Prepared by Debby Bloom-Hill CMA, CFM
Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis
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CHAPTER 4CHAPTER 4
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, and estimate the relation between cost and activity using account analysis and the high-low method.
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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 PatternsCommon Cost Behavior Patterns
Slide 4-4Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Common Cost Behavior PatternsCommon Cost Behavior Patterns
Slide 4-5Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-6 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-7Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Variable CostsVariable Costs
Total Variable Cost = $91 × Units producedSlide 4-8 Learning objective 1: Identify common cost behavior
patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-9 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Fixed CostsFixed Costs
Total fixed cost = $94,000
Slide 4-10Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-11Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-12 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Mixed CostsMixed Costs
Total cost = ($91 × Units produced) + $94,000Slide 4-13 Learning objective 1: Identify common cost behavior
patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-14Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Step Variable CostStep Variable Cost
Slide 4-15Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Step Fixed CostStep Fixed Cost
Slide 4-16Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
The Relevant RangeThe Relevant Range
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
Slide 4-18 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-19 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-20 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Account AnalysisAccount Analysis
Slide 4-21 Learning objective 1: Identify common cost behavior patterns, and 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
Slide 4-22Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
ScattergraphsScattergraphs
Is there a relationship between units produced and production costs? Describe the relationship.
Slide 4-23 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
in relation to the change in activity level Total cost at lowest or highest activity level minus
variable cost at that level equals fixed cost
Slide 4-24 Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
High-Low MethodHigh-Low Method
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Total cost at high activity level
Total cost at low activity
level
Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
High-Low MethodHigh-Low Method
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Month Cost
January 750 $170,000February 1,000 175,000March 1,250 205,000April 1,750 250,000May 2,000 265,000June 2,250 275,000July 3,000 400,000 HighAugust 2,750 350,000September 2,500 300,000October 1,250 210,000November 1,000 190,000December 500 150,000 Low
Total 20,000 $2,940,000
Production
Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Estimate Variable CostEstimate Variable Cost
Slide 4-27Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Estimate Fixed CostEstimate Fixed Cost
Slide 4-28Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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: cSlide 4-29
Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-30Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
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
Slide 4-31Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
The Relevant Range and Cost Estimation
The Relevant Range and Cost Estimation
Estimates of fixed and variable costs are valid for only a limited range of activity Known as the relevant range
Outside the relevant range, estimates of fixed and variable costs may not be useful
Actual costs may behave in a manner that is different from the common cost behavior patterns
Slide 4-32Learning objective 1: Identify common cost behavior patterns, and estimate the relation between cost and activity using account analysis and the high-low method.
Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis
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
Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis
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 $81.50 per unit Monthly fixed production cost $102,000 Monthly fixed selling and administrative $63,900
Find CodeConnect’s break-even point
Slide 4-34 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Cost-Volume-Profit AnalysisCost-Volume-Profit Analysis
Break-Even Point$0 = SP(x) – VC(x) – TFC$0 = $200.00 (x) – $81.50(x) – $165,900
$118.50(x) = $165,900
x = 1,400 units Always round up if the breakeven point is not a
whole number
Slide 4-35Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Break-Even PointBreak-Even Point
Slide 4-36Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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
Slide 4-37Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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) – $6,000$300(x) = $6,000x = $6,000 / $300 = 20 cakes to break even
Slide 4-38 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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
$280,000 and expected sales are $350,000, calculate the margin of safety
The margin of safety is:
$350,000 - $280,000= $70,000
Slide 4-39Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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
Slide 4-40Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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 $81.50
$200.00 – $81.50 = $118.50
Slide 4-41 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Contribution MarginContribution Margin
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
Slide 4-42Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Contribution MarginContribution Margin
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 * $118.50 = $11,850
Slide 4-43Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Units Needed for Target ProfitUnits Needed for Target Profit
Solve the profit equation for the sales quantity in units Unit sales (x) needed to attain a specified
profit =
Slide 4-44Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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 4-45Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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) / Sales
2. Unit contribution margin divided by selling price (SP – VC) / SP
Slide 4-46Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Contribution Margin RatioContribution Margin Ratio
For the Model DX375 bar code reader, the contribution margin ratio is
= 0.5925 This indicates that the company earns an
incremental $0.5925 for every dollar of sales If sales increase $10,000 the incremental profit
is 0.5925 * $10,000 = $5,925
Slide 4-47Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Dollar Sales Needed to Achieve Profit Target
Dollar Sales Needed to Achieve Profit Target
Calculate the amount of sales dollars needed to earn a monthly profit of $35,550
Slide 4-48Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
“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 affected by various options under consideration CodeConnect is selling 3,000 units at $200,
with variable cost of $81.50 and fixed cost of $165,900
Management is considering a change to $80.00 variable cost and fixed cost of $215,900
Slide 4-49Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
“What If” Analysis“What If” Analysis
Change in fixed and variable costs Without the change, the profit is
$200(3,000) - $81.50(3,000) - $165,900 = $189,600
If the price and quantity stay the same, the profit assuming the alternative is selected would be
$200(3,000) - $80(3,000) - $215,900 = $144,100
The alternative would hurt profitability
Slide 4-50 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
“What If” Analysis“What If” Analysis
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) - $81.50(3,000) - $165,900
SP(3,000) = $610,400
SP = $203.47
Slide 4-51 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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
Slide 4-52Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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 4-53Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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
Slide 4-54Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
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The sales mix is 2:1 Model A, Model B The company has fixed costs of $3,500,000
Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
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 4-56Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
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
Slide 4-57Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
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
Slide 4-58 Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
Can calculate the contribution margin ratio for each product line Can also easily calculate the break-even point for
the various product lines Break-even sales for garden tools is $95,000 / .1874
= $506,937 When total company sales increase, each
product line’s sales will increase proportionately Can use the contribution margin ratio to calculate
the increase in profit for each product line
Slide 4-59Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Multiproduct AnalysisMultiproduct Analysis
Slide 4-60Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
Assumptions in CVP AnalysisAssumptions in CVP Analysis
Assumptions can affect the validity of the analysis1. Costs can be separated into fixed and
variable components
2. 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
Slide 4-61Learning objective 2: Perform cost-volume profit analysis for single and multiple products.
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 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.
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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
Slide 4-63 Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.
ConstraintsConstraints
A company can produce Product A or Product B using the same machinery. Only 1,000 machine hours are available.
Slide 4-64Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.
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
Slide 4-65Learning objective 3: Discuss the effect of operating leverage, and use the contribution margin per unit of the constraint to analyze situations involving a resource constraint.
CHAPTER 4CHAPTER 4
Cost-Volume-Profit Analysis Appendix
Cost-Volume-Profit Analysis Appendix
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Regression AnalysisRegression Analysis
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Regression AnalysisRegression Analysis
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Regression AnalysisRegression Analysis
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