project was rejects, 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

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?

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

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 -$

Contribution MarginRatio Approach

= Contribution Margin / Sales

1st – Identify Contribution Margin $60,000

2nd – Identify Sales $180,000

= $60,000 / $180,000 = 0.33

What does this Ratio mean?

• Ratio means that every dollar of sales provides $0.33 to cover Fixed Costs

• After Fixed Costs are covered – Each $1 provides $0.33 of profit


Bright 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%


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




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

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 Unmber of units sold

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

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

Check Yourself



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.



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

Weighted-AverageContribution Margin per Unit

In the real world, a company is selling more than one product

Product AProduct B

Unit Selling Price $ 100 $ 200

Unit Variable Cost 40 60

Unit Fixed Cost 20 30

Total Units Sold 10,00020,000

• Step 1: Find the CM for each– Product A = 100 – 40 = 60/unit– Product B = 200 – 60 = 140/unit

• Step 2: Find the total # of units sold– 10,000 + 20,000 = 30,000

• Step 3: Find the % sold of each product– Product A = 10,000 / 30,000 = 33%– Product B = 20,000 / 30,000 = 67%

• Step 4: Find the Weighted CM– Product A = $ 60 * 33% = $19.80 / unit– Product B = $ 140 * 67% = $93.80 / unit– Total CM = $19.80 + $93.80 = $113.60 / unit

Documents

Chapter Three Cost – Volume – Profit Analysis. Jeff Jamail is evaluating a business opportunity to sell cookware at trade shows. Mr. Jamail can buy the