Cost - Volume - Profit (Break - Even) Analysis

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I. Cost - Volume - Profit (Break - Even) Analysis
A.
Definitions
1. Cost - Volume - Profit (CVP) Analysis: is a means of predicting the relationships
among revenues, variable costs, and fixed costs at various production levels.
It allows management to discern the probable effects of changes in sales volume,
sales price, product mix.

2. Breakeven Point: is the level of sales at which total revenues equal total costs.
No profit or loss at the breakeven point, i.e., operating income is Zero.

3.
Fixed Costs: remain unchanged over short periods regardless of changes in
volume. However, per-unit fixed costs varies directly with the activity level.
4.
Variable Costs: vary directly and proportionally with changes in volume. However,
the variable cost per unit remains constant.
5.
Relevant Range: is the range of activity over which cost relationships are valid, i.e.,
It establishes limits within which the cost and revenue relationships remain linear and fixed
costs are fixed.
6.
Margin of Safety: is the excess of budgeted sales dollars over breakeven sales
Dollars (or budgeted units over breakeven units)

7.
Sales Mix: is the composition of total sales in terms of various products, i.e., the
percentages of each product included in total sales.
8.
Unit Contribution Margin (UCM) (Target Profit): is the unit selling price minus the
unit variable cost. It is the contribution from the sale of one unit to cover fixed costs.
9.
Contribution Margin Ratio: is the unit contribution margin divided by the
unit-selling price.

10.
The Slope of a Line: (on a graph with the X Axis as volume and the Y Axis as $)
equals the contribution margin per unit of volume.
B.
Assumptions of CVP Analysis
1.
Costs and revenues are predictable and are linear over the relevant range.
2.
Al costs can be classified as either fixed or variable.
3.
Total variable costs change proportionally with activity level
4.
Unit variable costs are unchanged (fixed) .
5.
Fixed costs remain constant over the relevant range volume.
6.
Selling prices remain unchanged.
7.
Inventory is either zero or kept constant, i.e., production equal sales.
8.
There is only one product or product mix is constant.
9.
A relevant range exists in which the various relationships are true for a given time span.
10.
Sales volume is the only relevant factor affecting cost.
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C.
Breakeven Point (BEP) Methods
1. Equation method
Operating profit = Sales - Total Fixed Costs - Total Variable Costs
(Quantity x Unit Sel ing Price) (Quantity x Unit Variable Cost)

Because at the breakeven point operating profit is zero, the equation can be as follows:

Sales = Total Fixed Costs + Total Variable Costs

Example (1) :-
Lambers manufacturing company sells T- shirts at $100 per unit .The variable cost is

$30 per unit and total fixed are $ 21,000 . Required : What is the breakeven point ?

Solution
U = Units of Production = Sales

$100 U = $ 21,000 + $ 30 U

$ 70 U = $ 21,000

U = 300 units

This means that to cover $ 21,000 of fixed costs, 300 units must be sold to break even.

2. Contribution margin method Total fixed costs Total fixed costs

Breakeven Point in Quantity =

Unit contribution margin Unit sel ing price - Unit variable cost

Total fixed costs

Breakeven Point in Dollars =

Unit contribution margin %

(Unit Sel ing Price - Unit Variable Cost) ÷ Unit Sel ing Price

OR Breakeven Point in Dollars = Breakeven Point in Quantity x Unit Sel ing Price
Example (2):-
Using the same data in Example (1):

$ 21,000
Breakeven point in Quantity =
= 300 units

$ 100 - $ 30

$21,000
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Breakeven point in Dollars =
= $ 30,000

70%
OR
= 300 units x $ 100 = $ 30,000

3. Chart method
Total Revenue
$ Revenue (Y)

Breakeven Point Profit Area Total Cost
Variable Cost

Loss Area

Fixed Cost
Units (X)
If an amount of profit, either in dol ars or as a percentage of sales is required

Total Fixed Costs + Target Profit Before Tax
Target sales in Quantity (Units) =

Unit Sel ing Price - Unit Variable Cost

Total Fixed Costs + Target Profit Before Tax
Target sales in Dollars =

Unit Contribution Margin %
Target Profit After Tax = Target Profit After Tax / (1- Tax Rate)
Margin of Safety (in units or $ ) is the excess of actual or budgeted sales over sales at
the break - even point. It reveals the amount by which sales could decrease before losses
occur.
Margin of Safety (in units or $) = Target Sales Level (in units or $) - BEP (in units or $)

Target Sales
Margin of Safety Percentage =

Target Sales - Breakeven Point

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Example (3):-
Using the same data in example (1) plus the company wishes to achieve $ 7,000 before
tax profit .

$ 21,000 + $ 7,000

Target sales in Quantity = = 400 units
$ 100 - $ 30

$ 21,0000 + $ 7,000

Target Sales in Dol ars = = $ 40,000

70%

Note
If the desired profit were stated in total dollars ($ 7,000 above) , it would be treated as
a fixed cost ,and if the desired profit were stated in percentage , it would be treated as
a variable cost.

If multiple products are involved in calculating a breakeven point.
Example (4):-
If Y and Z account for 70% and 30% of total sales, respectively, and variable costs are
50% and 60%, respectively, what is the breakeven point, given fixed costs of $188,000?

Total Fixed Costs

Breakeven Point in Dol ars =

Weighted Average Contribution Margin

$188,000

Breakeven Point in Dol ars = = $400,000
(.50 x .7) + (.4 x .3)

Y = 400,000 x 70 % = 28,000
Z = 400,000 x 30 % = 120,000
III. Relevant Costs
•
Costs are relevant if they affect a decision.
•
Variable costs are relevant within the relevant range.
•
Fixed costs are irrelevant within the relevant range.

Example:
Lambers Company operates at 90 % of plant capacity, producing 90,000 units of product.

The total cost of manufacturing 90,000 units is $76,500 (variable costs = $49,500,

fixed cost = $27,000), resulting in a cost per unit of $ .85

Recently, a large customer, who purchases 15,000 units per year, canceled his orders for

the fol owing year. Rather than operate at 75 % of capacity, the company is seeking new

customers. A potential customer, Buy - More Co. has offered to purchase 20,000 units at

$ .65 per unit.
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Required: Should Lambers Co. accept this special order??

Solution:
Unit Sel ing Price $.65

Less: Unit Variable Cost $.55 ($49,500 ÷ 90,000)

Unit Contribution Margin $.10

Yes, Lambers Co. should accept this special order because it makes a contribution to the

recovery of fixed cost and profit.

1I. Direct Costing And Absorption Costing
Variable (Direct) Versus Absorption (Full) Costing
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Variable (Direct) Costing
Absorption (Ful ) Costing
An inventory costing method in
An inventory costing method
which only variable manufacturing
in which all manufacturing costs
costs are considered to be product
are considered to be product
(inventoriable) costs.
(inventoriable) costs.
1. Concept
Fixed Manufacturing Costs are

considered to be period costs
(expensed as incurred) because
they would have been incurred
even if there had been no
production.
Direct Material
Direct Material
2. Product
Direct Labor
Direct Labor
(Inventoriable)
Variable Manufacturing
Variable Manufacturing
Overhead.
Overhead.
Costs
Fixed Manufacturing
Overhead.
Fixed ManufacturingOverhead.
Sel ing and Administrative
3. Period Costs
Sel ing and Administrative
Costs.
Costs.

Classifies Costs by Behavior,
Classifies Costs by Business
i.e., variable and fixed.
Function, i.e, manufacturing,
4. Income
Operating Income and Cost of
selling and administrative.
Statement
Goods Sold always move in the
Operating Income and Costs of
same direction as sales volume.
Goods Sold may move in the opposite
direction from sales.
Inventory Valuation
Inventory Valuation
Income Measurement
Income Measurement
5. Uses
Relevant Cost (make or buy)

analysis.
Cost - Volume - Profit analysis
Short - Term Decision Making.
Acceptable only for Internal
Required to be used by
Reporting (not GAAP)
Generally Accepted Accounting
6. Acceptability
Not Acceptable for External
Principles (GAAP) for external
Reporting purposes (tax or S.E.C
reporting purposes (tax or S.E.C
reporting) because an element of
reporting).
inventory cost is excluded.

Example: Assume that Lambers Company, during its first month in business, produced 300 units of
product Y and sold 250 units at $ 6 each while incurring the following costs:

Direct Materials $ 150
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Direct Labor 250

Variable Overhead 200

Fixed Overhead 300

Total Manufacturing Costs $ 900

Variable Selling and Administrative Expenses $ 100

Fixed Selling and Administrative Expenses $ 50
Required: Prepare the income statement under both variable and absorption methods.

Solution:-
1)
Under Variable Costing method
* Unit Cost is $ 2 ($ 600 ÷ 300 units).
* Ending Inventory Cost is $ 100 (50 units x $ 2).

2)
Under Absorption Costing method
* Unit Cost is $ 3 ($ 900 ÷ 300 units).
* Fixed Manufacturing Overhead per unit is $ 1 ($300 ÷ 300 units)
* Ending Inventory Cost is $ 150 (50 units x $ 3).

Income Statement under the Two Costing Methods
Absorption Costing Income Statement
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Variable Costing Income Statement

Sales 1,500 Sales 1,500

Variable Cost of Goods Sold
Cost of Goods Sold
Beginning Inventory $ 0
Beginning Inventory $ 0
Variable Cost of Goods Manufactured 600
Cost of Goods Manufactured 900


Variable Manufacturing Cost of Goods
Cost of Goods Available for Sale 900
Available for Sale 600
Less: Ending Inventory (150)

Less: Ending Inventory (100)
Cost of Goods Sold 750

Variable Manufacturing Cost of Goods

Sold 500
Gross Profit 750
Manufacturing Contribution Margin 1,000 Less: Seling Expenses (150)


Less : Variable Selling (100)
O p
er
at i n g I n come 600
Contribution Margin 900

Less: Fixed Costs
Fixed Overhead (300)

Fixed Selling Expenses (50)
Operating Income 550
Notes:-
* The difference in operating income between the two methods is the dif erence in

ending inventory values. $ 50 ($150 - $100) which is the fixed overhead costs that

have been capitalized as an asset (inventory) because under absorption costing 50

units (300 - 250) of the month's production is stil on hand.

* The contribution margin is the dif erence between sales and total variable costs.
This term is only used with variable costing.
* The gross profit (margin) is the dif erence between sales and cost of goods sold.
This term is only used with absorption costing.

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A. Differences between Variable and Absorption Costing when Inventory
Changes:

Variable (Direct) Costing
Absorption (Full) Costing
Operating Profit
Operating Profit

When Production
and Sales are Equal
Operating Income is the Same in Both Methods
(No Changing in
Inventory)


Reports Lower Operating Income
Reports Higher Operating Income
than Absorption Costing.
than Variable Costing.
When Production


Exceeds Sales
Justification
Justification

Ending Inventory of the period
Ending Inventory of the period
(Ending Inventory
includes Fixed Costs, which are
includes Fixed Costs, which are
Increase)
transferred to the next period under transferred to the next period under
Absorption Costing, thereby
Absorption Costing, thereby
reducing the expense of the Current reducing the expense of the Current
Period.
Period.
When Sales Exceeds

Production
Reports Higher Operating Income
Reports Lower Operating Income
than Absorption Costing.
than Variable Costing.

(Ending Inventory


Justification
Justification
Decreased)
Beginning Inventory of the period
Beginning Inventory of the period
includes Fixed Costs, from the prior includes Fixed Costs, from the prior
period under Absorption Costing,
period under Absorption Costing,
therefore, the cost expensed during therefore, the cost expensed during
period are greater under Absorption period are greater under Absorption
Costing.
Costing.

If Production = Sales, Variable Operating Income = Absorption Operating Income
Shortcut
If Production > Sales, Variable Operating Income < Absorption Operating Income
If Production < Sales, Variable Operating Income > Absorption Operating Income

Differences in Operating Income between Variable and Absorption Costing =
Change in Inventory Quantity x Fixed Overhead per Unit

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(Ending Inventory - Beginning Inventory) (Total Fixed Overhead ÷ Units Produced)
IX. Spoilage, Reworked units, Scrab, And Waste A. Spoilage
Two types of spoilage
1.Normal Spoilage
a.
Spoilage that occurs under normal, efficient operating conditions .
b.
Uncontrol able in the short - run .
c.
Treated as a product cost and therefore should be included as apart of costs goods
manufactured .

2. Abnormal Spoilage
a.
Spoilage that is not expected to occur under normal, efficient operating conditions.
b.
Treated as a period cost (a loss) because of its unusual nature .
B. Reworked units
1.
Unacceptable units that are subsequently reworked and sold.
2.
Should be undertaken if it is expected that incremental revenues exceed incremental
costs.
3.
The cost of extra materials and labor are usually changed to factory overhead .
C. Scrap
1. Raw materials left over from the production cycle but stil useable for different
production process.
2. Process from sale of scrape are accounted for as follows :
•
Additional income, or
•
Reduce cost of sales, or
•
Reduce manufacturing overhead
D. Waste
1.Raw materials left over from the production that have no other production use .
2. Usually not salable at any price and must be discard .

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