# Cost-Volume-Profit Analysis

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```					Cost-Volume-Profit Analysis

Chapter 22
Objectives
   Identify how changes in volume affect
costs
   Use CVP analysis to compute breakeven
points
   Use CVP analysis for profit planning, and
graph the cost-volume-profit relations
   Use CVP methods to perform sensitivity
analyses
   Compute income using variable costing
and absorption costing
Types of Costs

Variable

Fixed

Mixed
Variable Costs Example

   Consider Grand Canyon Railway.
   Assume that breakfast costs Grand
Canyon Railway \$3 per person.
   If the railroad carries 2,000 passengers, it
will spend \$______ for breakfast services.
Variable Costs Example

\$24 –
Total Variable Costs
(thousands)

\$18 –
\$12 –
\$6 –
–

–

–

–
0      1     2     3     4       5
Volume
(Thousands of passengers)
Fixed Costs Example

   Grand Canyon Railway has to pay
   Its employees
   For maintenance, etc.
   Regardless of how many passengers there
are.
   Suppose its fixed costs are \$200,000
Fixed Costs Example

\$400 –
Total Fixed Costs
(thousands)

\$300 –
\$200 –
\$100 –
–

–

–
0      1     2     3     –
4       5
Volume
(Thousands of passengers)
Mixed Costs Example

   A mixed cost is part variable and part
fixed.
   Assume a department of a company
has fixed costs of \$50 per month
(\$600 per year).
   There are also variable costs of \$3
per hour.
Mixed Costs Example

\$2,850 –
Total Costs

\$2,100 –
Variable
\$1,350 –                           Cost

\$600 –                            Fixed
Cost
–

–

–
0    125 250 375 500 625–
Volume (hours)
Relevant Range...

…is a band of volume in which a specific
relationship exists between cost and
volume.
 Outside the relevant range, the cost either
increases or decreases.
 A fixed cost is fixed only within a given
relevant range and a given time span.
Relevant Range

\$160,000 –
Fixed Costs

\$120,000 –
Relevant Range
\$80,000 –

\$40,000
–

–

–
0   5,000 10,000 15,000 20,000 25,000
Volume in Units
Assumptions of CVP Analysis

1   Expenses can be classified as either
variable or fixed.
2   CVP relationships are linear over a wide
range of production and sales.
3   Sales prices, unit variable cost, and total
fixed expenses will not vary within the
relevant range.
Assumptions of CVP Analysis

4   Volume is the only cost driver.
5   The relevant range of volume is specified.
6   Inventory levels will be unchanged.
7   The sales mix remains unchanged during
the period.
Break Even Point

   Many times companies want to know how
much of an item they must sell to break
even or where income = 0.
   3 approaches
   Income Statement Approach
   Contribution Margin Approach
   Contribution Margin Ratio
Income Statement Approach
With the income statement approach, breakeven
sales in units is calculated as follows:

Unit sales price × Units sold

–    Variable unit cost × Units sold

–     Fixed expenses      =     Operating income
Income Statement Approach
Example
   Assume that fixed expenses amount to
\$90,000.
   How many devices must be sold at the
regular price of \$100 to break even?
   (\$100 × Units sold) – (\$70 × Units sold) –
\$90,000 = 0
   Units sold = ?
Contribution Margin

Sales Revenue – Variable Expenses

Per Unit Percent        Ratio
Sales price            \$100      100          1.00
Variable expenses         70      70           .70
Contribution margin    \$ 30       30           .30

The amount that goes toward covering fixed costs
and operating income
Contribution Margin Formula

(Fixed expenses + Operating income)
÷ Contribution margin per unit = Units

Assuming Fixed Expenses = \$90,000,
how many units need to be sold to break even?
Contribution Margin Ratio
Formula
Want to compute break even in terms of
sales dollars

(Fixed expenses + Operating income)
÷ Contribution margin ratio = \$ Sales

How much in sales is needed for break even?
Two Approaches to Compute
Profits

Conventional income statement

Contribution margin income statement
Conventional Income
Statement

Cost of       Gross
Sales    –              =
Goods Sold     Margin

Gross        Operating        Net
–             =
Margin       Expenses       Income
Contribution Margin
Income Statement

Variable     Contribution
Sales    –               =
Expenses       Margin

Contribution      Fixed            Net
–              =
Margin         Expenses        Income
Contribution Margin Example

   Luis and Tom manufacture a device that
allows users to take a closer look at
icebergs from a ship.
   The usual price for the device is \$100.
   Variable costs are \$70.
   They receive a proposal from a company
in Newfoundland to sell 20,000 units at a
price of \$85.
Contribution Margin Example

   There is sufficient capacity to produce the
order.
   How do we analyze this situation?
   \$85 – \$70 = \$15 contribution margin.
   \$15 × 20,000 units = \$300,000 (total
increase in contribution margin)
Using Cost-Volume-Profit Analysis
to Plan Profits
600
500                                 — Sales
400
— Fixed
\$ (000)

300
200
100
— Fixed +
Variable
0
0   1   2        3    4   5
Units (000)
Various Sales Levels Example
   Assume selling price is \$35 per unit.
   Variable expense is \$21 per unit.
   Fixed cost is \$7,000.
   What is the breakeven point (in units &
sales dollars)?
Cost-Volume-Profit Graph
\$40,000
\$35,000
\$30,000       Breakeven sales point
500 units or \$17,500
\$25,000
Dollars

\$20,000
\$15,000
\$10,000                                 Fixed expense line
\$5,000
\$0
0            300       500                     1000
Units
Various Sales Levels Example
   What operating income is expected when
sales are 300 units?
   (Contribution Margin per unit x Number of
Units) – Fixed Expenses = Operating
Income/Loss
Various Sales Levels Example

   What operating income is expected when
sales are 1,000 units?
Target Operating Income
Example
   Suppose that a business would be content
with operating income of \$45,000.
   Assuming \$100 per unit selling price,
variable expenses of \$70 per unit, and
fixed expenses of \$90,000, how many
units must be sold?
   (Fixed Expenses + Operating Income) /
Contribution Margin per unit = Units Sold
Sensitivity Analysis

   What if?
   Change an assumption/variable to see
what happens
Change in Sales Price
Example
   Suppose that the sales price per device is
\$106 rather than \$100.
   What is the revised breakeven sales in
units?
   New contribution margin =

   Number of Units =
Change in Variable Costs
Example
   Suppose that variable expenses per device
   Other factors remain unchanged.
   What is break even in units?

   What is break even in sales dollars?
Change in Fixed Costs
Example
   Suppose that rental costs increased by
\$30,000.
   What are the new fixed costs?

   What is the new breakeven point?
   In Units:

   In Sales Dollars:
Margin of Safety Example

   Margin of safety is the excess of expected
sales over breakeven sales.
   The cushion
   Assume Luis and Tom’s breakeven point is
3,000 devices.
   Suppose they expect to sell 4,000 during
the period.
   What is the margin of safety?
What is the margin of safety?
In
Units:
In Dollars:

Units as a %:

\$ as a %:
Variable & Absorption Costing
Absorption costing assigns all
manufacturing costs to products.
Financial statements prepared under
GAAP use absorption costing.

Variable costing assigns only variable
manufacturing costs to products.
Variable costing is for internal use only.
Product Costing Example

Assume the following costs:
Direct material unit cost                 \$6.00
Direct labor unit cost                    \$3.00
Variable marketing                        \$2.50
Fixed manufacturing overhead per unit     \$5.00

What is the product cost/unit?
Product Costing Example
Absorption Costing

Assigns both variable & fixed manufacturing
costs. Fixed manufacturing costs are considered
inventoriable product costs.
Product Costing Example
Variable Costing
Assigns variable manufacturing costs only. Fixed
manufacturing costs are considered period costs.
Contribution Margin Income
Statement (Exhibit 22-10)
Sales Revenue
Less: Variable Expenses
variable manufacturing COGS
variable nonmanufacturing expenses
Contribution Margin
Less: Fixed Expenses
Operating Income

*Subtracts all variable costs before & all fixed
costs after contribution margin
Absorption Costing – vs- Variable
Costing
   If units produced > units sold
   Absorption Costing Income > Variable Costing
Income
   If units produced < units sold
   Absorption Costing Income < Variable Costing
Income
   If units produced = units sold
   Absorption Costing Income = Variable Costing
Income
Review
   Variable, Fixed, & Mixed Costs
   Cost-Volume-Profit Analysis
   Computing Break Even
   Income statement approach
   Contribution margin approach
   Contribution margin ratio
   Using CVP
   Planning profits
   Sensitivity analysis
   Absorption Costing
   Variable Costing
Appendix

Effect of sales mix on CVP
analysis.
Sales Mix Example

   Suppose that Luis and Tom plan to sell
two types of devices instead of one.
   They estimate that sales will be 3,000
regular devices and 1,000 large devices.
   This is a 3:1 sales mix.
   They expect 3/4 of the devices sold to be
regular devices and 1/4 to be large
devices.
Sales Mix Example

Regular       Large
Sales price          \$100         \$154
Variable expenses      70          100
Contribution margin    30           54
Sales mix (units)       3            1
\$ 90         \$ 54
The total is \$144.
Sales Mix Example

Weighted-average
Breakeven sales
contribution margin
\$90,000 ÷ \$36 = 2,500
\$144 ÷ (3 + 1) = \$36

2,500 × 3/4 = 1,875      2,500 × 1/4 = 625
regular devices          large devices
Sales Mix Example

1,875 regular × \$100 = \$187,500
625 large× \$154 =    96,250
Breakeven              \$283,750

\$90,000 ÷ \$144 = 625
packages in the mix

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