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Chapter 5 Lecture Notes
5-1
Chapter 5 Lecture Notes
Chapter theme: Cost-volume-profit (CVP) analysis helps
managers understand the interrelationships among cost,
volume, and profit by focusing their attention on the
interactions among the prices of products, volume of
activity, per unit variable costs, total fixed costs, and
mix of products sold. It is a vital tool used in many
business decisions such as deciding what products to
manufacture or sell, what pricing policy to follow, what
marketing strategy to employ, and what type of productive
facilities to acquire.
I. Assumptions of CVP analysis
A. Four key assumptions underlie CVP analysis:
i. Selling price is constant.
ii. Costs are linear and can be accurately divided into
variable and fixed elements. The variable element
is constant per unit, and the fixed element is
constant in total over the entire relevant range.
iii. In multiproduct companies, the sales mix is
constant.
iv. In manufacturing companies, inventories do not
change. The number of units produced equals the
number of units sold.
Helpful Hint: Point out that nothing is sacred about
these assumptions. When violations of these
assumptions are significant, managers can and do
modify the basic CVP model. Spreadsheets allow
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practical models that incorporate more realistic
assumptions. For example, nonlinear cost functions
with step fixed costs can be modeled using “If…Then”
functions.
II. The basics of cost-volume-profit (CVP) analysis
Learning Objective 5-1: Explain how changes in
activity affect contribution margin and net operating
income.
A. The contribution income statement is helpful to
managers in judging the impact on profits of changes in
selling price, cost, or volume. For example, let's look at
a hypothetical contribution income statement for
Racing Bicycle Company (RBC). Notice:
i. The emphasis is on cost behavior. Variable costs
are separate from fixed costs.
ii. The contribution margin is defined as the amount
remaining from sales revenue after variable
expenses have been deducted.
iii. Contribution margin is used first to cover fixed
expenses. Any remaining contribution margin
contributes to net operating income.
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iv. Sales, variable expenses, and contribution margin
can also be expressed on a per unit basis. Thus:
1. For each additional unit RBC sells, $200
more in contribution margin will help to
cover fixed expenses and provide a profit.
2. Notice, each month RBC must generate at
least $80,000 in total contribution margin to
break-even (which is the level of sales at
which profit is zero).
3. Therefore, if RBC sells 400 units a month, it
will be operating at the break-even point.
4. If RBC sells one more bike (401 bikes), net
operating income will increase by $200.
v. You do not need to prepare an income statement to
estimate profits at a particular sales volume. Simply
multiply the number of units sold above break-even
by the contribution margin per unit.
1. For example, if RBC sells 430 bikes, its net
operating income will be $6,000.
B. CVP relationships in equation form (for those who
prefer an algebraic approach to solving problems in the
chapter):
i. The contribution format income statement can be
expressed in equation form as shown on this slide.
1. This equation can be used to show the profit
RBC earns if it sells 401 bikes. Notice, the
answer of $200 mirrors our earlier solution.
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ii. When a company has only one product we can
further refine this equation as shown on this slide.
1. This equation can also be used to show the
$200 profit RBC earns if it sells 401 bikes.
iii. The profit equation can also be expressed in terms
unit contribution margin as shown on this slide.
1. This equation can also be used to compute
RBC’s $200 profit if it sells 401 bikes.
Learning Objective 5-2: Prepare and interpret a cost-
volume-profit (CVP) graph and a profit graph.
C. CVP relationships in graphic form
i. The relationships among revenue, cost, profit, and
volume can be expressed graphically by preparing a
cost-volume-profit (CVP) graph. To illustrate, we
will use contribution income statements for RBC at
0, 200, 400, and 600 units sold.
Helpful Hint: Mention to students that the graphic form
of CVP analysis may be preferable to them if they are
uncomfortable with algebraic equations.
ii. In a CVP graph, unit volume is represented on the
horizontal (X) axis and dollars on the vertical (Y)
axis. A CVP graph can be prepared in three steps.
1. Draw a line parallel to the volume axis to
represent total fixed expenses.
2. Choose some sales volume (e.g., 400 units)
and plot the point representing total
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3. expenses (e.g., fixed and variable) at that
sales volume. Draw a line through the data
point back to where the fixed expenses line
intersects the dollar axis.
4. Choose some sales volume (e.g., 400 units)
and plot the point representing total sales
dollars at the chosen activity level. Draw a
line through the data point back to the
origin.
iii. Interpreting the CVP graph.
1. The break-even point is where the total
revenue and total expense lines intersect.
2. The profit or loss at any given sales level is
measured by the vertical distance between
the total revenue and the total expense lines.
Helpful Hint: Ask students what the CVP graph would
look like for a public agency like a county hospital
receiving a fixed budget each year and collecting fees
less than its variable costs. It would look like this:
This is the reverse of the usual situation. If such an
organization has volume above the break-even point, it
will experience financial difficulties.
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Total
expenses
Total
revenue
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iv. An even simpler form of the CVP graph is called
the profit graph. The profit graph is based on the
equation shown on this slide.
1. To plot the graph, compute the profit at two
different sales volumes, plot the points, and
then connect them with a straight line. This
slide contains the profit graph for RBC.
Notice:
a. The sales volumes plotted on this
graph are 300 and 500 bikes.
b. The break-even point is 400 bikes.
D. Contribution margin ratio (CM ratio)
Learning Objective 5-3: Use the contribution margin
ratio (CM ratio) to compute changes in contribution
margin and net operating income resulting from
changes in sales volume.
i. The CM ratio is calculated by dividing the total
contribution margin by total sales.
1. For RBC, the CM ratio is 40%. Thus, each
$1.00 increase in sales results in a total
contribution margin increase of 40¢.
ii. The CM ratio can also be calculated by dividing the
contribution margin per unit by the selling price
per unit.
1. For RBC the CM ratio is 40%.
2. If RBC increases sales from 400 to 500
bikes, the increase in contribution margin
($20,000) can be calculated by multiplying
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3. the increase in sales ($50,000) by the CM
ratio (40%).
Quick Check – contribution margin ratio
iii. The relation between profit and the CM ratio can
also be expressed in terms of the equation shown
on this slide.
1. For example, we can use this equation to
calculate RBC’s profit of $20,000 at a
volume of 500 bikes.
E. Applications of CVP concepts
Learning Objective 5-4: Show the effects on net
operating income of changes in variable costs, fixed
costs, selling price, and volume.
Helpful Hint: The five examples that are forthcoming
should indicate to students the range of uses of CVP
analysis. In addition to assisting management in
determining the level of sales that is needed to break-
even or generate a certain dollar amount of profit,
these examples illustrate how the results of alternative
decisions can be quickly determined.
i. The variable expense ratio.
1. Before proceeding with five examples that
demonstrate various applications of CVP
concepts, we need to define the variable
expense ratio as the ratio of variable
expenses to sales.
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ii. Change in fixed cost and sales volume.
1. What is the profit impact if RBC can
increase unit sales from 500 to 540 by
increasing the monthly advertising budget
by $10,000?
a. Preparing a contribution income
statement reveals a $2,000 decrease in
profits.
b. A shortcut solution using incremental
analysis also reveals a $2,000 decrease
in profits.
iii. Change in variable costs and sales volume.
1. What is the profit impact if RBC can use
higher quality raw materials, thus increasing
variable costs per unit by $10, to generate an
increase in unit sales from 500 to 580?
a. The contribution income statement
reveals a $10,200 increase in profits.
iv. Change in fixed cost, sales price, and sales
volume.
1. What is the profit impact if RBC: (1) cuts its
selling price $20 per unit, (2) increases its
advertising budget by $15,000 per month,
and (3) increases unit sales from 500 to 650
units per month?
a. The contribution income statement
reveals a $2,000 increase in profits.
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v. Change in variable cost, fixed cost, and sales
volume.
1. What is the profit impact if RBC: (1) pays a
$15 sales commission per bike sold instead
of paying salespersons flat salaries that
currently total $6,000 per month and (2)
increases unit sales from 500 to 575 bikes?
a. The contribution income statement
reveals a $12,375 increase in profits.
vi. Change in regular sales price.
1. If RBC has an opportunity to sell 150 bikes
to a wholesaler without disturbing sales to
other customers or fixed expenses, what
price should it quote to the wholesaler if it
wants to increase monthly profits by
$3,000?
a. The price quote should be $320 per
bike.
III. Break-even analysis
Learning Objective 5-5: Determine the break-even
point.
i. The equation and formula methods can be used to
determine the unit sales and dollar sales needed to
achieve a target profit of zero. For example, let’s
revisit the information from RBC:
1. Suppose RBC wants to know how many
bikes must be sold to break even (i.e. earn a
target profit of $0). The equation shown on
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this slide can be used to answer this
question.
a. The equation method reveals that 400
bikes must be sold to break even.
b. The formula method can also be used
to determine that 400 bikes must be
sold to break even.
2. Suppose RBC wants to compute the sales
dollars required to break even (i.e. earn a
target profit of $0). The equation shown here
can be used to answer this question.
a. The equation method reveals that
sales of $200,000 will enable the
company to break even.
b. The formula method can also be used
to determine that sales of $200,000
will enable the company to breakeven.
Quick Check – break-even calculations
B. Target profit analysis
Learning Objective 5-6: Determine the level of sales
needed to achieve a desired target profit.
C. We can compute the number of units that must be sold
to attain a target profit using either the equation
method or the formula method.
i. The equation method is summarized on this slide.
Our goal is to solve for the unknown “Q” which
represents the quantity of units that must be sold to
attain the target profit. For example:
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1. Suppose RBC wants to know how many
bikes must be sold to earn a target profit of
$100,000.
a. The equation method can be used to
determine that 900 bikes must be sold
to earn the desired target profit.
ii. The formula method is summarized on this slide.
It can also be used to compute the quantity of units
that must be sold to attain a target profit. For
example:
1. Suppose RBC wants to know how many
bikes must be sold to earn a target profit of
$100,000.
a. The formula method can be used to
determine that 900 bikes must be sold
to earn the desired target profit.
D. We can also compute the target profit in terms of sales
dollars using either the equation method or the
formula method.
i. The equation method is summarized on this slide.
Our goal is to solve for the unknown “Sales,”
which represents the dollar amount of sales that
must be sold to attain the target profit. For
example:
1. Suppose RBC wants to compute the sales
dollars required to earn a target profit of
$100,000.
a. The equation method can be used to
determine that sales must be $450,000
to earn the desired target profit.
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ii. The formula method is summarized on this slide.
It can also be used to compute the dollar sales
needed to attain a target profit. For example:
1. Suppose RBC wants to compute the dollar
sales required to earn a target profit of
$100,000.
a. The formula method can be used to
determine that sales must be $450,000
to earn the desired target profit.
Quick Check – target profit calculations
E. The margin of safety
Learning Objective 5-7: Compute the margin of safety
and explain its significance.
i. The margin of safety in dollars is the excess of
budgeted (or actual) sales over the break-even
volume of sales. For example:
1. If we assume that RBC has actual sales of
$250,000, given that we have already
determined the break-even sales to be
$200,000, the margin of safety is $50,000.
2. The margin of safety can be expressed as a
percent of sales. For example:
a. RBC’s margin of safety is 20% of
sales.
3. The margin of safety can be expressed in
terms of the number of units sold. For
example:
a. RBC’s margin of safety is 100 bikes.
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Quick Check – margin of safety calculations
III. CVP considerations in choosing a cost structure
A. Cost structure and profit stability
i. Cost structure refers to the relative proportion of
fixed and variable costs in an organization.
Managers often have some latitude in determining
their organization's cost structure.
ii. There are advantages and disadvantages to high
fixed cost (or low variable cost) and low fixed cost
(or high variable cost) structures.
1. An advantage of a high fixed cost structure
is that income will be higher in good years
compared to companies with a lower
proportion of fixed costs.
2. A disadvantage of a high fixed cost structure
is that income will be lower in bad years
compared to companies with a lower
proportion of fixed costs.
3. Companies with low fixed cost structures
enjoy greater stability in income across good
and bad years.
Learning Objective 5-8: Compute the degree of
operating leverage at a particular level of sales and
explain how it can be used to predict changes in net
operating income.
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B. Operating leverage
i. Operating leverage is a measure of how sensitive
net operating income is to percentage changes in
sales.
ii. The degree of operating leverage is a measure, at
any given level of sales, of how a percentage
change in sales volume will affect profits. It is
computed as shown on this slide.
iii. To illustrate, let’s revisit the contribution income
statement for RBC:
1. RBC’s degree of operating leverage is 5
($100,000/$20,000).
2. With an operating leverage of 5, if RBC
increases its sales by 10%, net operating
income would increase by 50%.
a. The 50% increase can be verified by
preparing a contribution approach
income statement.
Quick Check – operating leverage calculations
Helpful Hint: Emphasize that the degree of operating
leverage is not a constant like unit variable cost or unit
contribution margin that a manager can apply with
confidence in a variety of situations. The degree of
operating leverage depends on the level of sales and
must be recomputed each time the sales level changes.
Also, note that operating leverage is greatest at sales
levels near the break-even point and it decreases as
sales and profits rise.
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IV. Structuring sales commissions
A. Companies generally compensate salespeople by
paying them either a commission based on sales or a
salary plus a sales commission. Commissions based on
sales dollars can lead to lower profits in a company.
Consider the following illustration:
i. Pipeline Unlimited produces two types of
surfboards, the XR7 and the Turbo. The XR7 sells
for $100 and generates a contribution margin per
unit of $25. The Turbo sells for $150 and earns a
contribution margin per unit of $18.
ii. Salespeople compensated based on sales
commission will push hard to sell the Turbo even-
though the XR7 earns a higher contribution margin
per unit.
iii. To eliminate this type of conflict, commissions can
be based on contribution margin rather than on
selling price alone.
V. The concept of sales mix
Learning Objective 5-9: Compute the break-even point
for a multiproduct company and explain the effects of
shifts in the sales mix on contribution margin and the
break-even point.
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A. The term sales mix refers to the relative proportions in
which a company’s products are sold. Since different
products have different selling prices, variable costs,
and contribution margins, when a company sells more
than one product, break-even analysis becomes more
complex as the following example illustrates:
Helpful Hint: Mention that these calculations typically
assume a constant sales mix. The rationale for this
assumption can be explained as follows. To use simple
break-even and target profit formulas, we must assume
the firm has a single product. So we do just that – even
for multi-product companies. The trick is to assume the
company is really selling baskets of products and each
basket always contains the various products in the
same proportions.
i. Assume the RBC sells bikes and carts. The bikes
comprise 45% of the company’s total sales revenue
and the carts comprise the remaining 55%. The
contribution margin ratio for both products
combined is 48.2%.
ii. The break-even point in sales would be $352,697.
The bikes would account for 45% of this amount,
or $158,714. The carts would account for 55% of
the break-even sales, or $193,983.
1. Notice a slight rounding error of $175.
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