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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: 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 breakeven.
b. The formula method can also be used
to determine that 400 bikes must be
sold to breakeven.
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 break-
even.
Quick Check – break-even calculations
B. Target profit analysis
Learning Objective 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 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 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 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 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 $176.
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