16 -1
CHAPTER
Cost-VolumeProfit
Analysis: A
Managerial
Planning Tool
16 -2
Objectives
1. Determine the
number
of units
After
studying
this that must be
sold to breakchapter,
even oryou
earnshould
a target profit.
2. Calculate the amount
of to:
revenue required to
be able
break even or to earn a targeted profit.
3. Apply cost-volume-profit analysis in a
multiple-product setting.
4. Prepare a profit-volume graph and a costvolume-profit graph, and explain the meaning
of each.
16 -3
Objectives
5. Explain the impact of risk, uncertainty, and
changing variables on cost-volume-profit
analysis.
6. Discuss the impact of activity-based costing
on cost-volume-profit analysis
16 -4
Using Operating Income in CVP Analysis
Narrative Equation
Sales revenue
– Variable expenses
– Fixed expenses
= Operating income
16 -5
Using Operating Income in CVP Analysis
Sales (1,000 units @ $400)
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Operating income
$400,000
325,000
$ 75,000
45,000
$ 30,000
16 -6
Using Operating Income in CVP Analysis
Break Even in Units
0 = ($400 x Units) – ($325 x Units) – $45,000
$400,000 ÷
1,000
$325,000 ÷
1,000
16 -7
Using Operating Income in CVP Analysis
Break Even in Units
0 = ($400 x Units) – ($325 x Units) – $45,000
0 = ($75 x Units) – $45,000
$75 x Units = $45,000
Units = 600
Proof
Sales (600 units)
Less: Variable exp.
Contribution margin
Less: Fixed expenses
Operating income
$240,000
195,000
$ 45,000
45,000
$
0
16 -8
Achieving a Targeted Profit
Desired Operating Income of $60,000
$60,000 = ($400 x Units) – ($325 x Units) – $45,000
$105,000 = $75 x Units
Units = 1,400
Proof
Sales (1,400 units)
Less: Variable exp.
Contribution margin
Less: Fixed expenses
Operating income
$560,000
455,000
$105,000
45,000
$ 60,000
16 -9
Targeted Income as a Percent of Sales Revenue
Desired Operating Income of
15% of Sales Revenue
0.15($400)(Units) = ($400 x Units) – ($325 x Units) – $45,000
$60 x Units = ($400 x Units) – $325 x Units) – $45,000
$60 x Units = ($75 x Units) – $45,000
$15 x Units = $45,000
Units = 3,000
16 -10
After-Tax Profit Targets
Net income = Operating income – Income taxes
= Operating income – (Tax rate x Operating income)
= Operating income (1 – Tax rate)
Or
Operating income =
Net income
(1 – Tax rate)
16 -11
After-Tax Profit Targets
If the tax rate is 35 percent and a firm wants
to achieve a profit of $48,750. How much is
the necessary operating income?
$48,750 = Operating income – (0.35 x Operating income)
$48,750 = 0.65 (Operating income)
$75,000 = Operating income
16 -12
After-Tax Profit Targets
How many units would have to be sold to
earn an operating income of $48,750?
Units = ($45,000 + $75,000)/$75
Units = $120,000/$75
Proof
Sales (1,600 units)
$640,000
Units = 1,600
Less: Variable exp.
520,000
Contribution margin
$120,000
Less: Fixed expenses
45,000
Operating income
$ 75,000
Less: Income tax (35%) 26,250
Net income
$ 48,750
16 -13
Break-Even Point in Sales Dollars
First, the contribution margin
ratio must be calculated.
Sales
Less: Variable
expenses
Contribution
margin
Less: Fixed exp.
Operating income
$400,000 100.00%
325,000
81.25%
$ 75,000 18.75%
45,000
$ 30,000
16 -14
Break-Even Point in Sales Dollars
Given a contribution margin ratio of 18.75%, how
much sales revenue is required to break even?
Operating income = Sales – Variable costs – Fixed costs
$0 = Sales – (Variable costs ratio x Sales)
– $45,000
$0 = Sales (1 – 0.8125) – $45,000
Sales (0.1875) = $45,000
Sales = $240,000
16 -15
Relationships Among Contribution
Margin, Fixed Cost, and Profit
Fixed Cost = Contribution Margin
Fixed Cost
Contribution Margin
Revenue
Total Variable Cost
16 -16
Relationships Among Contribution
Margin, Fixed Cost, and Profit
Fixed Cost < Contribution Margin
Fixed Cost
Contribution Margin
Revenue
Total Variable Cost
Profit
16 -17
Relationships Among Contribution
Margin, Fixed Cost, and Profit
Fixed Cost > Contribution Margin
Fixed Cost
Contribution Margin
Revenue
Total Variable Cost
Loss
16 -18
Profit Targets and Sales Revenue
How much sales revenue must a firm generate to
earn a before-tax profit of $60,000. Recall that
fixed costs total $45,000 and the contribution
margin ratio is .1875.
Sales = ($45,000 + $60,000)/0.1875
= $105,000/0.1875
= $560,000
16 -19
Multiple-Product Analysis
Sales
Less: Variable expenses
Contribution margin
Less: Direct fixed expenses
Product margin
Less: Common fixed expenses
Operating income
Mulching
Mower
$480,000
390,000
$ 90,000
30,000
$ 60,000
Riding
Mower
Total
$640,000 $1,120,000
480,000
870,000
$160,000 $ 250,000
40,000
70,000
$120,000 $ 180,000
26,250
$ 153,750
16 -20
Income Statement: B/E Solution
Mulching
Mower
Sales
Less: Variable expenses
Contribution margin
Less: Direct fixed expenses
Segment margin
Less: Common fixed expenses
Operating income
$184,800
150,150
$ 34,650
30,000
$ 4,650
Riding
Mower
$246,400
184,800
$ 61,600
40,000
$ 23,600
Total
$431,200
334,950
$ 96,250
70,000
$ 26,250
26,250
$
0
16 -21
The profit-volume graph portrays
the relationship between profits
and sales volume.
16 -22
Example
The Tyson Company produces a single product
with the following cost and price data:
Total fixed costs
Variable costs per unit
Selling price per unit
$100
5
10
Profit-Volume Graph
(40, $100)
Profit $100—
or Loss
80—
I = $5X - $100
60—
40—
20—
Break-Even Point
(20, $0)
0— |
|
| |
|
|
| |
|
|
5 10 15 20 25 30 35 40 45 50
- 20—
Units Sold
- 40— Loss
-60—
-80—
-100— (0, -$100)
16 -23
16 -24
The cost-volume-profit graph
depicts the relationship among
costs, volume, and profits.
16 -25
Cost-Volume-Profit Graph
Revenue
$500 -450 -400 -350 -300 -250 -200 -150 -100 -Loss
50 -|
0 -- |
5 10
Total Revenue
Total Cost
Variable Expenses
($5 per unit)
Break-Even Point
(20, $200)
Fixed Expenses ($100)
|
|
|
|
15
20
25
30
|
|
35 40
|
|
|
45 50 55
Units Sold
|
60
16 -26
Assumptions of C-V-P Analysis
1. The analysis assumes a linear revenue function and a
linear cost function.
2. The analysis assumes that price, total fixed costs, and
unit variable costs can be accurately identified and
remain constant over the relevant range.
3. The analysis assumes that what is produced is sold.
4. For multiple-product analysis, the sales mix is assumed
to be known.
5. The selling price and costs are assumed to be known
with certainty.
16 -27
Relevant Range
$
Total Revenue
Total Cost
Units
Relevant Range
Alternative 1: If advertising expenditures increase by 16 -28
$8,000, sales will increase from 1,600 units to 1,725 units.
Units sold
Unit contribution margin
Total contribution margin
Less: Fixed expenses
Profit
BEFORE THE
INCREASED
ADVERTISING
WITH THE
INCREASED
ADVERTISING
1,600
x
$75
$120,000
45,000
$ 75,000
1,725
x
$75
$129,375
53,000
$ 76,375
DIFFERENCE IN PROFIT
Change in sales volume
Unit contribution margin
Change in contribution margin
Less: Change in fixed expenses
Increase in profits
125
x $75
$9,375
8,000
$1,375
Alternative 2: A price decrease from $400 to $375 per 16 -29
lawn mower will increase sales from 1,600 units to 1,900
units.
Units sold
Unit contribution margin
Total contribution margin
Less: Fixed expenses
Profit
BEFORE THE
PROPOSED
CHANGES
WITH THE
PROPOSED
CHANGES
1,600
x
$75
$120,000
45,000
$ 75,000
1,900
x $50
$95,000
45,000
$50,000
DIFFERENCE IN PROFIT
Change in contribution margin
Less: Change in fixed expenses
Decrease in profits
$ -25,000
-------$ -25,000
Alternative 3: Decreasing price to $375and increasing 16 -30
advertising expenditures by $8,000 will increase sales from
1,600 units to 2,600 units.
Units sold
Unit contribution margin
Total contribution margin
Less: Fixed expenses
Profit
BEFORE THE
PROPOSED
CHANGES
WITH THE
PROPOSED
CHANGES
1,600
x
$75
$120,000
45,000
$ 75,000
2,600
x
$50
$130,000
53,000
$ 77,000
DIFFERENCE IN PROFIT
Change in contribution margin
Less: Change in fixed expenses
Increase in profit
$10,000
8,000
$ 2,000
16 -31
Margin of Safety
Assume that a company has the following projected
income statement:
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Income before taxes
Break-even point in dollars (R):
$100,000
60,000
$ 40,000
30,000
$ 10,000
R = $30,000 ÷ .4 = $75,000
Safety margin = $100,000 - $75,000 = $25,000
16 -32
Degree of Operating Leverage (DOL)
DOL = $40,000/$10,000 = 4.0
Now suppose that sales are 25% higher than projected. What is
the percentage change in profits?
Percentage change in profits = DOL x percentage change in
sales
Percentage change in profits = 4.0 x 25% = 100%
16 -33
Degree of Operating Leverage (DOL)
Proof:
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Income before taxes
$125,000
75,000
$ 50,000
30,000
$ 20,000
16 -34
CVP and ABC
Assume the following:
Sales price per unit
$15
Variable cost
5
Fixed costs (conventional)
$180,000
Fixed costs (ABC) $100,000 with $80,000 subject to ABC analysis
Other Data:
Unit
Level of
Variable
Activity
Activity Driver
Costs
Driver
Setups
$500
100
Inspections
50
600
16 -35
CVP and ABC
1. What is the BEP under conventional
analysis?
BEP
= $180,000 ÷ $10
= 18,000 units
16 -36
CVP and ABC
2. What is the BEP under ABC analysis?
BEP
= [$100,000 + (100 x $500) + (600 x
$50)]/$10
= 18,000 units
16 -37
CVP and ABC
3. What is the BEP if setup cost could be reduced to
$450 and inspection cost reduced to $40?
BEP
= [$100,000 + (100 x $450) + (600 x $40)]/$10
= 16,900 units
16 -38
Chapter Sixteen
The End
16 -39