Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 19 1.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Cost-Volume-Profit Analysis

Chapter 19

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Types of Costs

The effect of volume of activity on costsVariable costs

Increase or decrease in total in direct proportion to changes in the volume of activity

Fixed costsDo not change over wide ranges of volume

Mixed costsHave both variable and fixed components

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Variable Costs

Total variable costs change in direct proportion to changes in the volume of activity

If activity increases, so does the costUnit variable cost remains constant

Volume can be measured in many different ways:

Number of units soldNumber of units producedNumber of miles driven by a delivery vehicleNumber of phone calls placed

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Total Variable Costs

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Fixed CostsTend to remain the same in amount, regardless of variations in level of activityExamples:

Straight-line depreciationSalaries

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

The more activity, the less the fixed cost per unit

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Total Fixed Costs and Fixed Costs per Unit

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Mixed CostsHave both a fixed and variable componentExample:

Utilities that charge a set fee per month, plus a charge for usageYour cell phoneprovider

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Mixed Costs

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High-Low MethodMethod to separate mixed costs into variable and fixed componentsIdentify the highest and lowest levels of activity over 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 the behavior of a mixed cost

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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


High-Low Method: Steps 1 and 2

Data

Step 1

Step 2

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Step 3

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

Now check your formula against the original data($2 x 480 + $1000 = $1960) or($2 x 240 + $1,000 = $1480)


Relevant RangeRange of volume:

Where total fixed costs remain constant and variable cost per unit remains constant

Outside the relevant range, costs can differ

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S19-1: VARIABLE, FIXED, AND MIXED COSTS

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

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1. Units of production depreciation on routers used to cut wood enclosures

2. Wood for speaker enclosures

3. Patents on crossover relays

4. Total compensation to salesperson, who receives a salary plus a commission based on meeting sales goals

5. Crossover relays

V

V

F

M

V


S19-1: VARIABLE, FIXED, AND MIXED COSTS

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

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6. Straight-line depreciation on manufacturing plant

7. Grill cloth

8. Cell phone costs of salesperson (plan includes 1,200 minutes; overseas calls are charged at an average of $0.15 per minute)

9. Glue

10. Quality inspector’s salary

F

V

M

V

F


S19-3: MIXED COSTS—HIGH-LOW METHOD

Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 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 activity volume

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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


S19-3: MIXED COSTS—HIGH-LOW METHOD

Martin owns a machine shop. In reviewing his utility bill for the last 12 months, he found that his highest bill of $2,800 occurred in August when his machines worked 1,400 machine hours. His lowest utility bill of $2,600 occurred in December when his machines worked 900 machine hours.

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

$ 0.40 per machine hour + $2,240

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

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Basic CVP AnalysisExpresses the relationships among costs, volume, and profit or lossAnswers:

How many products or services must the company sell to break even?What will profits be if sales double?How will changes in selling price, variable costs, or fixed costs affect profits?

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Basic CVP Analysis

Assumptions:Managers can classify each cost as either variable or fixedOnly factor that affects total costs is change in volume, which increases variable and mixed costs

Fixed costs do not change

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Breakeven PointSales level at which operating income is zero:

Total revenues equal total costs (expenses)Sales above breakeven result in a profitSales below breakeven result in a loss

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Breakeven Point

Two methods to compute breakeven point:Income statement approach

Sales revenue − Total costs = Operating income

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

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Break Even Example Data

Unit sale priceUnit variable costFixed costsUnit contribution margin

$200$80$12,000$120 ($200 - $80)

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Income Statement ApproachExpress income in equation form and then break it down into its components:

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Contribution Margin ApproachShortcut method

The contribution margin is sales revenue minus variable costs (expenses)

Called contribution margin because the excess of sales revenue over variable costs contributes to covering fixed costs

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Rearrange the income statement—use the contribution margin to develop a shortcut method

Shortcut equation:

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Contribution Margin Approach


Contribution Margin ApproachGiven fixed costs total $12,000. The contribution margin per event is $120 ($200 sale price – $80 variable cost)

Check your answer

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Contribution Margin RatioRatio of contribution margin to sales revenueUsed to compute the breakeven point in terms of sales dollars

Contribution margin is equal to:Sales price – variable cost

Contribution margin divided by sales revenue yields a percentage

Percentage of each dollar of sales revenue that contributes toward fixed costs and profit

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Contribution Margin RatioFormula:

Example:

Yields the same breakeven as the contribution margin approach earlier

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Unit CM $120Unit Sale Price $200


S19-4: COMPUTING BREAKEVEN POINT IN SALES UNITS

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-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 break

even. Perform a numerical proof to show that your answer is correct.

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Units sold = ($240,000 + 0) ÷ ($50 - $10)Units sold = $240,000 ÷ $40 = 6,000 units to breakeven


S19-4: COMPUTING BREAKEVEN POINT IN SALES UNITS

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-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 break

even. Perform a numerical proof to show that your answer is correct.

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Total sales revenue $300,000 (6,000 x 50)- Variable cost 60,000 (6,000 x 10) Contribution margin $240,000- Fixed cost 240,000 Operating income $ 0


S19-5: COMPUTING BREAKEVEN POINT IN SALES DOLLARS

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.1. Compute Story Park’s contribution margin ratio. Carry

your computation to two decimal places.

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$50 - $10 = $40$40 ÷ $50 = 0.80 or 80%

2. Use the contribution margin ratio CVP formula to determine the sales revenue Story Park needs to break even.

$240,000 ÷ 0.80 = $300,000


Use CVP analysis for profit planning, and graph the CVP relations

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3


Using CVP to Plan ProfitsManagers more interested in:

Sales level needed to earn a target profitProfits they can expect to earnHow many products or service events must be sold to earn a specific operating profit

Use either method (equation or CM)Set operating profit equal to desired profit

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Using CVP to Plan Profits

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Graphing Cost-Volume-Profit RelationsGraph provides a picture that shows how changes in the levels of sales will affect profitsFour steps:1. Choose a sales volume and plot the point for total

sales revenue at that volume2. Draw the fixed cost line3. Draw the total cost line (total costs are the sum of

variable costs plus fixed costs) 4. Identify the breakeven point and the areas of

operating income and loss

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Preparing a CVP Chart

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S19-6: COMPUTING CONTRIBUTION MARGIN, BREAKEVEN POINT, AND UNITS TO ACHIEVE OPERATING INCOME

Consider the following facts:

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A B CNumber of units 1,300 3,600 7.500

Sale price per unit $100 $40 $125

Variable costs per unit 40 10 100

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


S19-6: COMPUTING CONTRIBUTION MARGIN, BREAKEVEN POINT, AND UNITS TO ACHIEVE OPERATING INCOME

Consider the following facts:

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A B CNumber of units 1,300 3,600 7.,00

Sale price per unit $100 $40 $125

Variable costs per unit 40 10 100

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

$72,000/$60

($72,000 + $180,000)/$60


Sensitivity AnalysisPredict how changes in sale prices, cost, or volume affect profits“What-if?” analysisAllows managers to see how various business strategies affect profits

Changing selling priceChanging variable CostsChanging fixed Costs

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Sensitivity Analysis: ExampleHow will the lower sale price affect the breakeven point?

Lower price yields higher unit sales to breakevenHigher prices yields lower unit sales to breakeven

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Sensitivity Analysis: ExampleHow will increased costs affect the breakeven point?

Higher cost yields higher unit sales to breakevenLower cost yields lower unit sales to breakeven

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Sensitivity Analysis: ExampleHow will the increased fixed costs affect the breakeven point?

Higher fixed costs yields higher unit sales to breakevenLower fixed costs yields lower unit sales to breakeven

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Sensitivity Analysis Summary

Exhibit 19-6

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Margin of SafetyExcess of expected sales over breakeven salesCushion, drop in sales, a company can absorb without incurring a lossMargin of safety in units

Margin of safety in dollars

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S19-7: SENSITIVITY ANALYSIS OF CHANGING SALE PRICE AND VARIABLE COSTS ON BREAKEVEN POINT

Story Park competes with Splash World by providing a variety of rides. Story sells tickets at $50 per person as a one-day entrance fee. Variable costs are $10 per person, and fixed costs are $240,000 per month.1. Suppose Story Park cuts its ticket price from $50 to $40 to increase the number of tickets sold. Compute the new breakeven point in tickets and in sales dollars.

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$320,000 sales dollars to breakeven

Old Breakeven 6,000 units, $300,000


S19-7: SENSITIVITY ANALYSIS OF CHANGING SALE PRICE AND VARIABLE COSTS ON BREAKEVEN POINT

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

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= $400,000 in sales dollars


S19-9: COMPUTING MARGIN OF SAFETY

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

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

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Expected sales - Breakeven sales = Margin of safety in units6,200 – 6,000 = 200 in units

Margin of safety in units x Sales price = Margin of safety in dollars200 units x $50 = $10,000


Breakeven Point Multiple Product Lines

Selling prices and variable costs differ for each product

Different contribution to profits

Weighted-average contribution margin computedSales mix provides weights to make up total product sales

Weights equal 100% of total product sales

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Steps for Computing Breakeven Point with Multiple Product Lines

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

STEP 1: Calculate the weighted-average contribution margin per unitSTEP 2: Calculate the breakeven point in units for the “package” of productsSTEP 3: Calculate the breakeven point in units for each product and then multiply the “package” breakeven point in units by each product’s proportion of the sales mix

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

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

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

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ProofProve this breakeven point by preparing a contribution margin income statement:

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S19-10: CALCULATING WEIGHTED-AVERAGE CONTRIBUTION MARGINWet Weekend Swim Park sells individual and family tickets, which include a meal, three beverages, and unlimited use of the swimming pools. Wet Weekend has the following ticket prices and variable costs for 2012:

Wet Weekend expects to sell two individual tickets for every four family 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 to

break even.3. Calculate the number of individual tickets and the number of

family tickets the company must sell to break even.

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Individual Family

Sale price per ticket 30 90

Variable cost per ticket 15 60


S19-10: CALCULATING WEIGHTED-AVERAGE CONTRIBUTION MARGINWet Weekend expects to sell two individual tickets for every four family tickets. Wet Weekend’s total fixed costs are $75,000.1. Compute the weighted-average contribution margin per ticket.

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Individual Family Total

Sale price per ticket $ 30 $ 90


Contribution margin per unit 15 30

Sales mix in units 2 4 6

Contribution margin $30 $120 150

Weighted-average contribution margin per unit $25


S19-10: CALCULATING WEIGHTED-AVERAGE CONTRIBUTION MARGIN

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

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

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Individual Family Total

Sale price per ticket $ 30 $ 90


Contribution margin per unit 15 30

Sales mix in units 2 4 6

Contribution margin $30 $120 150

Weighted-average contribution margin per unit $25

$75,000 ÷ $25 = 3,000 total tickets

3,000 total tickets x 2/6 = 1,000 individual tickets3,000 total tickets x 4/6 = 2,000 family tickets

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 19 1.

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Transcript of Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 19 1.