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Managerial Accounting
Tenth Canadian Edition
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What You Really Need To Know
Chapter 4: Cost-Volume-Profit Relationships
A. The contribution margin is a key concept that will be used throughout the chapter and
in subsequent chapters.
1. The contribution margin is defined as the difference between total sales and
total variable expenses:
Sales ..................................................
Less variable expenses ......................
Contribution margin ..........................
XXX
XXX
XXX
2. The unit contribution margin is defined as the difference between the unit
selling price and the unit variable expenses:
Selling price per unit .........................
Less variable expenses per unit .........
Unit contribution margin ...................
XXX
XXX
XXX
3. The relation between the contribution margin and the unit contribution margin
is simple. The contribution margin is equal to the unit contribution margin
multiplied by the number of units sold:
Unit contribution margin ...................
× Unit sales .......................................
Contribution margin ..........................
XXX
XXX
XXX
The term “total contribution margin” is also commonly used to refer to the
contribution margin.
4. Operating income is equal to the contribution margin less fixed expenses.
Sales ..................................................
Less variable expenses ......................
Contribution margin ..........................
Less fixed expenses ...........................
Operating income ..............................
XXX
XXX
XXX
XXX
XXX
5. The break-even point is the sales at which profits are zero and the total
contribution margin just equals fixed expenses.
6. The relation between contribution margin and operating income provides a
very powerful planning tool. It gives the manager the ability to predict what
profits will be at various activity levels without the necessity of preparing
detailed income statements.
a. The contribution margin must first cover fixed expenses. If it doesn’t,
there is a loss. Below the break-even point, every unit sold reduces the
loss by the amount of the unit contribution margin.
b. Once the break-even point is reached, operating income will increase
by the amount of the unit contribution margin for each additional unit
sold.
B. CVP and break-even analysis can also be done graphically. Exhibits 7-1 and 7-2 show
how a CVP graph is prepared and interpreted. A cost-volume-profit graph depicts the
relations among sales, costs, and volume.
C. The contribution margin ratio (CM ratio), which expresses the contribution margin as
a percentage of sales, is another very powerful concept.
1. The contribution margin ratio is defined as follows:
CM ratio =
Contribution margin
Sales
2. In a company with only a single product, the CM ratio can also be computed
as follows:
CM ratio =
Unit contribution margin
Unit selling price
3. The contribution margin ratio is used to predict the change in total
contribution margin that would result from a given change in dollar sales:

=
Change in dollar sales ..................
CM ratio .......................................
Change in contribution margin ....
XXX
XXX
XXX
4. Assuming that fixed expenses are not affected, an increase (or decrease) in
contribution margin will be reflected dollar for dollar in increased (or
decreased) operating income.
5. The CM ratio is particularly useful when a company has multiple products. In
such situations, volume is most conveniently expressed in terms of total dollar
sales rather than in units sold.
D. Cost-volume-profit (CVP) concepts can be used in many day-to-day decisions.
Carefully study the examples given under the heading “Some Applications of CVP
Concepts” in the early part of the chapter.
1. Notice that each solution makes use of either the unit contribution margin or
the CM ratio. This underscores the importance of these two concepts.
2. Also notice that several of the examples use incremental analysis. An
incremental analysis is based on only those costs and revenues that differ
between alternatives.
E. Two particular examples of CVP analysis, called break-even analysis and target profit
analysis, are often used. Break-even analysis is a special case of target profit analysis, so
target profit analysis is considered first below.
1. Target profit analysis is used to find out how much would have to be sold to
attain a specific target profit. The analysis is based on the following equation:
Profits = Sales – Variable expenses – Fixed expenses
In CVP analysis, this equation is often rewritten as:
Sales = Variable expenses + Fixed expenses + Profits
All of the problems can be worked using this basic equation and simple
algebra. However, handy formulas are available for answering some of the
more common questions. These formulas are discussed below.
2. Target profit analysis is used in two basic variations. In the first variation, the
question is how many units would have to be sold to attain the target profit. In
the second variation, the question is how much total dollar sales would have to
be to attain the target profit. The formulas are:
Units sold to
=
attain target profit
Fixed expenses + Target profit
Unit contribution margin
Dollar sales to
=
attain target profit
Fixed expenses + Target profit
CM ratio
3. The target profit in the two equations for target profit is on a before-tax basis.
Therefore, a target profit stated on an after-tax basis must be converted to a
before-tax basis. The formula for this conversion is as follows:
After-tax target profit
(1 – Tax rate)
Before-tax target profit =
F. Break-even occurs when profit is zero. Thus, break-even analysis is a special case of
target profit analysis in which the target profit is zero. Therefore, the break-even formulas
can be stated as follows:
Breakeven point
in units sold
=
Breakeven point
in total sales dollars
Fixed expenses
Unit contribution margin
=
Fixed expenses
CM ratio
G. The margin of safety is the excess of budgeted (or actual) sales over the break-even
volume of sales. It is the amount by which sales can drop before losses begin to be
incurred. The margin of safety can be stated in terms of either dollars or as a percentage
of sales:
Total budgeted (or actual) sales .........
Less break-even sales ........................
Margin of safety ................................
Margin of safety
=
percentage
$XXX
XXX
$XXX
Margin of safety
Total budgeted (or actual) sales
H. Cost structure—the relative proportion of fixed and variable costs—has an impact on
how sensitive a company’s profits are to changes in sales. A company with low fixed
costs and high variable costs will tend to have a lower CM ratio than a company with a
greater proportion of fixed costs. Such a company will tend to have less volatile profits,
but at the risk of losing substantial profits if sales trend sharply upward.
I. Operating leverage refers to the effect a given percentage increase in sales will have on
operating income.
1. The degree of operating leverage is defined as:
Degree of operating
leverage
=
Contribution margin
Before-tax profit
2. To estimate the percentage change in operating income that would occur as
the result of a given percentage change in dollar sales, multiply the change in
sales by the degree of operating leverage.

=
Percentage change in dollar sales...............
Degree of operating leverage .....................
Percentage change in operating income .....
XXX
XXX
XXX
3. The degree of operating leverage is not constant. It changes as sales increase
or decrease. In general, the degree of operating leverage decreases the further
a company moves away from its break-even point.
J. When a company has more than one product, the sales mix can be crucial. The sales
mix refers to the relative proportions in which the company’s products are sold.
1. When CVP analysis involves more than one product, the analysis is normally
based on the overall contribution margin ratio. This is computed exactly like
the CM ratio is computed in a single product company except that overall
figures are used for both the contribution margin and sales:
Overall CM ratio =
Overall contribution margin
Overall sales
2. When the company has more than one product, the overall CM ratio is used in
the target profit and break-even formulas instead of the CM ratio.
3. As the sales mix changes, the overall CM ratio will also change. If the shift is
toward less profitable products, then the overall CM ratio will fall; if the shift
is toward more profitable products, then the overall CM ratio will rise.
K. CVP analysis ordinarily relies on the following assumptions:
1. The selling price is constant; it does not change as unit sales change.
2. Costs are linear. Costs can be accurately divided into variable and fixed
elements. The variable cost per unit is constant and the total fixed cost is
constant.
3. In multi-product situations, the sales mix is constant.
4. In manufacturing companies, inventories do not change.
What To Watch Out For (Hints, Tips and Traps)

Cost-volume-profit (CVP) analysis is a powerful tool that managers use to help
them understand the interrelationship among cost, volume and profit in an
organization by focusing on interactions among the following five elements:
prices of products, volume or level of activity, per unit variable costs, total fixed
costs, mix of products sold.

Some students may prefer the algebraic approach to CVP analysis. The basic
CVP model can be written as follows:
Profit = ( p – v ) q – F
or
Profit = cm  q – F
where p is the unit selling price, v is the variable cost per unit, q is the unit sales,
F is the fixed cost, and cm is the unit contribution margin.
Expressed in terms of the CM ratio, the basic equation is as follows:
Profit = CM ratio  sales – F
All CVP problems can be solved using these basic equations.

The degree of operating leverage is not constant as the level of sales changes. For
example, at the break-even point the degree of operating leverage is infinite since
the denominator of the ratio is zero. Therefore, the degree of operating leverage
should be used with some caution and should be recomputed for each level of
starting sales.

The term sales mix means the relative proportions in which a company’s products
are sold. Most companies have a number of products with differing contribution
margins. Thus, changes in the sales mix can cause variations in a company’s
profits. As a result, the break-even point in a multi-product company is dependent
on the mix in which the various products are sold. The assumption is usually
made in CVP analysis that the sales mix will not change. Under the constant sales
mix assumption, the break-even level of sales dollars can be computed using the
overall contribution margin (CM) ratio. In essence, the assumption is made that
the firm has only one product that consists of a basket of its various products in a
specified proportion. If the proportions in which products are sold change, then
the contribution margin ratio will change. Since the sales mix is not in reality
constant, the results of CVP analysis should be viewed with more caution in
multi-product firms than in single product firms.

Simple CVP analysis relies on simplifying assumptions. However, if a manager
knows that one of the assumptions is violated, the CVP analysis can often be
easily modified to make it more realistic. It may be useful to realize that there is
nothing sacred about the CVP assumptions. When violations of the assumptions
are significant, managers can and do modify the basic CVP model. Spreadsheets
make it fairly easy to build practical models that incorporate more realistic
assumptions. For example, nonlinear cost functions with stepped fixed costs can
be modeled using IF...THEN functions.