Prepared by Debby Bloom-Hill CMA, CFM. CHAPTER 4 Cost-Volume-Profit Analysis Slide 4-2

Prepared by Debby Bloom-Hill CMA, CFM

CHAPTER 4CHAPTER 4

Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis

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Management QuestionsManagement Questions

Planning What level of profit should be in the

budget for the coming year? Control

Did the manager responsible for production costs do a good job of controlling costs?

Decision making Should the price be increased?

Learning objective 1: Identify common cost behavior patterns

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Variable Costs Costs which change directly in

proportion to changes in quantity or activity

Fixed Costs Costs which do not change when

quantity or activity volume changes

Common Cost Behavior Patterns



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Mixed Costs Costs that have both variable and

fixed elements Step Costs

Fixed for a range of output, but increase when upper bound of range is exceeded




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Variable CostsVariable Costs Costs that change in proportion to

changes in volume or activity An automobile manufacturer will

need 400 tires to make 100 cars, but 4,000 tires to make 1,000 cars

A bakery will need 2 eggs to make 1 cake and 20 eggs to make 10 cakes

If activity increases by a certain percentage, cost increases by that same percentage


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A company has decided that direct labor costs are 100% variable. Last month total direct labor costs were $125,000 and total direct labor hours worked were 10,000.1.What is the direct labor cost per hour?

$125,000 / 10,000 hours = $12.50 per hour

2.Predict labor costs in a month when 12,000 labor hours are worked

$12.50 per hour × 12,000 hours = $150,000


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Variable CostsVariable Costs

Total Variable Cost = $91 × Units produced


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Fixed CostsFixed Costs

Do not change in response to changes in activity level

Typical fixed costs are depreciation, supervisory salaries, and building maintenance• Rent for a bakery will not double if

output increases from 100 to 200 cakes

If activity increases by a certain percentage, costs remain unchanged


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Fixed CostsFixed Costs

Total fixed cost = $94,000


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Fixed CostsFixed Costs Discretionary fixed costs

Management can easily change, e.g. advertising, research & development Many companies cut back on these costs

when sales drop. This can be shortsighted

A cut in research & development can have a negative effect on long run profitability

A cut in repair and maintenance can have a negative effect on the life of valuable assets

Committed fixed costs Cannot be easily changed, e.g. rent,

insurance Learning objective 1: Identify common cost behavior patternsSlide 4-11

Mixed CostsMixed Costs

Contain both variable and fixed cost elements

Can separate mixed costs into variable and fixed components Salesperson with base salary (fixed)

and commission on sales (variable) Base salary included with fixed costs Commission included with variable

costs


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Mixed CostsMixed Costs

Total cost = ($91 × Units produced) + $94,000


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Step CostsStep Costs

Fixed cost for a specific range of volume Increases to higher level when upper

bound of range is exceeded At that point, costs again remain fixed

until another upper bound is exceeded Step costs are often classified as either:

Step variable costs, if the range of activity where the cost is fixed is small, or

Step fixed costs, if the range of activity where the cost is fixed is large


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Step CostsStep Costs

Total step costs = $7,000 for relevant range 0 – 3,000 units

produced$14,000 for relevant range 3,001 – 6,000 units$21,000 for relevant range 6,001 – 9,000 units


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Relevant RangeRelevant Range


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The relevant range is the range of activity for which assumptions as to how costs behave are reasonably valid If it is known that production is going

to be within the relevant range, we can use assumptions about the fixed and variable costs

Making assumptions about fixed and variable costs at production levels well above or below this range would not be valid

The Relevant RangeThe Relevant Range

Learning objective 3: Perform cost-volume profit analysis for single products

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Cost Estimation MethodsCost Estimation Methods

Account Analysis Classify costs into variable and fixed

pools Scattergraphs

Can see cost relationships visually High-Low Method

Linear estimation connects high and low volume observations

Regression Analysis Linear estimation is best fit to observed

values

Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

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Account AnalysisAccount Analysis

Most common approach Requires professional judgment of

management Management classifies costs as

fixed, variable, or mixed Total variable costs divided by

activity equals variable cost per unit Variable cost per unit and total fixed

costs can be used in cost equation


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Account AnalysisAccount Analysis

Slide 4-20Learning objective 2: Estimate the relation between cost and activity using account analysis and the high-low method

ScattergraphsScattergraphs

Utilization of cost information from several previous periods

Weekly, monthly, or quarterly cost reports are useful

Plot the actual costs at the observed activity levels Look for relationship between cost

and activity, linear is ideal Use relationship to predict future

costs


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ScattergraphsScattergraphs

Is there a relationship between units produced and production costs? Describe the relationship.


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High-Low MethodHigh-Low Method

Utilization of cost information from previous periods

Fits a straight line from lowest activity level to highest activity level Slope of the line is the estimate of the

unit variable cost The slope measures the change in cost per unit change in activity level

Total cost at lowest or highest activity level minus variable cost at that level equals fixed cost


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Total cost at high

activity level

Total cost at low activity

level



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During the past year, Island Air flew 15,000 miles in August (its busiest month) and had total costs of $300,000. In November (its least busy month) the company flew 5,000 miles and had $200,000 of costs. Using the high-low method, estimate variable cost per mile and fixed cost per month.

a. $20 of variable cost and $100,000 fixedb. $15 of variable cost and $250,000 fixedc. $10 of variable cost and $150,000 fixedd. $5 of variable cost and $250,000 fixed

Answer: c


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During the past year, Island Air flew 15,000 miles in August (its busiest month) and had total costs of $300,000. In November (its least busy month) the company flew 5,000 miles and had $200,000 of costs. Using the high-low method, estimate variable cost per mile and fixed cost per month.

Estimate of variable cost = = = $10

Variable cost at low level = $10 * 5,000 miles = $50,000

Fixed cost = $200,000 total – $50,000 variable = $150,000


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Regression AnalysisRegression Analysis

Statistical technique Estimates the slope and intercept of a

cost equation Finds the best straight line fit to the

observations Typically statistical software packages

are utilized Spreadsheet applications like Excel®

typically include statistical operations See appendix fox Excel® example


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The Profit Equation

Profit = SP(x) – VC(x) – TFC

Where: x = Quantity of units produced and

sold SP = Selling price per unit VC = Variable cost per unitTFC = Total fixed cost

Fundamental to CVP analysis


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Break-Even Point Number of units sold that allow the

company to neither earn a profit nor incur a loss

$0 = SP(x) – VC(x) – TFC CodeConnect has the following cost

structure Selling price $200.00 per unit Variable cost $90.83 per unit Total fixed cost $160,285

Find CodeConnect’s break-even point


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Break-Even Point$0 = SP(x) – VC(x) – TFC$0 = $200.00 (x) – $90.83(x) – $160,285$0 = $109.17(x) – $160,285$109.17(x) = $160,285x = $160,285 / $109.17x = 1,468.21 units

Break-even point is 1,469 units (always round up)


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Break-Even PointBreak-Even Point


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Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000. What is the break-even point in number of units?

a. 200b. 20c. 12d. 100

Answer: b


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Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000. What is the break-even point in number of units?

0 = SP(x) – VC(x) – TFC0 = (SP – VC)(x) – TFC0 = (500 – 200)(x) – 6,0000 = 300(x) – 6,000300(x) = 6,000x = 6,000 / 300 = 20


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Margin of SafetyMargin of Safety

The margin of safety is the difference between the expected level of sales and break-even sales If breakeven sales for Model DX375 is

$293,600 and expected sales are $350,000, calculate the margin of safety

The margin of safety is: $350,000 - $293,600 = $56,400


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Margin of Safety RatioMargin of Safety Ratio

The margin of safety can also be expressed as a ratio Called the margin of safety ratio Equal to the margin of safety divided

by expected sales Shows what percentage sales would

have to drop before the product shows a loss

= = = 0.16


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Margin ofsafety ratio

Contribution MarginContribution Margin

Difference between revenue and variable costs Contribution margin = total revenue

minus total variable costs Contribution margin per unit =

selling price minus variable cost per unit For CodeConnect’s Model DX375, the contribution margin is the $200.00 selling price less the variable cost of $90.83

$200.00 – $90.83 = $109.17Learning objective 3: Perform cost-volume profit analysis for single products

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The contribution margin per unit measures the amount of incremental profit generated by selling an additional unit For CodeConnect, how much

incremental profit would be generated by selling 100 more units?

Incremental profit = number of units sold * contribution margin per unit

Incremental profit = 100 * $109.17 = $10,917


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The profit equation in terms of the contribution margin

Profit = SP(x) – VC(x) – TFC

Profit = (SP – VC)(x) – TFC

Profit = Contribution margin per unit(x) - TFC


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Units Needed for Target Profit

Units Needed for Target Profit

Solve the profit equation for the sales quantity in units Unit sales (x) needed to attain a

specified profit =

=


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Gabby’s Wedding Cakes creates elaborate wedding cakes. Each cake sells for $500. The variable cost of baking the cakes is $200 and the fixed cost per month is $6,000

1.Calculate the break-even point in units

= = = 20 cakes

2. How many cakes must be sold to earn a profit of $9,000?

= = = 50 cakes


Slide 4-42

Contribution Margin RatioContribution Margin Ratio

The unit contribution margin ratio measures the amount of incremental profit generated by an additional dollar of sales Two methods to calculate the

contribution margin ratio1. Contribution margin divided by

sales revenue (Sales – TVC) / Sales2. Unit contribution margin divided by

selling price (SP – VC) / SP


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Contribution Margin RatioContribution Margin Ratio

For the Model DX375 bar code reader, the contribution margin ratio is

= 0.54585 This indicates that the company earns

an incremental $0.54585 for every dollar of sales

If sales increase $10,000 the incremental profit is 0.54585 * $10,000 = $5,458.50


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“What If” Analysis“What If” Analysis

“What if” analysis examines what will happen if an action is taken The profit equation can show how

profit will be affect by various options under consideration CodeConnect is selling 3,000 units at $200, with variable cost of $90.83 and fixed cost of $160,285

Management is considering a change to $80.00 variable cost and fixed cost of $210,285


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Change in fixed and variable costs Without the change, the profit is

$200(3,000) - $90.83(3,000) - $160,285 = $167,225

If the price and quantity stay the same, the profit assuming the alternative is selected would be

$200(3,000) - $80(3,000) - $210,285 = $149,715

The alternative would hurt profitability


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Change in selling price Any one of the variables in the profit

equation can be considered For example, if CodeConnect sells

3,000 units, what selling price is required to earn a profit of $200,000?

$200,000 = SP(3,000) - $90.83(3,000) - $160,285SP(3,000) = $632,775SP = $210.93


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Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000?

a. $500

b. $350

c. $400

d. $200

Answer: c


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Matthews Consulting expects to work 5,000 hours next month. It has variable costs of $100 per hour and fixed costs of $600,000. What price must the company charge to earn a monthly profit of $900,000?

$900,000 = SP(5,000) - $100(5,000) - $600,000$900,000 = SP(5,000) - $1,100,000SP(5,000) = $2,000,000SP = $2,000,000 / 5,000 = $400


Slide 4-49

Multiproduct AnalysisMultiproduct Analysis

Contribution margin approach Used if the items sold are similar Calculate a weighted average

contribution margin per unit Use the weighted average contribution

margin in the profit formula to calculate breakeven point and target sales

The relative product mix is then used to calculate the required sales of individual items


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Learning objective 4: Perform cost-volume profit analysis for multiple products

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The company has fixed costs of $3,500,000

Multiproduct AnalysisMultiproduct Analysis Break-even sales in units

=

= 2,500 units

The 2,500 units is made up of the 2:1 mix, so Rohr must sell 1,667 Model A (2/3 of 2,500) and 833 Model B units (1/3 0f 2,500)


Slide 4-52


Contribution Margin Ratio Approach Products are substantially different

Calculate total company contribution margin ratio

Use total company contribution margin ratio to compute required sales in dollars Total company fixed costs (common

costs) are not included for contribution margin approach but used for contribution margin ratio approach


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A company with 4 divisions has the following information available:

Total sales $6,450,000Total variable costs $4,706,000Total direct fixed costs $484,000Total common fixed costs $1,120,000

1.Calculate total contribution margin ratio($6,450,000 – $4,706,000) / $6,450,000 = .2704

2.Calculate total company break-even sales in dollars($484,000 + $1,120,000) / .2704 = $5,931,953 Learning objective 4: Perform cost-volume profit analysis for multiple products

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Assumptions in CVP Analysis

Assumptions in CVP Analysis

Assumptions can affect the validity of the analysis1. Costs can be separated into fixed

and variable components2. Total fixed cost and unit variable

cost do not change over the levels of interest

3. Multiproduct analysis assumes the product mix does not change

Despite assumptions, CVP is useful


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Operating LeverageOperating Leverage

Level of fixed versus variable costs in a company

A company with a high level of fixed costs has a high operating leverage Companies with high operating

leverage have large fluctuations in profit when sales increase or decrease These companies are seen as more risky

High operating leverage is better when sales are expected to increase

Learning objective 5: Discuss the effect of operating leverage

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ConstraintsConstraints Due to shortages of space, equipment or

labor there can be constraints on how many items can be produced

Utilize contribution margin per unit to analyze situations Calculate contribution margin per unit of

constraint Produce product with highest

contribution margin per unit of constraint

Linear programming can solve multiple constraints

Learning objective 6: Use the cost per unit of the constraint to analyze situations involving a resource constraint

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ConstraintsConstraints

A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available

Product A Product BSelling price $500 $300Variable cost 300 200Contribution margin $200 $100Machine hours toproduce one unit 10 hours 2 hoursContribution marginper machine hour $20 $50


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ConstraintsConstraints With the 1,000 available machine

hours, Product A generates $20,000 of

contribution margin Product B generates $50,000 of

contribution margin Although Product A has the higher

contribution margin per unit, Product B has the higher contribution margin per unit of constraint


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CHAPTER 4CHAPTER 4

Cost-Volume-Profit Analysis

Appendix

Cost-Volume-Profit Analysis

Appendix

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CopyrightCopyright© 2010 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.Slide 4-64

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Prepared by Debby Bloom-Hill CMA, CFM. CHAPTER 4 Cost-Volume-Profit Analysis Slide 4-2