Cost-Volume-Profit Analysis

Short Term Business Decisions

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Teacher: Saqib Aziz Copy right:Pearson EducationFFBC, Univ-Lille2

Economic & Accounting view of Cost

• Economist view: long term and wide ranging output (Cost-Revenue interaction in profit making; curved lines)

• Accountant view: Short term perspective focused on limited range of activity (straight line graph)

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Cost-Volume-Profit (CVP) Analysis

• Is a powerful tool that helps managers make important business decisions

• Is a relationship among costs, volume, and profit or loss

• Determines how much the company must sell each month just to cover costs or to break even

• Helps managers decide how sales volume would need to change to achieve the same profit level

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Components of CVP Analysis• CVP analysis relies on the interdependency of

five components or pieces of information– Sales price per unit– Volume sold– Variable costs per unit– Fixed costs– Operating income

• If you know or can estimate four of these five components, you can compute the remaining unknown amount

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CVP Assumptions

1. Change in volume is only factor that affects costs

2. Managers can classify each cost as either variable or fixed• These costs are linear throughout relevant range

3. Revenues are linear throughout relevant range 4. Inventory levels will not change5. The sales mix of products will not change

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CVP Example Facts: Kay’s PostersKay has an e-tail poster business. She currently sells each poster for $35, while each poster has a variable cost of $21. Kay has fixed costs of $7,000. Kay is currently selling 550 posters. Kay’s relevant range extends from 0 to 2000 posters a month. Beyond this level he needs upgradation of site and an employee to handle increase in volume.

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Contribution Margin Income Statement

Kay’s e-tail poster example from prior slide

Sales revenue (550 posters)..................................... $ 19,250Less: Variable expenses ............................................ (11,550)Contribution margin ................................................. 7,700Less: Fixed expenses.................................................. (7,000)Operating income...................................................... $ 700

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Unit Contribution MarginKay’s e-tail poster example from previous slides Sales price per unit $ 35- Variable costs per unit (21)

Contribution margin per unit $ 14

Now assume sales are 650 units:

Contribution margin ( 650 sales X $14) $ 9,100- Fixed cost (7,000) Operating Income $ 2,100

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Contribution Margin Ratio

Contribution margin ratio

Unit contribution margin = $14 Sales price per unit $35

= 40%

Contribution margin ratio

Contribution margin = $ 7,700 Sales revenue $19,250

= 40%

Contribution margin ratio = percentage of each sales dollar that is available for covering fixed expenses and generating a profit.

Numbers above are from the Kay’s e-tail poster example on previous slides.

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Example 1Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers.

a. What is the contribution margin per passenger? Sales revenue (1 passenger)..................................... $ 50Less: Variable expenses ............................................ (20)Contribution margin ................................................. 30

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Example1 (continued)b. What is the contribution margin ratio?

c. Use the unit contribution margin to project operating income if monthly sales total 10,000 passengers.

d. Use the contribution margin ratio to project operating income if monthly sales revenue totals $400,000.Contribution margin ( $400,000 sales X 60%) $ 240,000Fixed cost (210,000)Operating Income $ 30,000

Contribution margin ratio =

Unit contribution margin = $ 30 Sales price per unit = $ 50

= 60%

10,000 x $30 = $300,000

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Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers.

• If Bay Cruiseline sells an additional 500 tickets, by what amount will its operating income increase (or operating loss decrease)?

Contribution Margin per unit x additional tickets 500 tickets X $30 = $15,000

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Example 2

CVP & Breakeven PointBreakeven point:

• Sales level at which operating income is zero– If sales above breakeven, then profit– If sales below breakeven, then loss

• Fixed expenses = total contribution margin

• Total sales = total expenses

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Calculating Breakeven PointThree approaches to calculating breakeven:

1.Income statement approach2.Shortcut approach using unit contribution

margin3.Shortcut approach using contribution margin

ratio (sales dollar)

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Income Statement ApproachContribution Margin Income Statement for Kay’s e-tail

Sales- Variable Expenses Contribution Margin- Fixed Expenses Operating Income

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Short-Cut Approach to Calculating Breakeven Using the Unit Contribution Margin

Fixed expenses + Operating income Contribution margin per unit

Units sold =

$7,000 + $0 $14

Units sold =

= 500 posters

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Short-Cut Using the Unit Contribution Margin Ratio

Fixed expenses + Operating income Contribution margin ratio

Sales in $ =

$7,000 + $0 0.40

Sales in $ =

= $17,500

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Finding the Volume Needed for a Target Profit Using Unit CM

CVP analysis helps managers determine what theyneed to sell to earn a target amount of profit.

Fixed expenses + Operating income Contribution margin per unit

Units sold =

$7,000 + $4,900 $14

Units sold = =

= 850 posters

$11,900 $14

= 850 posters x $35 = $29,750

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Finding the Volume Needed for a Target Profit Using Ratio

CVP analysis helps managers determine what theyneed to sell to earn a target amount of profit.

Fixed exp + Target operating income Contribution margin ratio

Units sold =

$7,000 + $4,900 0.40

Units sold = =

= 29,750 posters

$11,900 0.40

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Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.a. Use the income statement equation approach.

($50 x units) – ($20 x units) - $210,000 = $0 ($50 – $20 ) x units - $210,000 = $0

$30 x units = $210,000 units = $210,000/$30 units = 7,000

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Example 3

Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.b. Using the shortcut unit contribution margin approach, perform

a numerical proof to ensure that your answer is correct.

Fixed expenses + Operating income Contribution margin per unit

Units sold =

$210,000 + $0 $30

Units sold =

= 7,000 tickets

$210,000$30

Units sold =

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Example 3 (continued)

Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.c. Use your answers from a and b to determine the sales revenue needed to break even.

7,000 units to break even X $50 sales price = $350,000

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Example 3 (continued)

Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.d. Use the shortcut contribution margin ratio approach to verify the sales revenue needed to break even.

Fixed expenses + Operating income Contribution margin ratio

Sales in $ =

$210,000 + 0 0.60

Sales in $ =

= $350,000

$210,0000.60

Sales in $ =

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Example 3 (continued)

Graphing the CVP Relationships

Step 1: – Choose a sales volume (Units x $Price)– Plot point for total sales revenue – Draw sales revenue line from origin through

the plotted point

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Preparing a CVP Chart

$0

$5 000

$10 000

$15 000

$20 000

0 500 1 000 1 500

Volume of Units

Do

llars

Revenues

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Preparing a CVP ChartStep 2: Draw the fixed cost line

$4,000

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Preparing a CVP Chart

$0

$5 000

$10 000

$15 000

$20 000

0 500 1 000 1 500

Volume of Units

Do

llars Revenues

Fixed costs

Total cost

Step 3: Draw the total cost line (fixed plus variable)

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Step 4: Identify the breakeven point and the areas of operating income and loss

Preparing a CVP Chart

$0

$5 000

$10 000

$15 000

$20 000

0 500 1 000 1 500

Volume of Units

Do

llars

Breakeven point

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Step 5: Mark operating income and operating loss areason graph

Preparing a CVP Chart

$0

$5 000

$10 000

$15 000

$20 000

0 500 1 000 1 500

Volume of Units

Do

llar

s

Operating Loss

Operating Income

Breakeven point

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$-

$100 000

$200 000

$300 000

$400 000

$500 000

$600 000

$700 000

0 2 500 5 000 7 500 10000

Tickets

Do

llars

(in

th

ou

san

ds)

Revenues

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CVP Chart for Bay Cruisline

$-

$100 000

$200 000

$300 000

$400 000

$500 000

$600 000

$700 000

2 500 5 000 7 500 10000

Tickets

Do

llar

s (i

n t

ho

usa

nd

s)

Fixed Cost

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CVP Chart for Bay Cruisline

$-

$100 000

$200 000

$300 000

$400 000

$500 000

$600 000

$700 000

2 500 5 000 7 500 10000

Tickets

Do

llars

(in

th

ou

san

ds)

Total Cost

Breakeven Point

Income Area

Loss Area

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CVP Chart for Bay Cruisline

Sensitivity AnalysisManagers need to be prepared for increasing costs, pricing pressure from competitors, and other changing business conditions.

Sensitivity Analysis: •Conducts “What if” analysis

– What if the sales price changes?– What if costs change?– What if the sales mix changes?

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What if the Sales Price Changes?• Calculate a new unit contribution margin using

the new sales price• Use the new unit contribution margin to

compute breakeven sales in units• Use the new unit contribution margin to

compute breakeven sales to maintain target profit

• Using the new breakeven numbers, decide if a change should be made

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What if Variable Cost Change?• Calculate a new unit contribution margin using

the new cost• Use the new unit contribution margin to

compute breakeven sales in units• Use the new unit contribution margin to

compute breakeven sales to maintain target profit

• Using the new breakeven numbers, decide if a change should be made

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What if Fixed Costs Change?

• Changes in fixed costs do not affect the contribution margin

• Breakeven point changes because fixed costs change

• Use the unit contribution margin to compute the new breakeven sales in units

• Use the unit contribution margin to compute breakeven sales to maintain target profit

• Using the new breakeven numbers, decide if a change should be made

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Operational Risk Indicators

• Excess of expected sales over breakeven sales• Drop in sales that the company can absorb

before incurring a loss• Used to evaluate the risk of current operations

as well as the risk of new plans

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Safety Margin

•Safety Margin•Operating Leverage

Breakeven sales in units

Margin of safetyin units

Expected sales in units

= −

Breakeven sales

Margin of safetyin dollars

Expected sales= −

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Calculating Safety Margin

Operating Leverage

• How responsive a company’s operating income is to changes in volume– Lowest possible value for this factor is 1, if the company has

no fixed costs

Operating leverage factor = Contribution marginOperating income

Operating leverage factor = $13,300 $6,300

= 2.11 (rounded)39

The relevant amount of fixed and variable cost s that make up a company’s total cost

Operating Leverage Factor

High Operating Leverage• High operating leverage companies have:

– Higher levels of fixed costs and lower levels of variable costs– Higher contribution margin ratios

• For high operating leverage companies, changes in volume significantly affect operating income, so they face:– Higher risk– Higher potential for reward

• Examples include golf courses, hotels, rental car agencies, theme parks, airlines, cruise lines

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Low Operating Leverage

• Low operating leverage companies have:– Higher levels of variable costs and lower levels of fixed costs– Lower contribution margin ratios

• For low operating leverage companies, changes in volume do NOT have as significant an effect on operating income, so they face:– Lower risk– Lower potential for reward

• Examples include merchandising companies.

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