Cost-Volume-Profit Analysis

Chapter 19

Identify how changes in volume affectcosts

Use CVP analysis to compute breakevenpoints

Use CVP analysis for profit planning, andgraph the CVP relations

Use CVP methods to perform sensitivityanalyses

Calculate the breakeven point for multipleproducts or services

Distinguish between variable costing andabsorption costing (see Appendix 19A,located at myaccountinglab.com)

Identify how changes in volume affect costs

The effect of volume of activity on costs

Variable costs

Increase or decrease in total in direct proportionto changes in the volume of activity

Fixed costs

Do not change over wide ranges of volume

Mixed costs

Have both variable and fixed components

Total variable costs change in direct proportionto changes in the volume of activity

If activity increases, so does the cost

Unit variable cost remains constant

Volume can be measured in many differentways:

Number of units sold

Number of units produced

Number of miles driven by a delivery vehicle

Number of phone calls placed

Tend to remain the same in amount, regardlessof variations in level of activity

Examples:

Straight-line depreciation

Salaries

Part-time manager’s salary

Total fixed costs do not change, but the fixedcost per event depends on the number of events

The more activity, the less the fixed cost per unit

Total Fixed Costs and Fixed Costs per Unit

Have both a fixed and variable component

Example:

Utilities that charge a set fee per month, plus acharge for usage

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Method to separate mixed costs into variableand fixed components

Identify the highest and lowest levels of activityover a period of time

STEP 1: Calculate variable cost per unit

STEP 2: Calculate total fixed cost

STEP 3: Create and use equation to show thebehavior of a mixed cost

Variable cost per unit = Change in total cost ÷ Change in activity volume

Total fixed cost = Total mixed cost – Total variable cost

Total mixed cost = (Variable cost per unit X number of units) + Total fixed costs

Data

Step 1

Step 2

($2 x 400 event-playing hours) + $1,000 = $1,800

Now check your formula against the original data

Range of volume:

Where total fixed costs remain constant and variablecost per unit remains constant

Outside the relevant range, costs can differ

Philadelphia Acoustics builds innovative speakers formusic and home theater systems. Consider thefollowing costs. Identify the costs as variable (V), fixed(F), or mixed (M).

1. Units of production depreciation on routers usedto cut wood enclosures

2. Wood for speaker enclosures

3. Patents on crossover relays

4. Total compensation to salesperson, who receivesa salary plus a commission based on meeting salesgoals

5. Crossover relays

Philadelphia Acoustics builds innovative speakers formusic and home theater systems. Consider thefollowing costs. Identify the costs as variable (V), fixed(F), or mixed (M).

6. Straight-line depreciation on manufacturing plant

7. Grill cloth

8. Cell phone costs of salesperson (plan includes1,200 minutes; overseas calls are charged at anaverage of $0.15 per minute)

9. Glue

10. Quality inspector’s salary

Martin owns a machine shop. In reviewing his utility bill for the last12 months, he found that his highest bill of $2,800 occurred inAugust when his machines worked 1,400 machine hours. His lowestutility bill of $2,600 occurred in December when his machinesworked 900 machine hours.

1.Calculate (a) the variable rate per machine hour and (b)Martin’s total fixed utility cost.

Variable cost per unit = Change in total cost ÷ Change in activityvolume

a. Variable cost per unit = ($2,800 - $2,600) ÷ (1,400 – 900)

Variable cost per unit = $200 ÷ 500 + 0.40 per machine hour

b. Total fixed cost = Total mixed cost – Total variable cost

Total fixed cost = $2,800 – (0.40 X 1,400)

Total fixed cost = $2,800 - $560

Total fixed cost = $2,240

Martin owns a machine shop. In reviewing his utility bill for thelast 12 months, he found that his highest bill of $2,800 occurred inAugust when his machines worked 1,400 machine hours. Hislowest utility bill of $2,600 occurred in December when hismachines worked 900 machine hours.

2. Show the equation for determining the total utility cost forMartin’s.

$ 0.40 per machine hour + $2,240

Martin owns a machine shop. In reviewing his utility bill for thelast 12 months, he found that his highest bill of $2,800 occurred inAugust when his machines worked 1,400 machine hours. Hislowest utility bill of $2,600 occurred in December when hismachines worked 900 machine hours.

3. If Martin’s anticipates using 1,200 machine hours in January,predict his total utility bill using the equation from Requirement 2.

($ 0.40 per machine hour x 1.200 machine hours) + $2,240

$480 +$2,240 = $2,720

4. Draw a graph illustrating your total cost under this plan. Label theaxes, and show your costs at 900, 1,200, and 1,400 machine hours.

Use CVP analysis to compute breakeven points

Expresses the relationships among costs, volume, andprofit or loss

Answers:

How many products or services must the company sell tobreak even?

What will profits be if sales double?

How will changes in selling price, variable costs, or fixedcosts affect profits?

Assumptions:

Managers can classify each cost as either variable or fixed

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

Fixed costs do not change

Sales level at whichoperating income is zero:

Total revenues equal total costs (expenses)

Sales above breakeven result in a profit

Sales below breakeven result in a loss

Two methods to compute breakeven point:

Income statement approach

Sales revenue − Total costs = Operating income

Contribution margin approach

Sales revenue – Variable costs = Contribution margin –Fixed costs = Operating income

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Express income in equation form and then breakit down into its components:

Shortcut method

The contribution margin is sales revenue minusvariable costs (expenses)

Called contribution margin because the excessof sales revenue over variable costs contributesto covering fixed costs

Rearrange the income statement—use thecontribution margin to develop a shortcutmethod

Shortcut equation:

Given fixed costs total $12,000. Thecontribution margin per event is $120 ($200 saleprice – $80 variable cost)

Check your answer

Ratio of contribution margin to sales revenue

Used to compute the breakeven point in terms ofsales dollars

Contribution margin is equal to:

Sales price – variable cost

Contribution margin divided by sales revenueyields a percentage

Percentage of each dollar of sales revenue thatcontributes toward fixed costs and profit

Formula:

Example:

Yields the same breakeven as the contributionmargin approach earlier

Story Park competes with Splash World by providing avariety of rides. Story sells tickets at $50 per person as aone-day entrance fee. Variable costs are $10 per person,and fixed costs are $240,000 per month.

1. Compute the number of tickets Story must sell to breakeven. Perform a numerical proof to show that youranswer is correct.

Units sold = ($240,000 + 0) ÷ ($50 - $10)

Units sold = $240,000 ÷ $40

= 6,000 units to breakeven

1. Compute the number of tickets Story must sell to breakeven. Perform a numerical proof to show that youranswer is correct.

Total sales revenue $300,000

-Variable cost 60,000

Contribution margin $240,000

- Fixed cost 240,000

Operating income $ 0

1. Compute Story Park’s contribution margin ratio. Carryyour computation to two decimal places.

$50 - $10 = $40

$40 ÷ $50 = 0.80 or 80%

2. Use the contribution margin ratio CVP formula todetermine the sales revenue Story Park needs to breakeven.

$240,000 ÷ 0.80 = $300,000

Use CVP analysis for profit planning, andgraph the CVP relations

Managers more interested in:

Sales level needed to earn a target profit

Profits they can expect to earn

How many products or service events must be soldto earn a specific operating profit

Use either method

Set operating profit equal to desired profit

Graph provides a picture that shows how changes in thelevels of sales will affect profits

Four steps:

1.Choose a sales volume and plot the point for totalsales revenue at that volume

2.Draw the fixed cost line

3.Draw the total cost line (total costs are the sum ofvariable costs plus fixed costs)

4.Identify the breakeven point and the areas ofoperating income and loss

Consider the following facts:

Number of units

1,300

3,600

7.500

Sale price per unit

$100

$40

$125

Variable costs per unit

100

Total fixed costs

72,000

60,000

40,000

Target operating income

180,000

75,000

100,000

Calculate:

Contribution margin per unit

Contribution margin ratio

Breakeven points in units

Breakeven point in sales dollars

Units to achieve target operating income

Consider the following facts:

Number of units

1,300

3,600

7.,00

Sale price per unit

$100

$40

$125

Variable costs per unit

100

Total fixed costs

72,000

60,000

40,000

Target operating income

180,000

75,000

100,000

Calculate:

Contribution margin per unit

$60

$30

$25

Contribution margin ratio

60%

75%

20%

Breakeven points in units

1,200

2,000

1,600

Breakeven point in sales dollars

$120,000

$80,000

$200,000

Units to achieve target operating income

4,200

4,500

5,600

John Kyler is considering starting a Web-based educationalbusiness, e-Prep MBA. He plans to offer a short-course review ofaccounting for students entering MBA programs. The materialswould be available on a password-protected Web site; studentswould complete the course through self-study. Kyler would have tograde the course assignments, but most of the work is in developingthe course materials, setting up the site, and marketing.Unfortunately, Kyler’s hard drive crashed before he finished hisfinancial analysis.

However, he did recover the following partial CVP chart:

1. Label each axis, the sales revenue line, the total costs line, thefixed costs, the operating income area, and the breakeven point.

2. If Kyler attracts 300 students to take the course, will the venturebe profitable?

3. What are the breakeven sales in students and dollars?

1.Label each axis, the sales revenue line, the total costs line, thefixed costs, the operating income area, and the breakeven point.

2. If Kyler attracts 300 students to take the course, will the venturebe profitable?

3. What are the breakeven sales in students and dollars?

Sales Revenue

Total Cost

Fixed Cost

Operating

income

Breakeven

Will not be profitable. Possible loss of $8,000

Breakeven at 400 students, $40,000 in sales

Use CVP methods to perform sensitivity analysis

Predict how changes in sale prices, cost, orvolume affect profits

“What-if?” analysis

Allows managers to see how various businessstrategies affect profits

Changing selling price

Changing variable Costs

Changing fixed Costs

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How will the lower sale price affect thebreakeven point?

Lower price yields higher unit sales to breakeven

Higher prices yields lower unit sales to breakeven

How will increased costs affect the breakevenpoint?

Higher cost yields higher unit sales to breakeven

Lower cost yields lower unit sales to breakeven

How will the increased fixed costs affect thebreakeven point?

Higher fixed costs yields higher unit sales tobreakeven

Lower fixed costs yields lower unit sales tobreakeven

Exhibit 19-6

Excess of expected sales over breakeven sales

Cushion, drop in sales, a company can absorbwithout incurring a loss

Margin of safety in units

Margin of safety in dollars

1. Suppose Story Park cuts its ticket price from $50 to $40to increase the number of tickets sold. Compute the newbreakeven point in tickets and in sales dollars.

Units sold = ($240,000 + 0) ÷ ($40 - $10)

Units sold = $240,000 ÷ $30

= 8,000 units to breakeven

$320,000 sales dollars to breakeven

2. Ignore the information in Requirement 1. Instead,assume that Story Park increases the variable cost from$10 to $20 per ticket. Compute the new breakeven point intickets and in sales dollars.

Units sold = ($240,000 + 0) ÷ ($50 - $20)

Units sold = $240,000 ÷ $30

= 8,000 units to breakeven

= $400,000 in sales dollars

1. If Story Park expects to sell 6,200 tickets, compute themargin of safety in tickets and in sales dollars.

Expected sales - Breakeven sales = Margin of safety in units

6,200 – 6,000 = 200 in units

Margin of safety in units x Sales price = Margin of safety in dollars

200 units x $50 = $10,000

Calculate the breakeven point for multipleproduct lines or services

Selling prices and variable costs differ for eachproduct

Different contribution to profits

Weighted-average contribution margincomputed

Sales mix provides weights to make up totalproduct sales

Weights equal 100% of total product sales

Steps for Computing Breakeven Point with Multiple Product Lines

To compute breakeven sales in units for multipleproducts, complete the following three steps:

STEP 1: Calculate the weighted-averagecontribution margin per unit

STEP 2: Calculate the breakeven point in units forthe “package” of products

STEP 3: Calculate the breakeven point in units foreach product and then multiply the “package”breakeven point in units by each product’sproportion of the sales mix

Calculate the weighted-average contributionmargin per unit:

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

Calculate the breakeven point in units for eachproduct. Multiply the “package” breakevenpoint in units by each product’s proportion ofthe sales mix:

Prove this breakeven point by preparing acontribution margin income statement:

Wet Weekend Swim Park sells individual and family tickets, whichinclude a meal, three beverages, and unlimited use of the swimmingpools. Wet Weekend has the following ticket prices and variablecosts for 2012:

Wet Weekend expects to sell two individual tickets for every fourfamily tickets. Wet Weekend’s total fixed costs are $75,000.

1. Compute the weighted-average contribution margin per ticket.

2. Calculate the total number of tickets Wet Weekend must sell tobreak even.

3. Calculate the number of individual tickets and the number offamily tickets the company must sell to break even.

Individual

Family

Sale price per ticket

Variable cost per ticket

Wet Weekend expects to sell two individual tickets for every fourfamily tickets. Wet Weekend’s total fixed costs are $75,000.

1. Compute the weighted-average contribution margin per ticket.

Individual

Family

Total

Sale price per ticket

$ 30

$ 90

Variable cost per ticket

Contribution margin per unit

Sales mix in units

Contribution margin

$30

$120

150

Weighted-averagecontribution margin per unit

$25

2. Calculate the total number of tickets Wet Weekend must sell tobreak even.

3. Calculate the number of individual tickets and the number offamily tickets the company must sell to break even.

Individual

Family

Total

Sale price per ticket

$ 30

$ 90

Variable cost per ticket

Contribution margin per unit

Sales mix in units

Contribution margin

$30

$120

150

Weighted-averagecontribution margin per unit

$25

$75,000 ÷ $25 = 3,000 total tickets

3,000 total tickets x 2/6 = 1,000 individual tickets

3,000 total tickets x 4/6 = 2,000 family tickets

Distinguish between variable costing andabsorption costing

(Appendix 19A—online at myaccountinglab.com

Absorption costing:

Considers fixed manufacturing costs asinventoriable product costs

Variable costing:

Considers fixed manufacturing costs as period costs(expenses)

Summary of Differences Between Absorption Costing and Variable Costing

Type of Cost

Absorption Costing

Variable Costing

Product Costs(capitalized as Inventoryuntil expensed as Cost ofgoods sold)

Direct materials

Direct labor

Variable manufacturingoverhead

Fixed manufacturing overhead

Direct materials

Direct labor

Variable manufacturingoverhead

Period Costs (expensedin period incurred)

Variable nonmanufacturingcosts

Fixed nonmanufacturing costs

Fixed manufacturingoverhead

Variable nonmanufacturingcosts

Fixed nonmanufacturingcosts

Income StatementFormat

Conventional incomestatement

Contribution marginincome statement

Variable costs are those costs that increase ordecrease in total as the volume of activityincreases or decreases. Fixed costs are costs thatdo not change over wide ranges of volume. Coststhat have both variable and fixed components arecalled mixed costs.

The high-low method is an easy way to separatemixed costs into variable and fixed componentsby requiring you to identify the highest andlowest levels of activity over a period of time.The relevant range is the range of activity wheretotal fixed cost stays the same and variable costper unit stays the same.

The breakeven point is the sales level at whichoperating income is zero—total revenues equaltotal costs. The breakeven point can be found byusing the income statement approach, using zerofor operating income. The breakeven point canalso be found by dividing total fixed cost by thecontribution margin per unit (sales price per unit –variable cost per unit).

Breakeven analysis can be used to calculate thesales volume needed to earn a certain amount ofprofit, called target profit. Target profit is theoperating income that results when sales revenueminus variable costs and minus fixed costs equalsmanagement’s profit goal.

Graphing various activity levels and costs gives avisual representation of operating levels thatgenerate net income and operating levels thatresult in net loss.

Sensitivity analysis is a “what if” technique thatasks what results are likely if selling price orcosts change or if an underlying assumptionchanges. The income statement approach tobreakeven is just adjusted for the new proposedvalues.

The margin of safety is the “cushion” or drop insales that the company can absorb beforeincurring a loss.

Most companies sell more than one product.Selling price and variable costs differ for eachproduct, so each product makes a differentcontribution to profits. To calculate break even foreach product, we compute the weighted-averagecontribution margin of all the company’s products.

The combination of products that make up totalsales, called the sales mix (or product mix),provides the weights that make up total productsales.

Variable costing assigns only variablemanufacturing costs to products. Fixedmanufacturing costs are considered period costsand are expensed immediately because thecompany incurs these fixed costs whether or not itproduces any products or services.

In variable costing, fixed manufacturing costs arenot treated as product costs. Managementaccountants often prefer variable costing becausecontribution margin is readily apparent on thevariable costing income statement.

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