Cost volume profit

1
Cost volume profit

• Richard E. McDermott Ph.D.

2
Costs Volume Profit

• In this chapter we study what happens to both
  cost and profit as volume changes.
• The tools we will use will be helpful in the
  development of flexible budgets.
• I am going to begin by giving you some basic
  definitions.
• I will then give you what I feel are the best
  formulas to use in working the problems you will
  be assigned.

3
Definitions

• Variable Costs Costs that vary in total,
  directly and proportionately, with changes in
  production (also called activity level).
• If the activity level increases by 50, variable
  costs increase by 50.

4
Examples of Variable Costs

• Direct labor
• Direct materials
• Variable overhead

5
Definitions

• Mixed Costs costs that contain both a fixed and
  a variable element.
• Mixed cost change in total, but not
  proportionately, with changes in the activity
  level.
• An example of a mixed cost might be maintenance
  cost on a taxi.
• Maintenance costs increase as miles increase.
  Even if the truck is never driven, however, it is
  a good idea to change the oil every three months
  to keep it from degenerating.

6
Separating Fixed and Variable Costs

• If you will look at a general ledger, you will
  never 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 separate
  fixed and variable costs.
• There are three methods to do this
• Scatter graph method
• High-low method
• Least squares method

The best method is the least squares method, but
since the author does not teach it we will not
cover it either.
7
Definitions

• Fixed Costs Costs that do not change with
  increases or decreases in production volume.
• It is important to add, there is usually a
  relevant range.
• For example, a plant may be built to manufacture
  1 to 10,000 shoes per month.
• Fixed costs would not change within this
  relevant range.
• If a company wanted to manufacture 12,000 shoes
  per month, however, there of course would be a
  new relevant range and the fixed costs might
  increase.

8
Examples of Fixed Costs

• Rent on a factory
• Depreciation straight-line method
• Heating and air-conditioning expense
• Housekeeping

It is important to emphasize that what might be a
fixed cost in one factory, could be a variable
cost in another, depending upon the way the firm
does business.
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Other Definitions

• Contribution Margin Revenue (or unit price)
  minus total variable costs (or unit variable
  costs).
• Example

Note that contribution margin is what is left
after paying variable costs.
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Other Definitions
After fixed costs are paid, where does the
contribution margin go? To the bottom line!
11
Notation

• I will use the following notation when referring
  to contribution margin
• CMu contribution margin per unit of produce,
  calculated as follows Price Variable Cost Per
  Unit Cmu.
• CMt contribution margin total calculated as
  follows Total Sales Total Variable Costs CMt
• CMr contribution margin ratio calculated as
  follows CMt/Total Sales or CMu/Price.

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Tip for Examination

• In any problem where the only change is volume
  (i.e. variable costs per unit, and fixed costs do
  not change), then the impact of the change on
  operating income can be calculated simply by
  calculating the change in total contribution
  margin.
• The change in total contribution margin will
  equal the change in operating income.
• We will illustrate this in a moment.

13
Here Are Some Formulas I Would like You to Learn

• PX VX F P
• where
• P unit price
• X volume of units sold
• V variable cost per unit
• F total fixed price
• P operating income or profit

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Breakeven

• Breakeven is defined as the point where the firm
  neither makes nor loses money.
• The formula for breakeven is
• PX VX F 0
• Let us illustrate the solution for breakeven with
  an example.

15
Example

• Morris Electronics makes calculators.
• The market dictates a price of 30 for a model
  with their particular features.
• Variable costs per unit are 16, total fixed
  costs are 200,000.
• What is the breakeven point in units for sales of
  the calculators?

16
Solution

• PX - VX F 0
• 30X 16X 200,000 0
• 14X 200,000
• X 14,285.714286 calculators

Note that at breakeven, contribution margin
equals fixed costs.
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New Problem

• Most companies are not in the business to
  breakeven.
• Assume that Morris Electronics wants to make
  50,000.
• How many calculators will they have to sell to
  achieve that objective?
• We are solving for target sales

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Solution

• PX - VX F P
• 30X 16X 200,000 50,000
• 14X 250,000
• X 17,857.14285 calculators
• What if we want to know the sales dollar volume
  to break even?
• 17,857.14285 x 30 535,714

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Deriving an Alternate Formula

• PX VX F P
• Simplifying the equation
• X(P V) F P
• But we know that price per units minus variable
  cost per unit equals the contribution margin
• Since (P V) CMu
• (CMu)(X) F P
• X (F P)/CMu when we want to know target sales
  in units for a specific level of profits
• If we are solving for target sales at breakeven,
  P 0 so
• X F/CMu

Formulas for target sales with a profit and no
profit (breakeven)
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Example Problem

• Let us use the same data from Morris Electronics,
  where the company wants to earn a 50,000 profit.
• X (F P)/CMu
• X (200,000 50,000)/14
• X 250,000/14
• X 17,857.142858 units breakeven
• Or
• Sale at breakeven 17,857.142858 x 30 535,714

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Now Finding Breakeven Sales Dollar Volume

• We can either multiply 17,857.142858 times the
  sales price of 30, or use this formula
• S (F P)/CMr where S sales dollars, CMr
  stands for contribution margin ratio, and the
  contribution margin ratio is defined thus
• CMr Total Contribution Margin/Sales
• Or CMr Unit Contribution Margin/Price
• CMr in this problem is 14/30 .466667
• So sales in dollars (200,000 50,000)/.466667
  
• 535,714

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Therefore the Formula For Breakeven Would Be

• S (F P)/CMr
• Or
• S (F 0)/CMr
• Or
• S F/CMr
• Two formulas to get the same answers!
• To get breakeven in dollars use F/CMr where CMr
  is the contribution margin ration (contribution
  margin divided by sales).

23
Let Us Solve Another Problem

• Assume that Morris Electronics can only
  manufacture 15,000 units a year.
• The variable cost is 16 per unit, and fixed
  costs are 200,000 per year.
• Assuming that they want to earn 50,000 per year,
  what must the price be to obtain their net profit
  objective?

24
Solution

• PX VX F ?
• P(15,000) 16(15,000) 200,000 50,000
• 15,000P 240,000 200,000 50,000
• 15,000P 490,000
• P 32.6667
• To 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 units
  where of course ? is 0
• Or
• S (F ?)/CMr to solve for breakeven in sales
  dollars 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

• Traditional income statement

• CVP Income Statement

A better income statement to use for internal
reporting, especially when management wants to do
CVP analysis, is the CVP income statement shown
above.
27
Income Statements
It is better, because it gives us the figures
needed for CVP analysis.
FASB still requires the traditional income
statement for external reporting, however.
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One More Concept . . .

• Margin of Safety The difference between actual
  or expected sales and sales at the break 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 of
  product 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 Variable Costs

• One method (a very inaccurate method) of
  separating fixed and variable costs is the
  high-low method.
• The method is inaccurate because it depends upon
  only two data points, a high and low point.
• The small sample size, plus the fact that high
  and/or low points are often outliers caused by
  inaccurate readings make it inadvisable to use in
  the real world.
• Nevertheless, since the book teaches it, so will
  I (sigh).

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Steps

• Use the following formula to determine variable
  costs.

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Steps

• Calculate total variable cost and total costs at
  high or low activity.
• Subtract total variable costs from total costs
  (at high or low activity) to determine total
  fixed costs.

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Example

• Community Hospitals controller has provided you
  with the following information. Using the
  high-low method, divide payroll into fixed and
  variable costs.

High
Low
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Solution
1. Calculate variable costs using this formula.
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Solution

• 2. Calculate variable costs at high or low (we
  will use high here).
• 12 variable cost per x-ray x 875 x-rays
  10,500
• 3. Subtract variable costs at high or low (we
  will use low here) from total costs to get fixed
  costs.
• 12,500 total costs 10,500 variable costs
  2,000 fixed costs
• Summary variable costs 12 per unit and fixed
  costs 2,000 per period (per month in this
  case)

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Question

• Given this data what would be the total cost at
  1,145 x-rays?
• Variable costs 12 x 1,145 13,740
• Fixed costs 2,000
• Total costs at 1,145 x-rays 15,740

The best method, the least squares method can
be worked using Excel or a financial calculator.
If you want to learn how to do it on a financial
calculator, look in the hp 10bII instruction book
under regression).
37
Brief Exercise 5-1

• Monthly costs for two levels of production are
  given below. From this information determine
  which costs are variable, fixed, and mixed, and
  give the reason for each answer.

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Brief Exercise 5-1
Indirect labor is obviously variable, as it
varies proportionally with volume. When volume
doubles, costs double.
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Brief Exercise 5-1
Supervisory salaries are obviously fixed, since
they stay the same At different levels of
production.
40
Brief Exercise 5-1
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 of
  production 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 the
  relevant 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 20,000 plus
  16 per direct labor hour.
• Diagram the behavior of the cost using increments
  of 500 hours up to 2,500 hours on the 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 manufacturing a
  new product.
• It projects the costs of direct materials and
  rents for a range of output as shown on the
  following slide.

46
(No Transcript)
47
Exercise 5-2
Relevant Range
48
Exercise 5-2
Relevant Range
49
Exercise 5-2

• The relevant range is 4,000 9,000 units of
  output since a straight-line relationship exists
  for 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 furniturevariable
• Fuel used in delivery trucks variable
• Straight-line depreciation on factory buildings
  fixed
• Screws used in production of furniture variable
• Sales staff salaries fixed
• Sales commissions variable
• Property taxes fixed

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Exercise 5-4

• Insurance on buildings fixed
• Hourly wages of furniture craftsman fixed
• Salaries of factory supervisor fixed
• Utilities expense mixed
• Telephone 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 fixed cost
  of 187,200.
• Compute the breakeven in units using the
  mathematical equation and contribution margin per
  unit.

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Mathematical Equation

• PX VX F ?
• 520X 286X 187,200 0
• 234X 187,200
• X 800

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Contribution Margin Per Unit

• Breakeven F/CMu
• 187,200/(520 286)
• 187,200/234
• X 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, and total revenues
  of 300,000.
• Compute the required sales in dollars to break
  even.

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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 160,000
• We know that CMr is CMt/Sales (CMt total
  contribution margin from income statement)
• From the data given in the problem we know the
  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.
• Managements net income goal is 75,000.
• Compute the required sales in dollars needed to
  achieve managements target net income if
  75,000.
• Use the contribution margin approach.

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Brief Exercise 5-10

• S (target sales) (F ?)/CMr
• S (195,000 75,000)/.40
• How did I get .40 for CMr? One trick to remember
  is that contribution margin ratio is (1
  variable expense ratio)
• Thus CMr is 1 - .60 .40
• S 270,000/.40
• S 675,000

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Exercise 5-8

• Green with Envy provides environmentally friendly
  lawn services for homeowners.
• Its operating costs are as follows
• Depreciation 1,500/month
• Advertising 200/month
• Insurance 2,000/month
• Weed and feed materials 13/lawn
• Direct labor 12/lawn
• Fuel 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 month
• Variable costs are 13 12 2 27 per lawn
• PX - VX - F 0
• 60X 27X 3,700 0
• 33X 112.12 lawns
• Breakeven 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 Spa services
  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 dollars
• Per unit
• And as a ratio?

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Contribution Margin
In dollars . . .
Per unit . . .
23,940/570 42
As a ratio . . .
42/120 .35
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Breakeven Point

• Breakeven in F/CMr
• Breakeven in 21,000/.35 60,000
• Breakeven in Units F/CMu
• Breakeven in Units 21,000/42
• Breakeven in Units 500

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Exercise 5-14

• Lynn Company had 150,000 of net income in 2008
  when selling price per unit was 150.
• Variable costs were 90.
• Fixed costs were 570,000.
• Management expects per-unit data and total fixed
  cost to remain the same in 2009.
• Management is under pressure to increase net
  income by 60,000 in 2009.

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Exercise 5-14

• Compute the number of units sold in 2008
• PX VX F P
• 150X 90X 570,000 150,000
• 60X 720,000
• X 12,000 units

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Exercise 5-14

• Question How many units would have had to have
  been sold in 2009 to reach the stockholders
  desired profit level?
• Target sales in units P
• PX VX F P
• 150X 90X - 570,000 (150,000 60,000)
• 60X 570,000 150,000 60,000
• 60X 780,000
• X 13,000 units

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Exercise 5-14

• Assume Lynn Company sells he same number of units
  in 2009 as it did in 2008.
• What would the selling price have to be in order
  to reach the stockholders desired profit level?
• PX VX F P
• 12,000P (90)(12,000) 570,000 210,000
• 12,000P 1,860,000
• P 155

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The End!