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COST VOLUME PROFIT
Richard E. McDermott Ph.D.
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Costs Volume Profit
In this chapter we study what happens to bothcost and profit as volume changes.The tools we will use will be helpful in thedevelopment of flexible budgets.I am going to begin by giving you some basicdefinitions.
I will then give you what I feel are the bestformulas to use in working the problems youwill be assigned.
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Definitions
Variable Costs: Costs that vary in total, directlyand proportionately, with changes inproduction (also called activity level).
If the activity level increases by 50%, variablecosts increase by 50%.
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Examples of Variable Costs
Direct laborDirect materialsVariable overhead
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Definitions
Mixed Costs: costs that contain both a fixedand a variable element.Mixed cost change in total, but not
proportionately, with changes in the activitylevel.An example of a mixed cost might bemaintenance cost on a taxi.
Maintenance costs increase as miles increase.Even if the truck is never driven, however, it is agood idea to change the oil every three months tokeep it from degenerating.
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Separating Fixed and VariableCosts
If you will look at a general ledger, you willnever find accounts labeled ―variable labor‖ or ―fixed labor‖ or ―variable overhead‖ or ―fixed
overhead.‖ In order to perform cost volume profit analysis,therefore, it is usually necessary to separatefixed and variable costs.
There are three methods to do this:Scatter graph methodHigh-low methodLeast squares method
The best method is theleast squares method,but since the authordoes not teach it we willnot cover it either.
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Definitions
Fixed Costs: Costs that do not change withincreases or decreases in production volume.It is important to add, there is usually a relevantrange.For example, a plant may be built to manufacture1 to 10,000 shoes per month.Fixed costs would not change within this ―relevant
range.‖ If a company wanted to manufacture 12,000shoes per month, however, there of course wouldbe a new relevant range and the fixed costs might
increase.
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Examples of Fixed Costs
Rent on a factoryDepreciation – straight-line methodHeating and air-conditioning expenseHousekeeping
It is important to emphasize that what might be a
fixed cost in one factory, could be a variable cost inanother, depending upon the way the firm doesbusiness.
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Other Definitions
Contribution Margin: Revenue (or unit price)minus total variable costs (or unit variablecosts).
Example:Contribution Margin IncomeStatement
Sales $100,000Less variable costs 60,000Contribution margin $40,000Less fixed costs 30,000Income from
operations
$10,000
Note thatcontributionmargin is
what is leftafter payingvariablecosts.
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Notation
I will use the following notation when referringto contribution margin:
CMu = contribution margin per unit of produce,
calculated as follows: Price – Variable Cost PerUnit = Cmu.CMt = contribution margin total calculated asfollows: Total Sales – Total Variable Costs = CMtCMr = contribution margin ratio calculated asfollows: CMt/Total Sales or CMu/Price.
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Tip for Examination
In any problem where the only change isvolume (i.e. variable costs per unit, and fixedcosts do not change), then the impact of the
change on operating income can be calculatedsimply by calculating the change in totalcontribution margin.The change in total contribution margin willequal the change in operating income.We will illustrate this in a moment.
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Here Are Some Formulas I Wouldlike You to Learn
PX – VX – F = P
whereP = unit priceX = volume of units soldV = variable cost per unitF = total fixed priceP = operating income or profit
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Breakeven
Breakeven is defined as the point where thefirm neither makes nor loses money.The formula for breakeven is:PX – VX – F = 0Let us illustrate the solution for breakeven withan example.
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Example
Morris Electronics makes calculators.The market dictates a price of $30 for a modelwith their particular features.Variable costs per unit are $16, total fixedcosts are $200,000.What is the breakeven point in units for sales
of the calculators?
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Solution
PX - VX – F = 030X – 16X – 200,000 = 014X = 200,000X = 14,285.714286calculators
Income statement
Sales $428,571
Variable cost 228,571
Contributionmargin
$200,000
Fixed cost 200,000
Operatingincome
$0
Note that at breakeven, contribution margin equals fixedcosts.
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New Problem
Most companies are not in the business tobreakeven.Assume that Morris Electronics wants to make$50,000.How many calculators will they have to sell toachieve that objective?
We are solving for ―target sales‖
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Solution
PX - VX – F = P
30X – 16 X – 200,000 = 50,00014X = 250,000
X = 17,857.14285 calculatorsWhat if we want to know the sales dollarvolume to break even?17,857.14285 x 30 = $535,714
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Deriving an Alternate Formula
PX – VX – F = PSimplifying the equationX(P – V) – F = PBut we know that price per units minus variable costper unit equals the contribution marginSince (P – V) = CMu(CMu)(X) = F + PX = (F + P)/CMu when we want to know target sales
in units for a specific level of profitsIf we are solving for target sales at breakeven, P = 0soX = F/CMu
Formulas for target sales with a profit and no profit (breake
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Example Problem
Let us use the same data from MorrisElectronics, where the company wants to earna $50,000 profit.
X = (F + P)/CMuX = (200,000 + 50,000)/14X = 250,000/14X = 17,857.142858 units breakevenOrSale at breakeven = 17,857.142858 x 30 =$535,714
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Now Finding Breakeven SalesDollar Volume
We can either multiply 17,857.142858 times thesales price of $30, or use this formulaS = (F + P)/CMr where S = sales dollars, CMrstands for contribution margin ratio, and thecontribution margin ratio is defined thus:CMr = Total Contribution Margin/SalesOr CMr = Unit Contribution Margin/Price
CMr in this problem is 14/30 = .466667So sales in dollars = (200,000 + 50,000)/.466667=$535,714
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Therefore the Formula ForBreakeven Would Be:
S = (F + P)/CMrOrS = (F + 0)/CMr
OrS = F/CMrTwo formulas to get the same answers!
To get breakeven in dollars use F/CMr whereCMr is the contribution margin ration(contribution margin divided by sales).
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Let Us Solve Another Problem
Assume that Morris Electronics can onlymanufacture 15,000 units a year.The variable cost is $16 per unit, and fixedcosts are $200,000 per year.Assuming that they want to earn $50,000 peryear, what must the price be to obtain their net
profit objective?
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Solution
PX – VX – F = P(15,000) – 16(15,000) – 200,000 = 50,00015,000P – 240,000 – 200,000 = 50,00015,000P = 490,000P = $32.6667To check:$490,000 – 240,000 – 200,000 = $50,000
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Alternate Formulas
We could have used:X = (F + )/CMu to solve for breakeven in unitswhere of course is 0OrS = (F + )/CMr to solve for breakeven in salesdollars to get the same results (again at
breakeven is 0).In this case, S is of course sales dollars.
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Income Statements
Sales $xxx
Cost of Goods Sold xxxGross Margin xxx
Administrative andSelling Expense
xxx
Income xx
Traditional income statement CVP Income Statement
Sales $xxx
Variable Costs xxxContribution Margin xxx
Fixed Costs xxx
Income xx
A better income statement to use for internal reporting,especially when management wants to do CVP analysis,is the CVP income statement shown above.
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Income Statements
It is better, because it gives us the figures needed forCVP analysis.
FASB still requires the traditional income statement forexternal reporting, however.
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One More Concept . . .
Margin of Safety: The difference betweenactual or expected sales and sales at thebreak even point.
The formula is:Actual (expected) sales – breakeven sales =margin of safety in dollars.
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Problem
Johnson Foundry currently sells $1,500,000 ofproduct a year.Their breakeven point is $1,250,000.What is their margin of safety?$1,500,000 – $1,250,000 = $250,000
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Separating Fixed and VariableCosts
One method (a very inaccurate method) ofseparating fixed and variable costs is the high-lowmethod.
The method is inaccurate because it dependsupon only two data points, a high and low point.The small sample size, plus the fact that highand/or low points are often outliers caused byinaccurate readings make it inadvisable to use inthe real world.Nevertheless, since the book teaches it, so will I(sigh).
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Steps
Use the following formula to determinevariable costs.
( )( )
high costs low costsvariablecosts per unit highactivity lowactivity
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Steps
Calculate total variable cost and total costs athigh or low activity.Subtract total variable costs from total costs (athigh or low activity) to determine total fixedcosts.
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Example
Community Hospital’s controller has providedyou with the following information. Using thehigh-low method, divide payroll into fixed and
variable costs. Chest Labor
X-rays Dollars
January 1,200 16,400
February 1,400 18,800
March 900 12,800
April 875 12,500
May 1,300 17,600
June 1,350 18,200
High
Low
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Solution
( )high costs low costsvariablecosts per unit high activity lowactivity
$18,800 $12,500$12/
1, 400 875
xray
1. Calculate variable costs using this formula.
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Solution
2. Calculate variable costs at high or low (we willuse high here).$12 variable cost per x-ray x 875 x-rays =
$10,5003. Subtract variable costs at high or low (we willuse low here) from total costs to get fixed costs.
$12,500 total costs – 10,500 variable costs =$2,000 fixed costsSummary: variable costs = $12 per unit andfixed costs = $2,000 per period (per month in
this case)
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Question
Given this data what would be the total cost at1,145 x-rays?Variable costs = $12 x 1,145 = $13,740Fixed costs = $2,000Total costs at 1,145 x-rays = $15,740
The best method, the least squares methodcan beworked using Excel or a financial calculator. Ifyouwant to learn how to do it on a financialcalculator, look in the hp 10bII instruction book
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Brief Exercise 5-1
Monthly costs for two levels of production aregiven below. From this information determinewhich costs are variable, fixed, and mixed, and
give the reason for each answer.Cost 3000 units 6000 units
Indirect labor $10,000 $20,000
Supervisory salaries $5,000 $5,000
Maintenance 4,000 7,000
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Brief Exercise 5-1
Cost 3000 units 6000 unitsIndirect labor $10,000 $20,000
Supervisory salaries $5,000 $5,000Maintenance 4,000 7,000
Indirect labor is obviously variable, as it varies proportionally
with volume. When volume doubles, costs double.
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Brief Exercise 5-1
Cost 3000 units 6000 unitsIndirect labor $10,000 $20,000
Supervisory salaries $5,000 $5,000Maintenance 4,000 7,000
Supervisory salaries are obviously fixed, since they stay the sa
At different levels of production.
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Brief Exercise 5-1
Cost 3000 units 6000 unitsIndirect labor $10,000 $20,000
Supervisory salaries $5,000 $5,000Maintenance 4,000 7,000
Maintenance salaries are mixed, since they increase,
but not proportional to increase in production volume.
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Brief Exercise 5-2
For Loder Company, the relevant range ofproduction is 40% to 80% of capacity.At 40% of capacity, variable cost is $4000 and
fixed cost $6,000.Diagram the behavior of each costs within therelevant range assuming the behavior is linear.
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Brief Exercise 5-2
To create these graphs I used Excel.
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Brief Exercise 5-3
For Hunt Company, a mixed cost is $20,000plus $16 per direct labor hour.Diagram the behavior of the cost using
increments of 500 hours up to 2,500 hours onthe horizontal access, and increments of$20,000 up to $80,000 on the vertical axis
Note to students: I think the question would have been clearer if the author had said “fixed cost is $20,000 plus$16 per direct labor hour.”
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Brief Exercise 5-3
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Exercise 5-2
Kozy Enterprises is considering manufacturinga new product.It projects the costs of direct materials and
rents for a range of output as shown on thefollowing slide.
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Output in Units Rent Expense Direct Materials1000 5000 4000
2000 5000 6000
3000 5000 7800
4000 7000 8000
5000 7000 10,000
6000 7000 12,000
7000 7000 14,000
8000 7000 16,000
9000 7000 18,00010,000 10,000 23,000
11,000 10,000 28,000
12,000 10,000 36,000
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Exercise 5-2
Relevant Range
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Exercise 5-2
Relevant Range
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Exercise 5-2
The relevant range is 4,000 – 9,000 units ofoutput since a straight-line relationship existsfor both direct materials and rent within this
range.
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Exercise 5-4
Identify each of the following costs as variable,fixed, or mixed.Wood used in production of furniture —variable
Fuel used in delivery trucks – variableStraight-line depreciation on factory buildings – fixedScrews used in production of furniture – variableSales staff salaries – fixedSales commissions – variableProperty taxes – fixed
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Exercise 5-4
Insurance on buildings – fixedHourly wages of furniture craftsman – fixedSalaries of factory supervisor – fixedUtilities expense – mixedTelephone bill – mixed
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Brief Exercise 5-8
Larisa Company has a unit selling price of$520, variable costs per unit of $286, and fixedcost of $187,200.
Compute the breakeven in units using themathematical equation and contributionmargin per unit.
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Mathematical Equation
PX – VX – F = 520X – 286X – 187,200 = 0234X = 187,200X = 800
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Contribution Margin Per Unit
Breakeven = F/CMu187,200/(520 – 286)187,200/234X = 800 units
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Brief Exercise 5-9
Turgro Corp. had total variable cost of$180,000 total fixed costs of $160,000, andtotal revenues of $300,000.
Compute the required sales in dollars to breakeven.
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Brief Exercise 5-9
We know that at breakeven, fixed costs =contribution margin.Since fixed costs are $160,000 then the
contribution margin must be $160,000We know that CMr is CMt/Sales (CMt = totalcontribution margin from income statement)
From the data given in the problem we knowthe CMr is (300,000 – 180,000)/300,000 =40%So when CMt is $160,000, then sales must be$160,000/.40 = $400,000
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Brief Exercise 5-10
For MeriDen Company, variable costs are 60%of sales and fixed costs are $195,000.Management’s net income goal is $75,000.
Compute the required sales in dollars neededto achieve management’s target net income if $75,000.
Use the contribution margin approach.
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Brief Exercise 5-10
S (target sales) = (F + )/CMrS = (195,000 + 75,000)/.40
How did I get .40 for CMr? One trick to remember
is that contribution margin ratio is (1 – variableexpense ratio)Thus CMr is 1 - .60 = .40
S = $270,000/.40S = $675,000
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Exercise 5-8
Green with Envy provides environmentallyfriendly lawn services for homeowners.Its operating costs are as follows:
Depreciation = $1,500/monthAdvertising = $200/monthInsurance = $2,000/monthWeed and feed materials = $13/lawn
Direct labor = $12/lawnFuel = $2/lawn
Compute breakeven in units and dollars.
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Exercise 5-8
Fixed costs are $1,500 + $200 + $2,000 =$3,700 per monthVariable costs are $13 + $12 + $2 = $27 perlawnPX - VX - F = 060X – 27X – 3,700 = 033X = 112.12 lawnsBreakeven sales dollars = 112.12 x 60 =$6,727.27
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Exercise 5-10 (Not assigned)
During the month of March, New Day Spaservices 570 clients at an average price of$120. During the month, fixed costs were
$21,000 and variable costs were 65% of sales.What was the contribution margin . . .
In dollarsPer unitAnd as a ratio?
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Contribution Margin
Sales (570 x $120) $68,400
Variable costs (.65 x $68,400) 44,460
Contribution margin $23,940
In dollars . . .
Per unit . . .
$23,940/570= $42
As a ratio . . .
42/120 = .35
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Breakeven Point
Breakeven in $ = F/CMrBreakeven in $ = $21,000/.35 = $60,000Breakeven in Units = F/CMuBreakeven in Units = $21,000/$42Breakeven in Units = 500
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Exercise 5-14
Lynn Company had $150,000 of net income in2008 when selling price per unit was $150.Variable costs were $90.
Fixed costs were $570,000.Management expects per-unit data and totalfixed cost to remain the same in 2009.
Management is under pressure to increase netincome by $60,000 in 2009.
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Exercise 5-14
Compute the number of units sold in 2008PX – VX – F = P
150X – 90X – 570,000 = 150,00060X = 720,000X = 12,000 units
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Exercise 5-14
Question: How many units would have had tohave been sold in 2009 to reach thestockholder’s desired profit level? Target sales in units = PPX – VX – F = P150X – 90X - $570,000 = ($150,000 +$60,000)
60X = $570,000 + $150,000 + $60,00060X = $780,000X = 13,000 units
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Exercise 5-14
Assume Lynn Company sells he same numberof units in 2009 as it did in 2008.What would the selling price have to be in
order to reach the stockholder’s desired profitlevel?PX – VX – F = P
12,000P – (90)(12,000) – 570,000 = 210,00012,000P = 1,860,000P = $155