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COST-VOLUME-PROFIT ANALYSIS
Key Terms and Concepts to Know
Contribution Income Statement:
Separates expenses into variable and fixed.
Sales – Variable Expenses = Contribution Margin.
Contribution Margin – Fixed Expenses = Net Income (Loss).
Contribution Margin:
The amount of sales available to cover fixed expenses with any remaining
contribution margin providing profits.
If the contribution margin is not sufficient to cover fixed expenses, there will be a
net loss for the period.
Contribution Margin Ratio:
Sales, variable expenses and contribution margin are all variable, and therefore
may be expressed as a percent of revenue.
The contribution margin ratio is calculated as the contribution margin dollars as a
percent of sales dollars.
The variable expense ratio is the complement to the contribution margin ratio. It
represents the percent of sales dollars not included in the contribution margin
ratio.
In a company producing a single product, this relationship applies to either total
sales dollars and total contribution margin or per-unit sales dollars and
contribution margin dollars.
In a company producing multiple products, each product will have its own unique
contribution margin ratio. The contribution margin for the entire company will be
calculated only for total contribution margin dollars as a percent of total sales
dollars.
Break Even Point:
At the breakeven point:
Operating Income = 0
Total revenue = total expenses
Fixed Expenses = Contribution Margin
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Target Profit:
Rather than setting operating income = 0, target profit calculations assume a
certain operating income and calculate the sales dollars and units sold necessary
to achieve it.
The same equations are used as to calculate the breakeven point, except that a
non-zero operating income term is included in the numerator.
Margin of Safety:
The margin of safety is the excess of budgeted or actual sales over the breakeven
volume of sales.
It is expressed as both the dollar amount of the difference and as a percent of
budgeted or actual sales.
Sales Mix:
Companies that sell more than one product make the breakeven and target profit
calculations a bit more complex.
Each product has its own breakeven equation and sales volume, none of which
represents the breakeven equation for the entire company. A breakeven equation
can be developed for the whole company by combining the breakeven equations
and sales volumes (the sales mix) for the individual products.
The sales mix is assumed to remain constant to simplify the calculations.
Changes in sales volume are assumed to be in the constant sales mix.
Operating Leverage:
Operating leverage quantifies, at a given level of sales, the percent change in
operating income caused by a percent change in sales.
Leverage calculations are a two-step process:
o First, calculate the Degree of Leverage or Leverage Factor
Degree of Leverage
=
Contribution Margin
Operating Income
o Second, calculate the percent change in operating income:
Percent change in
operating income
=
Degree of Leverage
x
Operating Income
Cost Structure and Profit Volatility:
Cost structure refers to the proportion of variable costs and fixed costs in the total
costs incurred during the period.
No one cost structure is the right one. Different industries have different cost
structures and management may work to change the company’s cost structure in
response to changing business conditions and expectations.
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Key Topics to Know
Breakeven Equations
The breakeven point is expressed in sales dollars and units sold. The link
between the two is selling price per unit, meaning that breakeven units sold x
selling price per unit = breakeven sales.
The breakeven equations are:
=
Fixed expenses + operating income
Contribution margin ratio
=
Fixed expenses + operating income
Contribution margin $ per unit
Note that since operating income = 0 at the breakeven point, this term is
frequently dropped from the equations.
Breakeven problems are made more complex because some information is given
in per-unit amounts, other information is given in total dollars and still other
information is not dollars but units sold.
A useful tool to collect and analyze the various data items is:
Per Unit
Percent
Total
Units
1
Sales
100%
– Variable costs
= Contribution Margin
– Fixed costs
= Operating Income
o The Units line may be given or may be a variable to solve for.
o The Per Unit column records only the three variable items: sales, variable
costs and contribution margin.
o The Percent column calculates the three variable items: sales, variable costs
and contribution margin as a percent of sales.
o The Total column contains the entire income statement.
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Example # 1
Lowman Corporation sells only one product with a selling price of $200 and a variable
cost of $80 per unit. The company’s monthly fixed expense is $60,000.
Required:
Determine the breakeven point in units sold and sales dollars.
Solution # 1
CM ratio
=
Sales – variable expenses
=
$200–80=120
Sales
$200
=
60%
Breakeven sales
=
Fixed expenses + operating income
=
$60,000 + $0
Contribution margin ratio
60%
=
$100,000
Breakeven units
=
Fixed expenses + operating income
=
$60,000 + $0
Contribution margin $ per unit
$120
=
500 units
Target Profit
The same equations are used as to calculate the breakeven point, except that the
target profit is included in the numerator.
An alternative solution starting from the breakeven point is also possible.
Example # 2
Lowman Corporation sells only one product with a selling price of $200 and a variable
cost of $80 per unit. The company’s monthly fixed expense is $60,000. The corporation
would like to achieve a profit of $30,000 next year.
Required:
Determine the units to be sold and sales dollars necessary to
achieve the target profit.
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Solution # 2
CM ratio
Sales – variable expenses
$200–80=120
60%
Sales
$200
Sales
Fixed expenses + operating
income
$60,000 +
$30,000
$150,000
Contribution margin ratio
60%
Units
Fixed expenses + operating
income
$60,000 +
$30,000
750 units
Contribution margin $ per unit
$120
OR
Units
Sales
$150,000
750 units
Selling price per unit
$200
Alternate Solution:
Additional units
Target profit
$30,000
250 units
Contribution margin $
per unit
$120
Total units
Breakeven units +
units to reach target
500 + 250
750 units
Additional sales
Additional units x
selling price
250 x $200
$50,000
Total sales
Additional sales +
breakeven sales
$150,000 +
50,000
$200,000
Example #3
Star Products sells pillows for $90 per unit. The variable expenses are $63 per pillow
and the fixed costs are $135,000 per month. The company sells 8,000 pillows per
month. The sales manager is recommending a 10% reduction in selling price, which he
believes will produce a 25% increase in the number of pillows, sold each month.
Required:
Prepare contribution margin income statements for current
operating conditions and if the proposed changes are made.
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Solution #3
Present
Proposed
Per Unit
%
Total
Per Unit
%
Total
Units
1
8,000
1
10,000
Sales
$90
100.0
$720,000
$81
100.0
$810,000
Variable expenses
63
70.0
504,000
63
77.8
630,000
Contribution Margin
27
30.0
216,000
18
22.2
180,000
Fixed expenses
135,000
135,000
Operating income
$81,000
$45,000
8000 Pillows X 1.25 = 10,000 pillows; $90 per pillow X .9 = $81 per pillow
Since the operating income decreased by $36,000, from $81,000 to $45,000, the sales
manager’s suggestion should not be implemented.
Margin of Safety
Example #4
Using the data in Example #3, determine the margin of safety under current operating
conditions.
Solution #4
Present
Breakeven
Per Unit
%
Total
Total
Units
1
8,000
5,000
$450,000/$90
Sales
$90
100.0
$720,000
$450,000
$135,000/30%
Variable expenses
63
70.0
504,000
315,000
$450,000×70%
Contribution Margin
27
30.0
216,000
135,000
fixed + OI
Fixed expenses
135,000
135,000
stays the same
Operating income
$81,000
$0
Always $0
Margin of Safety = $720,000 – $450,000 = $270,000 or 37.5%
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Sales Mix
Example #5
Sanchez Co. sells two models of doghouses, the Puppy Palace and the Canine Castle.
Puppy
Palace
Canine
Castle
Sales price per unit
$50
$75
Variable cost per unit
30
50
Contribution margin per unit
$20
$25
Sanchez has determined that it would break even at an annual sales volume of 50,000
units, of which 75% would be Puppy Palaces.
Required:
a)
What are the contribution margin ratios for each product and the
company?
b)
What is the amount of Sanchez’s estimated annual fixed costs?
c)
What is the sales mix?
in volume.
Volume