Cost Profit Volume Relationship WHBM19.ppt

Accounting

1. © The McGraw-Hill Companies, Inc., 2002
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Cost-Volume-Profit
Analysis
Chapter
19

2. © The McGraw-Hill Companies, Inc., 2002
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CVP analysis is used to answer questions
such as:
How much must I sell to earn my desired income?
How will income be affected
if I reduce selling prices to
increase sales volume?
What will happen to
profitability if I expand
capacity?
Questions Addressed by
Cost-Volume-Profit Analysis

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Number of Local Calls
Monthly Basic Telephone Bill
Total fixed costs remain unchanged
when activity changes.
Your monthly basic
telephone bill probably
does not change when
you make more local calls.
Total Fixed Cost

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Number of Local Calls
Monthly Basic Telephone
Bill per Local Call
Fixed costs per unit decline
as activity increases.
Your average cost per
local call decreases as
more local calls are made.
Fixed Cost Per Unit

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Minutes Talked
Total Long Distance
Telephone Bill
Total variable costs change
when activity changes.
Your total long distance
telephone bill is based
on how many minutes
you talk.
Total Variable Cost

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Minutes Talked
Per Minute
Telephone Charge
Variable costs per unit do not change
as activity increases.
The cost per long distance
minute talked is constant.
For example, 10
cents per minute.
Variable Cost Per Unit

7. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinSummary of Variable and Fixed Cost Behavior
Cost In Total Per Unit
Variable
Changes as activity level
changes.
Remains the same over wide
ranges of activity.
Fixed
Remains the same even
when activity level changes.
Dereases as activity level
increases.
Cost Behavior Summary

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Mixed costs contain a fixed portion that is
incurred even when facility is unused, and a
variable portion that increases with usage.
Example: monthly electric utility charge
Fixed service fee
Variable charge per
kilowatt hour used
Mixed Costs

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Variable
Utility Charge
Activity (Kilowatt Hours)
Total Utility Cost
Fixed Monthly
Utility Charge
Slope is
variable cost
per unit
of activity.
Mixed Costs

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Activity
Cost
Total cost remains
constant within a
narrow range of
activity.
Stair-Step Costs

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Activity
Cost
Total cost increases to a
new higher cost for the
next higher range of
activity.
Stair-Step Costs

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Total Cost
Relevant Range
A straight line
closely (constant
unit variable cost)
approximates a
curvilinear variable
cost line within
the relevant range.
Volume of Output
Curvilinear
Cost Function
Curvilinear Costs

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Let’s extend our
knowledge of
cost behavior to
CVP analysis.
Cost-Volume-Profit
(CVP) Analysis

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The break-even point (expressed in units of
product or dollars of sales) is the unique
sales level at which a company neither
earns a profit nor incurs a loss.
Computing Break-Even Point

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Contribution margin is amount by which revenue
exceeds the variable costs of producing the revenue.Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even Point

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How much contribution margin must this company
have to cover its fixed costs (break even)?Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even Point

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How much contribution margin must this company
have to cover its fixed costs (break even)?
Answer: $30,000Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even Point

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How many units must this company sell to cover its
fixed costs (break even)?Total Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even Point

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How many units must this company sell to cover its
fixed costs (break even)?
Answer: $30,000 ÷$20 per unit = 1,500 unitsTotal Unit
Sales Revenue (2,000 units) 100,000$ 50$
Less: Variable costs 60,000 30
Contribution margin 40,000$ 20$
Less: Fixed costs 30,000
Operating income 10,000$
Computing Break-Even Point

20. © The McGraw-Hill Companies, Inc., 2002
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We have just seen one of the basic CVP
relationships –thebreak-evencomputation.
Break-even point in units =
Fixed costs
Contribution margin per unit
Finding the Break-Even Point
Unit sales price less unit variable cost
($20 in previous example)
Formula for Computing
Break-Even Sales (in Units)

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The break-even formula may also be
expressed in sales dollars.
Break-even point in dollars =
Fixed costs
Contribution margin ratio
Unit sales price
Unit variable cost
Formula for Computing
Break-Even Sales (in Dollars)

22. © The McGraw-Hill Companies, Inc., 2002
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ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs are
$3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
Computing Break-Even Sales
Question 1

23. © The McGraw-Hill Companies, Inc., 2002
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ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs are
$3.00 per unit, how many units must be sold to
break even?
a. 100,000 units
b. 40,000 units
c. 200,000 units
d. 66,667 units
Unit contribution = $5.00 -$3.00 = $2.00
Fixed costs
Unit contribution
=
$200,000
$2.00 per unit
= 100,000 units
Computing Break-Even Sales
Question 1

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Use the contribution margin ratio formula to
determine the amount of sales revenue ABC must
have to break even. All information remains
unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Computing Break-Even Sales
Question 2

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Use the contribution margin ratio formula to
determine the amount of sales revenue ABC must
have to break even. All information remains
unchanged: fixed costs are $200,000; unit sales
price is $5.00; and unit variable cost is $3.00.
a. $200,000
b. $300,000
c. $400,000
d. $500,000
Unit contribution = $5.00 -$3.00 = $2.00
Contribution margin ratio = $2.00 ÷$5.00 = .40
Break-even revenue = $200,000 ÷.4 = $500,000
Computing Break-Even Sales
Question 2

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Volume in Units
Costs and Revenue
in Dollars
Revenue
Starting at the origin, draw the total revenue
line with a slope equal to the unit sales price.
Total fixed cost
Total fixed cost
extends horizontally
from the vertical axis.
Preparing a CVP Graph

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Total cost
Volume in Units
Costs and Revenue
in Dollars
Total fixed cost
Break-
even
Point
Profit
Loss
Draw the total cost line with a slope
equal to the unit variable cost.
Revenue
Preparing a CVP Graph

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Break-even formulas may be adjusted to
show the sales volume needed to earn
any amount of operatingincome.
Unit sales =
Fixed costs + Target income
Contribution margin per unit
Dollar sales =
Fixed costs + Target income
Contribution margin ratio
Computing Sales Needed to
Achieve Target Operating Income

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ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to earn operatingincome of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
Computing Sales Needed to
Achieve Target OperatingIncome

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ABC Co. sells product XYZ at $5.00 per unit. If
fixed costs are $200,000 and variable costs
are $3.00 per unit, how many units must be
sold to earn operatingincome of $40,000?
a. 100,000 units
b. 120,000 units
c. 80,000 units
d. 200,000 units
= 120,000 units
Unit contribution = $5.00 -$3.00 = $2.00
Fixed costs + Target income
Unit contribution
$200,000 + $40,000
$2.00 per unit
Computing Sales Needed to
Achieve Target OperatingIncome

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Margin of safety is the amount by which sales may
decline before reaching break-even sales:
Margin of safety provides a quick means of
estimating operating income at any level of sales:
Margin of safety = Actual sales -Break-even sales
Operating Margin Contribution
Income of safety margin ratio
= ×
What is our Margin of Safety?

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Oxco’s contribution margin ratio is 40
percent. If sales are $100,000 and break-
even sales are $80,000, what is operating
income?
Operating Margin Contribution
Income of safety margin ratio
= ×
Operating
Income
= $20,000 ×.40 = $8,000
What is our Margin of Safety?

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Once break-even is reached, every additional dollar
of contribution margin becomes operating income:
Oxco expects sales to increase by $15,000. How
much will operating income increase?
Change in
operating income
= $15,000 ×.40 = $6,000
Change in Change in Contribution
operating income sales volume margin ratio
= ×
What Change in Operating Income
Do We Anticipate?

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Business Applications of CVP

35. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinTotal Per Unit Percent
Sales (500 bikes) 250,000$ 500$ 100%
Less: variable expenses150,000 300 60%
Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000
Operating income 20,000$
Consider the following information
developed by the accountant at CyclCo, a
bicycle retailer:
Business Applications of CVP

36. © The McGraw-Hill Companies, Inc., 2002
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Should CyclCo spend $12,000 on
advertising to increase sales by 10 percent? Total Per Unit Percent
Sales (500 bikes) 250,000$ 500$ 100%
Less: variable expenses150,000 300 60%
Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000
Operating income 20,000$
Business Applications of CVP

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Bikes Bikes
Sales 250,000$ 275,000$
Less: variable expenses150,000 165,000
Contribution margin 100,000$ 110,000$
Less: fixed expenses 80,000 92,000
Operating income 20,000$ 18,000$
550 ×$300
$80K + $12K
No, income is decreased.
550 ×$500
Business Applications of CVP
Should CyclCo spend $12,000 on
advertising to increase sales by 10 percent?

38. © The McGraw-Hill Companies, Inc., 2002
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Bikes
Sales 250,000$
Less: variable expenses150,000
Contribution margin 100,000$
Less: fixed expenses 80,000
Operating income 20,000$
Now, in combination with the advertising,
CyclCo is considering a 10 percent price reduction that will
increase sales by 25 percent. What is the income effect?
Business Applications of CVP

39. © The McGraw-Hill Companies, Inc., 2002
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Bikes Bikes
Sales 250,000$ 281,250$
Less: variable expenses150,000 187,500
Contribution margin 100,000$ 93,750$
Less: fixed expenses 80,000 92,000
Operating income 20,000$ 1,750$
625 ×$300
$80K + $12K
Income is decreased even more.
625 ×$450
Now, in combination with the advertising,
CyclCo is considering a 10 percent price reduction that will
increase sales by 25 percent. What is the income effect?
1.25 ×500
Business Applications of CVP

40. © The McGraw-Hill Companies, Inc., 2002
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Bikes
Sales 250,000$
Less: variable expenses150,000
Contribution margin 100,000$
Less: fixed expenses 80,000
Operating income 20,000$
Business Applications of CVP
Now, in combination with advertising and a price cut, CyclCo
will replace $50,000 in sales salaries with a $25 per bike
commission, increasing sales by 50 percent above the
original 500 bikes. What is the effect on income?

41. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/Irwin 500 750
Bikes Bikes
Sales 250,000$ 337,500$
Less: variable expenses150,000 243,750
Contribution margin 100,000$ 93,750$
Less: fixed expenses 80,000 42,000
Operating income 20,000$ 51,750$
The combination of advertising, a price cut,
and change in compensation increases income.
750 ×$325
$92K -$50K
750 ×$450
Business Applications of CVP
Now, in combination with advertising and a price cut, CyclCo
will replace $50,000 in sales salaries with a $25 per bike
commission, increasing sales by 50 percent above the
original 500 bikes. What is the effect on income?
1.5 ×500

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Different products with
different contribution margins.
Determining semivariable
cost elements.
Complying with the
assumptions of CVP analysis.
Additional Considerations in CVP

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Sales mix is the relative combination in which
a company’s different products are sold.
Different products have different selling
prices, costs, and contribution margins.
If CyclCo sells bikes and carts, how
will we deal with break-even analysis?
CVP Analysis When a Company
Sells Many Products

44. © The McGraw-Hill Companies, Inc., 2002
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CyclCo provides us with the following
information: Bikes Carts Total
Sales 250,000$ 100% 300,000$ 100% 550,000$ 100%
Var. exp. 150,000 60% 135,000 45% 285,000 52%
Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000
Net income 95,000$
CVP Analysis When a Company
Sells Many Products

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The overall contribution margin ratio is:
$265,000
$550,000
= 48% (rounded) Bikes Carts Total
Sales 250,000$ 100% 300,000$ 100% 550,000$ 100%
Var. exp. 150,000 60% 135,000 45% 285,000 52%
Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000
Net income 95,000$
CVP Analysis When a Company
Sells Many Products

46. © The McGraw-Hill Companies, Inc., 2002
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Break-even in sales dollars is:
$170,000
.48
= $354,167 (rounded) Bikes Carts Total
Sales 250,000$ 100% 300,000$ 100% 550,000$ 100%
Var. exp. 150,000 60% 135,000 45% 285,000 52%
Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%
Fixed exp. 170,000
Operating income 95,000$
CVP Analysis When a Company
Sells Many Products

47. © The McGraw-Hill Companies, Inc., 2002
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OwlCo recorded the following production activity
and maintenance costs for two months:
Using these two levels of activity, compute:
the variable cost per unit.
the total fixed cost.
total cost formula.Units Cost
High activity level 9,000 9,700$
Low activity level 5,000 6,100
Change 4,000 3,600$
The High-Low Method

48. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinUnits Cost
High activity level 9,000 9,700$
Low activity level 5,000 6,100
Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
in cost
in units
$3,600
4,000
The High-Low Method

49. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinUnits Cost
High activity level 9,000 9,700$
Low activity level 5,000 6,100
Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost –Total variable cost
in cost
in units
$3,600
4,000
The High-Low Method

50. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinUnits Cost
High activity level 9,000 9,700$
Low activity level 5,000 6,100
Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost –Total variable cost
Fixed cost = $9,700 –($0.90 per unit ×9,000 units)
Fixed cost = $9,700 –$8,100 = $1,600
in cost
in units
$3,600
4,000
The High-Low Method

51. © The McGraw-Hill Companies, Inc., 2002
McGraw-Hill/IrwinUnits Cost
High activity level 9,000 9,700$
Low activity level 5,000 6,100
Change 4,000 3,600$
Unit variable cost = = = $0.90 per unit
Fixed cost = Total cost –Total variable cost
Fixed cost = $9,700 –($0.90 per unit ×9,000 units)
Fixed cost = $9,700 –$8,100 = $1,600
Total cost = $1,600 + $.90 per unit
in cost
in units
$3,600
4,000
The High-Low Method

52. © The McGraw-Hill Companies, Inc., 2002
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If sales commissions are $10,000 when 80,000 units
are sold and $14,000 when 120,000 units are sold,
what is thevariable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit
The High-Low Method
Question 1

53. © The McGraw-Hill Companies, Inc., 2002
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If sales commissions are $10,000 when 80,000 units
are sold and $14,000 when 120,000 units are sold,
what is thevariable portion of sales commission per
unit sold?
a. $.08 per unit
b. $.10 per unit
c. $.12 per unit
d. $.125 per unit$4,000 ÷40,000 units
= $.10 per unitUnits Cost
High level120,000 14,000$
Low level 80,000 10,000
Change 40,000 4,000$
The High-Low Method
Question 1

54. © The McGraw-Hill Companies, Inc., 2002
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If sales commissions are $10,000 when 80,000 units
are sold and $14,000 when 120,000 units are sold,
what is thefixedportion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000
The High-Low Method
Question 2

55. © The McGraw-Hill Companies, Inc., 2002
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If sales commissions are $10,000 when 80,000 units
are sold and $14,000 when 120,000 units are sold,
what is thefixedportion of the sales commission?
a. $ 2,000
b. $ 4,000
c. $10,000
d. $12,000Total cost =Total fixed cost +
Total variable cost
$14,000=Total fixed cost +
($.10 × 120,000 units)
Total fixed cost=$14,000 - $12,000
Total fixed cost =$2,000
The High-Low Method
Question 2

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A limited range of activity, called therelevant
range, where CVP relationships are linear.
Unit selling price remains constant.
Unit variable costs remain constant.
Total fixed costs remain constant.
Sales mix remains constant.
Production = sales (no inventory changes).
Assumptions Underlying
CVP Analysis

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End of Chapter 19