Chapter Three
Cost – Volume – Profit Analysis
• Jeff Jamail is evaluating a business
opportunity to sell cookware at trade
shows. Mr. Jamail can buy the cookware
at a wholesale cost of $210 per set. He
plans to sell the cookware for $350 per
set. He estimates fixed costs such as
plane fare, booth rental cost, and lodging
to be $5,600 per trade show.
• How many cookware sets must Mr. Jamail
sell in order to breakeven?
Cost-Volume-Profit Relationship
There are 3 methods to analyze:
(1.) Contribution Margin per Unit
(2.) Contribution Ratio
(3.) Equation Method
NOTE: Each method yields the same
results.
Cost-Plus Pricing Strategy
• It sets prices at cost plus a mark-up
• For example:
– Product cost $20 to make
– Mgmt decides to mark-up 30%
– Selling Price = $20 + ($20 * 30%) = $26
Break-Even Point
Point where Total Revenue = Total Costs
Break-even Volume in Units =
Fixed Costs / Contribution Margin per Unit
Once fixed costs have been covered, net income will
increase per unit contribution margin for each
additional unit sold
Determining the Break-even Point
Bright Day produces one produce called Delatine. The
company uses a cost-plus-pricing strategy; it sets prices
at cost plus a markup of 50% of cost. Delatine cost $24
per bottle to manufacture, so a bottle sells for $36 ($24
+ [50% × $24]). The contribution margin per bottle is:
Sales revenue per bottle
Variable cost per bottle
Contribution margin per bottle
$ 36
24
$ 12
The company’s first concern is if can sell enough bottles
of Delatine to cover it fixed costs and make a profit!
Determining the Break-even Point
The break-even point is the point where total revenue
equals total costs (both variable and fixed). For Bright
Day, the cost of advertising is estimated to be $60,000.
Advertising costs are the fixed costs of the company. We
use the following formula to determine the break-even
point in units.
Break-even
Fixed costs
=
volume in units
Contribution margin per unit
=
$60,000
= 5,000 units
$12
Determining the Break-even Point
For Delatine, the break-even point in sales dollars is
$180,000 (5,000 bottles × $36 selling price).
Determining the Break-even Point
Once all fixed costs have been covered (5,000 bottles
sold), net income will increase by $12 per unit
contribution margin.
Revenue @ $36
Variable Expenses @ $24
Contribution Margin @$12
Fixed Expenses
Net Income
4,998
$ 179,928
(119,952)
59,976
(60,000)
$
(24)
Number of Units Sold
4,999
5,000
5,001
$ 179,964
$ 180,000
$ 180,036
(119,976)
(120,000)
(120,024)
59,988
60,000
60,012
(60,000)
(60,000)
(60,000)
$
(12)
$
$
12
5,002
$ 180,072
(120,048)
60,024
(60,000)
$
24
$12
What will be the increase in net income if units sold
increase from 5,000 units to $5,600 units?
Determining the Break-even Point
What will be the increase in net income if units sold
increase from 5,000 units to $5,600 units?
New Units Sold
Previous Units Sold
Increase in Units Sold
Contribution Margin Per Unit
Increase in Income
Revenue @ $36
Variable Expenses @ $24
Contribution Margin @$12
Fixed Expenses
Net Income
5,600
5,000
600
$
12
$ 7,200
Number of Units Sold
5,000
5,600
$ 180,000
$ 201,600
(120,000)
(134,400)
60,000
67,200
(60,000)
(60,000)
$
$ 7,200
Reaching a Target Profit Level
Bright Day’s president wants the advertising campaign
to produce profits of $40,000 to the company.
Break-even
Fixed costs + Desired profit
=
volume in units Contribution margin per unit
=
$60,000 + $40,000
$12
= 8,333.33 units
Reaching a Target Profit Level
At $36 per unit selling price, the sales dollars are equal to
$300,000, as shown below:
Units sold
Revenue @ $36
Variable Expenses @ $24
Contribution Margin @$12
Fixed Expenses
Net Income
Income
8,333.33
$ 300,000
(200,000)
100,000
(60,000)
$ 40,000
Check Yourself
Matrix, Inc. manufactures one model of lawnmower the
sells for $175 each. Variable expenses to produce the
lawnmower are $100 per unit. Total fixed costs are
$225,000 per month, and management wants to
earn a profit in the coming month of $37,500. Matrix
must sell the following number of lawnmowers:
1. 3,000.
2. 3,500.
3. 4,000.
4. 4,500.
$225,000 + $37,500
= 3,500
$75
Effects of Changes in Sales Price
The Marketing Department at Bright Day suggests
that a price drop from $36 per bottle to $28 per
bottle will make Delatine a more attractive product
to sell. The president wants to know what such a
price drop would have on the company’s stated goal
of producing a $40,000 profit.
You have been asked to determine the number of
bottles that must be sold to earn the $40,000 profit
at the new $28 selling price per bottle. See if you
can provide an answer to the president before going
to the next screen!
Effects of Changes in Sales Price
Step 1
New Selling Price Per Bottle $ 28
Variable Expenses Per Bottle
24
New Contribution Margin
$ 4
Step 2
Break-even
Fixed costs + Desired profit
=
volume in units Contribution margin per unit
Step3
$60,000 + $40,000
=
= 25,000 units
$4
Effects of Changes in Sales Price
The required sales volume in dollars is $700,000 (25,000
units × $28 per bottle) as shown below:
Units sold
Revenue @ $28
Variable Expenses @ $24
Contribution Margin @$4
Fixed Expenses
Net Income
Income
25,000
$ 700,000
(600,000)
100,000
(60,000)
$ 40,000
Target Costing
1. Determine the market price at which
product will sell
•
This is the Target Price
2. Must develop the product at a cost that
will enable company to be profitable
selling the product at the
target price
•
This is known as
TARGET COSTING
Changes in Variable Costs
Bright Day is considering an alternative mixture for
Delatine along with new packaging. This new product
would sell for $28 per bottle and have a variable cost per
bottle of $12. The president is not in favor of the new
product but wants to know how many units must be sold
to produce the desired profit of $40,000.
You have been asked to determine the units that must be
sold and the total sales revenue that will be produced!
Changes in Variable Costs
Step 1
New Selling Price Per Bottle $ 28
Variable Expenses Per Bottle
12
New Contribution Margin
$ 16
Step 2
Break-even
Fixed costs + Desired profit
=
volume in units Contribution margin per unit
Step3
$60,000 + $40,000
=
$16
= 6,250 units
Changes in Variable Costs
At $28 per unit selling price, the sales dollars are equal to
$175,000 as shown below:
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
Income
6,250
$ 175,000
(75,000)
100,000
(60,000)
$ 40,000
Changes in Fixed Costs
Bright Day’s president has asked you to determine the
required sales volume if advertising costs were reduced
to $30,000, from the planned level of $60,000.
Break-even
$30,000 + $40,000
=
volume (units)
$16
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
= 4,375 units
Income
4,375
$ 122,500
(52,500)
70,000
(30,000)
$ 40,000
Calculating the Margin of Safety
The margin of safety measures the cushion between
budgeted sales and the break-even point. It quantifies the
amount by which actual sales can fall short of expectations
before the company will begin to incur losses. With a
selling price of $28 per unit and variable costs of $12 per
unit, and a desired profit of $40,000, budgeted sales were:
Break-even
$30,000 + $40,000
=
volume (units)
$16
= 4,375 units
Break-even unit sales assuming no profit would be:
Break-even
=
volume (units)
$30,000
= 1,875 units
$16
Calculating the Margin of Safety
Budgeted sales
Break-even sales
Margin of safety
In Units
4,375
(1,875)
2,500
In Dollars
$ 122,500
(52,500)
$ 70,000
Management considers a new product, Delatine
that has a sales price of $36 and variable costs
of $24 per bottle. Fixed costs are $60,000. Breakeven is 5,000 units.
Management want to earn a $40,000 profit on
Delatine. The sales volume to achieve this
profit level is 8,334 bottles sold.
Marketing advocates a target price of $28 per
bottle. The sales volume required to earn a
$40,000 profit increases to 25,000 bottles.
Target costing is employed to reengineer the
product and reduces variable cost per unit to
$12. To earn the desired profit of $40,000, sales
volume decreases to 6,250 units.
Target costing is applied and fixed costs are
reduced to $30,000. The sales volume to earn
the desired $40,000 profit is 4,375 units.
Decrease in Sales Price with an
Increase in Sales Volume
The marketing manager believes reducing the sales price
per bottle to $25 will increase sales volume by 625 units.
Previous sales volume was:
Break-even
$30,000 + $40,000
=
volume (units)
$16
= 4,375 units
Anticipated changes:
In Dollars
New selling price
Variable costs per unit
Contribution margin
$ 25
(12)
$ 13
Previous units sold
Additional units sold
Expected sales volume
In
4,375
625
5,000
Decrease in Sales Price with an
Increase in Sales Volume
Current Situation
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
Income
4,375
$ 122,500
(52,500)
70,000
(30,000)
$ 40,000
Because budgeted
income will fall by
$5,000, the proposal
should be rejected!
Proposed Situation
Units sold
Revenue @ $25
Variable Expenses @ $12
Contribution Margin @$13
Fixed Expenses
Net Income
Income
5,000
$ 125,000
(60,000)
65,000
(30,000)
$ 35,000
Increased in Fixed Costs and
Increase in Sales Volume
After the previous project was rejects, the advertising manager
believes that buying an additional $12,000 in advertising can
increase sales volume to 6,000 units. The contribution margin will
remain at $16. Should the company buy the additional advertising?
Profit = Contribution margin – Fixed cost
Profit = (6,000 × $16) – $42,000 = $54,000
Proposed Situation
Current Situation
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
Income
4,375
$ 122,500
(52,500)
70,000
(30,000)
$ 40,000
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
Income
6,000
$ 168,000
(72,000)
96,000
(42,000)
$ 54,000
Change in Several Variables
Management has been able to reduce variable costs
to $8 per bottle and decides to reduce the selling
price per bottle to $25 (so the contribution margin is
now $17). Further, management believes that if
advertising is cut to $22,000, the company can still
expect sales volume to be 4,200 units.
Should management adopt this plan?
Change in Several Variables
Profit = Contribution margin – Fixed cost
Profit = (4,200 × $17) – $22,000 = $49,400
Proposed Situation
Current Situation
Units sold
Revenue @ $28
Variable Expenses @ $12
Contribution Margin @$16
Fixed Expenses
Net Income
Income
4,375
$ 122,500
(52,500)
70,000
(30,000)
$ 40,000
Units sold
Revenue @ $25
Variable Expenses @ $8
Contribution Margin @$17
Fixed Expenses
Net Income
Income
4,200
$ 105,000
(33,600)
71,400
(22,000)
$ 49,400
Contribution Margin Ratio
The contribution margin ratio is the contribution margin
divided by sales, computed using either total figures or
per unit figures. Here is the total dollar, per unit and
contribution margin (CM) ratio for Bright Day when sales
volume is 5,000 bottles.
Revenue
Variable Expenses
Contribution Margin
Fixed Expenses
Net Income
Total
$ 180,000
(120,000)
60,000
(60,000)
$
-
Per
Unit
$ 36
24
$ 12
CM
Ratio
100.00%
66.67%
33.33%
Contribution Margin
Ratio Approach
= Contribution Margin / Sales
1st – Identify Contribution Margin
$60,000
2nd – Identify Sales
$180,000
= $60,000 / $180,000 = 0.33
What does this Ratio mean?
• Ratio means that every dollar of sales
provides $0.33 to cover Fixed Costs
• After Fixed Costs are covered – Each $1
provides $0.33 of profit
Contribution Margin Ratio
Bright Day is considering the introduction of a new
product called Multi Minerals. Here is some per unit
information about Multi Minerals:
Sales revenue per unit
Variable cost per unit
Contribution margin per unit
$ 20
12
$ 8
100%
60%
40%
Bright Day expects to incur $24,000 in fixed
marketing costs in connection with Multi Minerals.
Let’s look at the calculation of the break-even
point in units and dollars.
Contribution Margin Ratio
Break-even in Units
Break-even in Dollars
Fixed costs
CM per unit
Fixed costs
CM ratio
$24,000
= 3,000 units
$8
$24,000 = $60,000
40%
Contribution Margin Ratio
Break-even in Units
Break-even in Dollars
Fixed costs + Desired profit
CM per unit
Fixed costs + Desired profit
CM ratio
Bright Day desires to earn a profit of $8,000 on the sale
of Multi Minerals
$24,000 + $8,000
= 4,000 units
$8
$24,000 + $8,000
= $80,000
40%
The Equation Method
At the break-even point:
Sales = Variable cost + Fixed cost
We can look at the above equation like this:
Selling price per unit
×
Number of units sold
=
Variable cost per unit
×
Unmber of units sold
+
Fixed cost
The Equation Method
Let’s use our information from Multi Minerals to solve
the equation for the number of units sold.
$ 20 ×
$ 8 ×
Units
Units
Units
=
=
=
$ 12 × Units
$ 24,000
3,000
+
$ 24,000
If we want to consider the desired profit of $8,000 the
solution would be:
$ 20 ×
$ 8 ×
Units
Units
Units
=
=
=
$ 12 × Units
$ 32,000
4,000
+
$ 32,000
Check Yourself
Matrix, Inc. manufactures one model of lawnmower the
sells for $175 each. Variable expenses to produce the
lawnmower are $100 per unit. Total fixed costs are
$225,000 per month, and management wants to
earn a profit in the coming month of $37,500. Use
the equation method to determine how many
lawnmowers Matrix must sell next month:
1. 3,000.
2. 3,500.
3. 4,000.
4. 4,500.
$ 175 × Units =
$ 75 × Units =
Units =
$ 100 × Units + $ 262,500
$ 262,500
3,500
Weighted-Average
Contribution Margin per Unit
In the real world, a company is selling more
than one product
Unit Selling Price
Unit Variable Cost
Unit Fixed Cost
Total Units Sold
Product A
$ 100
40
20
10,000
Product B
$ 200
60
30
20,000
• Step 1: Find the CM for each
– Product A = 100 – 40 = 60/unit
– Product B = 200 – 60 = 140/unit
• Step 2: Find the total # of units sold
– 10,000 + 20,000 = 30,000
• Step 3: Find the % sold of each product
– Product A = 10,000 / 30,000 = 33%
– Product B = 20,000 / 30,000 = 67%
• Step 4: Find the Weighted CM
– Product A = $ 60 * 33% = $19.80 / unit
– Product B = $ 140 * 67% = $93.80 / unit
– Total CM = $19.80 + $93.80 = $113.60 / unit