CostVolumeProfit Relationships

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Cost-Volume-Profit Relationships
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The Basics of Cost-Volume-Profit (CVP) Analysis
Contribution Margin (CM) is the amount remaining
from sales revenue after variable expenses have
been deducted.
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The Basics of Cost-Volume-Profit (CVP) Analysis
SQ -VQ (S-V)Q -F OI
Contribution Margin (CM) is the amount remaining
from sales revenue after variable expenses have
been deducted.
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An identityI True by definitiondentity (true by
definition)
A model implicit assumptions about the Behavior
of costs and revenues
SQ -VQ (S-V)Q -F OI
Identity SQ VQ F OI Model
OI SQ VQ -F
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Breakeven chartOI SQ VQ - F
500Q-300Q-80,000
Dollars
Units
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Profit-volume chartOI (S-V)Q -F
OI
Slope 200
Q400
Dollars
Q
80,000
OI 200Q 80,000
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Contribution Margin Ratio

• The contribution margin ratio isTotal
  contribution margin/Total sales
• For Wind Bicycle Co. the ratio is

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Contribution Margin Ratio

• Or, in terms of units, the contribution margin
  ratio isFor Wind Bicycle Co. the ratio is

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• Applications of profit-volume analysis
• 1. Breakeven point, units of output sales
  dollars
• Target profits, before tax
• Target profits, after tax
• Target return on sales (ROS)
• Margin of safety
• Operating leverage
• Comparisons of cost structures
• Absorption costing profits
• Breakeven with absorption costing
• Target profits with absorption costing
• CPV with multiple products
• Opportunity costs of scarce resources

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The Breakeven Point

• The breakeven point may be computed in terms of
  either units sold or sales dollars.

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The Breakeven Point

• The breakeven point may be computed in terms of
  either units sold or sales dollars.

Q 80,000 / 200 Q 400 units
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The Breakeven Point

• The breakeven point may be computed in terms of
  either units sold or sales dollars.

Q 80,000 / 200 Q 400 units
Break-even point in total sales dollars
Fixed expenses CM ratio

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The Breakeven Point

• The breakeven point may be computed in terms of
  either units sold or sales dollars.

Q 80,000 / 200 Q 400 units
Break-even point in total sales dollars
Fixed expenses CM ratio

SQ 80,000 / .40 SQ 200,000
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Target Profit Analysis, before tax

• Suppose Wind Co. wants to know how many bikes
  must be sold to earn a pre-tax profit of
  100,000.
• We can use our CVP formula to determine the sales
  volume needed to achieve a target profit figure.

OI 200Q - 80,000 Q (80,000 OI) / 200
Q (80,000 100,000) / 200 Q 900u
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Target Profit Analysis, after tax

• Suppose Wind Co. wants to know how many bikes
  must be sold to earn an after-tax profit of
  90,000. The income tax rate is 40.

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Target Profit Analysis, after tax

• Suppose Wind Co. wants to know how many bikes
  must be sold to earn an after-tax profit of
  90,000. The income tax rate is 40.
• We must first convert the after tax profit to
  before tax profit, as follows
• OI(AT) OI(BT) x (1-T)
• OI(BT) OI(AT) / (1 T)

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Target Profit Analysis, after tax

• Suppose Wind Co. wants to know how many bikes
  must be sold to earn an after-tax profit of
  90,000. The income tax rate is 40.
• We must first convert the after tax profit to
  before tax profit, as follows
• OI(AT) OI(BT) x (1-T)
• OI(BT) OI(AT) / (1 T)
• 90,000 / (1 - .4)
• 150,000

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Target Profit Analysis, after tax

• OI(BT) OI(AT) / (1 T)
• 90,000 / (1 - .4)
• 150,000

OI 200Q - 80,000 Q (80,000 OI) / 200
Q (80,000 150,000) / 200 Q 1,150u
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Target Profit Analysis, after tax

• OI(BT) OI(AT) / (1 T)
• 90,000 / (1 - .4)
• 150,000

OI 200Q - 80,000 Q (80,000 OI) / 200
Q (80,000 150,000) / 200 Q 1,150u
Question Suppose that the first 30,000
of income is taxed at 10 and the remainder is
taxed at 40. How will this change your answer
above?
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Question Suppose that the first 30,000
of income is taxed at 10 and the remainder is
taxed at 40. How will this change your answer
above?
OI(AT) OI(BT) x (.60) (.30 x 30,000)
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Question Suppose that the first 30,000
of income is taxed at 10 and the remainder is
taxed at 40. How will this change your answer
above?
OI(AT) OI(BT) x (.60) (.30 x 30,000)
OI(AT) OI(BT) x (.60) (.30 x 30,000)
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Question Suppose that the first 30,000
of income is taxed at 10 and the remainder is
taxed at 40. How will this change your answer
above?
OI(AT) OI(BT) x (.60) (.30 x 30,000)
OI(AT) OI(BT) x (.60) (.30 x 30,000) OI(BT)
(90,000 - 9,000) / .60 135,000
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Target Return on Sales (ROS)

• Suppose Wind Co. wants to know the sales level
  at which profits will equal fifteen percent of
  sales.
• OI CM(SQ) F

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Target Return on Sales (ROS)

• Suppose Wind Co. wants to know the sales level
  at which profits will equal fifteen percent of
  sales.
• OI CM(SQ) F
• ROS(SQ) CM(SQ) F

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Target Return on Sales (ROS)

• Suppose Wind Co. wants to know the sales level
  at which profits will equal fifteen percent of
  sales.
• OI CM(SQ) F
• ROS(SQ) CM(SQ) F
• SQ F / (CM - ROS)

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Target Return on Sales (ROS)

• Suppose Wind Co. wants to know the sales level
  at which profits will equal fifteen percent of
  sales.
• OI CM(SQ) F
• ROS(SQ) CM(SQ) F
• SQ F / (CM - ROS)
• 80,000 / (.40 - .15)

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Target Return on Sales (ROS)

• Suppose Wind Co. wants to know the sales level
  at which profits will equal fifteen percent of
  sales.
• OI CM(SQ) F
• ROS(SQ) CM(SQ) F
• SQ F / (CM - ROS)
• 80,000 / (.40 - .15)
• 320,000 (or 640 units)

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The Margin of Safety

• The percentage by which sales can drop before
  losses begin to be incurred.

Margin of safety Total sales - Break-even
sales Total sales
The margin of safety can be expressed as 20 of
sales.(250,000 - 200,000) / 250,000
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Operating Leverage

• A measure of how sensitive net operating income
  is to percentage changes in sales.
• With high leverage, a small percentage increase
  in sales can produce a much larger percentage
  increase in net operating income.

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Operating Leverage
100,000 20,000
5
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Operating Leverage

• With a operating leverage of 5, if Wind increases
  its sales by 10, net operating income would
  increase by 50.

Heres the verification!
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Operating Leverage
10 increase in sales from 250,000 to 275,000 .
. .
. . . results in a 50 increase in income from
20,000 to 30,000.
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Note that operating leverage is not a constant
for a given firm. The degree of operating
leverage depends upon the level of output. To
illustrate this point, re-compute Wind Companys
operating leverage at a sales level of 550 units.
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Comparisons of alternative cost structures
Assume that Wind Company may replace its existing
equipment with a more capital intense technology.
The new equipment would result in a reduction of
variable costs per unit from 300 to 250, and
would increase annual fixed costs from 80,000 to
120,000. Question At what level of output
would the new technology result In higher profits
for Wind?
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Comparisons of alternative cost structures
Assume that Wind Company may replace its existing
equipment with a more capital intense technology.
The new equipment would result in a reduction of
variable costs per unit from 300 to 250, and
would increase annual fixed costs from 80,000 to
120,000. Question At what level of output
would the new technology result In higher profits
for Wind?
Current cost structure TC 80,000
300Q Alternative cost structure TC 120,000
250Q Difference in costs 40,000 - 50Q Output
level with equal total costs 800 units
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Comparisons of alternative cost structures
Assume that Wind Company may replace its existing
equipment with a more capital intense technology.
The new equipment would result in a reduction of
variable costs per unit from 300 to 250, and
would increase annual fixed costs from 80,000 to
120,000. Question At what level of output
would the new technology result In equal profits
for Wind? Question At that level of output,
what amount of profit would be earned?
Question At 800 units, which cost structure has
the higher operating leverage? Which has the
higher breakeven point?
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CPV Analysis with Absorption Costing Let QM
units produced Let QS units sold Let FM/QM
fixed manufacturing cost per unit Let FSfixed
selling and administrative costs OI (S V
FM/QM) QS - FS
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CPV Analysis with Absorption Costing OI (S
V FM/QM) QS - FS OI (S V) QS FM (QS/QM)
FS Note If QM QS, then OI is the same
using either variable or absorption costs.
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Consider the original data for the Wind
Company. Using variable costing, the firms
breakeven point is 400 units. Assume instead
that the firm uses absorption costing in
measuring operating income. The firm intends to
manufacture 500 units in the coming period. In
addition, assume that Winds total fixed costs of
80,000 consists of 50,000 fixed manufacturing
costs, and 30,000 fixed selling and
administrative costs. Question What is the
firms absorption cost profit equation?
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Consider the original data for the Wind
Company. Using variable costing, the firms
breakeven point is 400 units. Assume instead
that the firm uses absorption costing in
measuring operating income. The firm intends to
manufacture 500 units in the coming period. In
addition, assume that Winds total fixed costs of
80,000 consists of 50,000 fixed manufacturing
costs, and 30,000 fixed selling and
administrative costs. Question What is the
firms absorption cost profit equation? OI (S
V FM/QM) QS - FS (500-300-50,000/500)QS
30,000
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Question If the firm produces 500 units and
sells 400 units, what will be the resulting
operating income?
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Question If the firm produces 500 units and
sells 400 units, what will be the resulting
operating income? OI (S V FM/QM) QS - FS
(500-300-50,000/500)QS 30,000
(500-300-50,000/500)400 30,000 10,000
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Question If the firm produces 500 units and
sells 400 units, what will be the resulting
operating income? OI (S V FM/QM) QS - FS
(500-300-50,000/500)QS 30,000
(500-300-50,000/500)400 30,000
10,000 Question If the firm produces 500
units, what will be the breakeven point using
absorption costing?
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Question If the firm produces 500 units and
sells 400 units, what will be the resulting
operating income? OI (S V FM/QM) QS - FS
(500-300-50,000/500)QS 30,000
(500-300-50,000/500)400 30,000
10,000 Question If the firm produces 500
units, what will be the breakeven point using
absorption costing? OI (S V FM/QM) QS -
FS O (500-300-50,000/500)QS 30,000 QS
30,000 / (500-300-100) QS 300 units
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Assumptions of CVP Analysis

• Selling price is constant.
• Costs are linear.
• In multi-product companies, the sales mix is
  constant.
• In manufacturing companies, inventories do not
  change (units produced units sold). Otherwise,
• the equations must incorporate the impact of
  absorption costing.

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The Concept of Sales Mix

• Sales mix is the relative proportions in which a
  companys products are sold.
• Different products have different selling prices,
  cost structures, and contribution margins.
• Lets assume Wind sells bikes and carts and see
  how we deal with break-even analysis.

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Multi-product break-even analysis

• Wind Bicycle Co. provides the following
  information

265,000 550,000
48.2 (rounded)
Note (45x40) (55x55) 48.2
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Multi-product break-even analysis
Note that the dollar amount of sales
must maintain the existing sales mix
proportions (45 bikes and 55 carts).At any
other sales mix, the breakeven sales amount would
differ.
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CPV Graph, Multi-Product Firm
CM.55
CM.40
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Extending CVP Analysis

• Multi-product firms must make
• product mix decisions that earn the best total
  contribution
• margin for the firm. To
• accomplish this objective, we need to focus on
  the contribution margin earned by each unit of
  scarce input.

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Decisions Involving Limited Resources

• Firms often face the problem of deciding how
  limited resources are going to be used.
• Usually, fixed costs are not affected by this
  decision, so management can focus on maximizing
  total contribution margin.
• Lets look at an example.

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Limited Resources

• Martin, Inc. produces two products and selected
  data is shown below

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Limited Resources

• Martin, Inc. produces two products and selected
  data is shown below

Questions Assume that total fixed costs are
48,000. What is Martins profit-volume
equation? What is Martins breakeven point?
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Limited Resources

• The lathe is the scarce resource because there is
  excess capacity on other machines. The lathe is
  being used at 100 of its capacity.
• The lathe capacity is 2,400 minutes per week.
• Should Martin focus its efforts
• on Webs or Tins?

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Limited Resources

• Lets calculate the contribution margin per unit
  of the scarce resource, the lathe.

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Limited Resources

• Lets calculate the contribution margin per unit
  of the scarce resource, the lathe.

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Limited Resources

• Lets calculate the contribution margin per unit
  of the scarce resource, the lathe.

Tins should be emphasized. It is the more
valuable use of the scarce resource the lathe,
yielding a contribution margin of 30 per minute
as opposed to 24 per minute for the Webs.
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Limited Resources
If there are no other considerations, the best
plan would be to produce to meet current demand
for Tins. If demand is sufficient, Martin would
produce a total of 4,800 Tins, and earn a total
contribution margin of 72,000 (4,800 x 15).
What would be the value to Martin of an
additional 90 minutes of lathe time?
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Suppose that the maximum demand for Tins is 4,000
units. What mix of Webs and Tins would be best
for Martin? In this case,What would be the
benefit to Martin if the demand for Tins could
be expanded to 4,500 units?
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Limited Resources
Assume in addition that material used in the
manufacture of both products is in short supply.
Each unit of Webs requires 2 pounds and each unit
of Tins requires 4 pounds of material. The total
available material is 7,200 pounds per week.
Question If there was unlimited lathe
capacity, what product mix would be optimal for
Martin? What is the value to Martin of an
additional 150 pounds of material?
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Limited Resources
Assume in addition that material used in the
manufacture of both products is in short supply.
Each unit of Webs requires 2 pounds and each unit
of Highs requires 4 pounds of material. The total
available material is 7,200 pounds per week.
Question If there was unlimited lathe
capacity, what product mix would be optimal for
Martin? What is the value to Martin of an
additional 150 pounds of material? Question If
the lathe time and the material are both scarce,
what product mix would be optimal?
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Extending CVP Analysis

• Multi-product profit-volume analysis with changes
  in product mix is an application of Linear
  Programming. This
• decision tool begins with the
• profit volume equation, and
• deals with capacity limitations.

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End of Cost-Volume-Profit discussion.
Review class handout 4.
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The End