Chapter 5 Cost-Volume-Profit Relationships
Key assumptions of CVP analysis
(1)
Selling price is constant.
(2)
Costs are linear.
(3)
In multi-product companies, the sales mix is constant.
(4)
In manufacturing companies, the level of inventories does not change.
LO1: How do changes in activity affect contribution margin and net operating
income?
1.
The contribution income statement variable costs from fixed costs.
(1)
Contribution margin, which is
sales revenue minus variable expenses
, is
used first to cover fixed expenses. Any remaining contribution margin contributes
to net operating income.
(2)
Sales, variable expenses, and contribution margin can also be expressed on
a
per unit
basis.
(3)
The contribution format income statement can be expressed in the
following equation: Profit =
(Sales – Variable expenses) – Fixed expenses
.
(4)
When a company has only one product we can further refine this equation
as Profit =
(P × Q – V × Q) – Fixed expenses
,
where P is unit selling price, Q is units sold, and V is unit variable expenses.
(5)
Since Unit CM = P – V, we can express the simple profit equation as
Profit =
Unit CM * Q – Fixed expenses
.
Example
: A hypothetical contribution income statement for Racing Bicycle Company:
Racing Bicycle Company
Contribution Income Statement
For the Month of June
500 bikes
Per Unit
400 bikes
401 bikes
430 bikes
Sales
250,000
500
200,000
200,500
215,000
Less: Variable expenses
150,000
300
120,000
120,300
129,000
Contribution margin
100,000
200
80,000
80,200
86,000
Less: Fixed expenses
80,000
80,000
80,000
80,000
Net operating income
20,000
0
200
6,000
We can learn the following from the statement:
A.
Each month RBC must generate at least
$80,000
in total contribution
margin to break-even (when revenues equal expenses, and profit is zero).
Therefore, if RBC sells
400
units a month, it will be operating at the break-even
point.
B.
For each additional unit RBC sells,
$200
more in contribution margin will
help to cover fixed expenses and provide a profit. In other words, if RBC sells one
more bike (401 bikes), net operating income will increase by
$200
.
C.
There is no need to prepare an income statement to estimate profits at a
particular sales volume. We can simply follow the following formula:
1