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. All 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.



C. Breakeven Point (BEP) Methods
1. Equation method
Operating profit = Sales - Total Fixed Costs - Total Variable Costs

(Quantity x Unit Selling 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 selling price - Unit variable cost


Total fixed costs
Breakeven Point in Dollars =
Unit contribution margin %


(Unit Selling Price - Unit Variable Cost) ÷ Unit Selling Price


OR Breakeven Point in Dollars = Breakeven Point in Quantity x Unit Selling Price


Example (2):-
Using the same data in Example (1):


$ 21,000
Breakeven point in Quantity = = 300 units
$ 100 - $ 30

$21,000
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 dollars or as a percentage of sales is required


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


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 Dollars = = $ 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 Dollars =
Weighted Average Contribution Margin


$188,000
Breakeven Point in Dollars = = $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 following 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.

Required: Should Lambers Co. accept this special order??


Solution:
Unit Selling 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

Variable (Direct) Costing Absorption (Full) Costing
1. Concept • An inventory costing method in which only variable manufacturing costs are considered to be product (inventoriable) costs.
• 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. • An inventory costing method in which all manufacturing costs are considered to be product (inventoriable) costs.


2. Product
(Inventoriable)
Costs • Direct Material
• Direct Labor
• Variable Manufacturing Overhead. • Direct Material
• Direct Labor
• Variable Manufacturing Overhead.
• Fixed Manufacturing Overhead.
3. Period Costs • Fixed ManufacturingOverhead.
• Selling and Administrative Costs. • Selling and Administrative Costs.


4. Income
Statement • Classifies Costs by Behavior, i.e., variable and fixed.
• Operating Income and Cost of Goods Sold always move in the same direction as sales volume. • Classifies Costs by Business Function, i.e, manufacturing, selling and administrative.
Operating Income and Costs of Goods Sold may move in the opposite direction from sales.
5. Uses • Inventory Valuation
• Income Measurement
• Relevant Cost (make or buy) analysis.
• Cost - Volume - Profit analysis
• Short - Term Decision Making. • Inventory Valuation
• Income Measurement
6. Acceptability • Acceptable only for Internal Reporting (not GAAP)
• Not Acceptable for External Reporting purposes (tax or S.E.C reporting) because an element of inventory cost is excluded. • Required to be used by Generally Accepted Accounting Principles (GAAP) for external reporting purposes (tax or S.E.C reporting).



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
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




Variable Costing Income Statement
Absorption Costing Income Statement


Sales 1,500


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


Variable Manufacturing Cost of Goods
Available for Sale 600

Less: Ending Inventory (100)


Variable Manufacturing Cost of Goods
Sold 500


Manufacturing Contribution Margin 1,000


Less : Variable Selling (100)


Contribution Margin 900


Less: Fixed Costs
Fixed Overhead (300)
Fixed Selling Expenses (50)


Operating Income 550
Sales 1,500


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


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

Cost of Goods Sold 750


Gross Profit 750


Less: Selling Expenses (150)


Operating Income 600




Notes:-
* The difference in operating income between the two methods is the difference 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 still on hand.


* The contribution margin is the difference between sales and total variable costs.
This term is only used with variable costing.


* The gross profit (margin) is the difference between sales and cost of goods sold.
This term is only used with absorption costing.


























A. Differences between Variable and Absorption Costing when Inventory Changes:
Variable (Direct) Costing Operating Profit
Absorption (Full) Costing
Operating Profit




When Production and Sales are Equal


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


(Ending Inventory
Increase)
Reports Lower Operating Income than Absorption Costing.


Justification
Ending Inventory of the period includes Fixed Costs, which are transferred to the next period under Absorption Costing, thereby reducing the expense of the Current Period.
Reports Higher Operating Income than Variable Costing.


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


(Ending Inventory
Decreased)
Reports Higher Operating Income than Absorption Costing.


Justification
Beginning Inventory of the period includes Fixed Costs, from the prior period under Absorption Costing, therefore, the cost expensed during period are greater under Absorption Costing.
Reports Lower Operating Income than Variable Costing.


Justification
Beginning Inventory of the period includes Fixed Costs, from the prior period under Absorption Costing, therefore, the cost expensed during period are greater under Absorption Costing.
Shortcut
If Production = Sales, Variable Operating Income = Absorption Operating Income
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


(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. Uncontrollable 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 still 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 .




































III. Cost Classifications
Classification of costs is necessary inorder to determine the most suitable method of
accumulating and allocating costs. The principle methods of accumulating costs are
described below.
a) Classification by Nature
b) Classification by Variability
c) Classification by Department
d) Classification by Inventoriable
e) Classification by Period Covered
f) Classification by Controllability


A) Classification by Nature
1. Manufacturing Costs
Cost associated with the manufacturing activities which include:
a. Direct Materials
The costs of raw materials that can feasibly be traced to a particular product or job.
Examples include wood used in making furniture and iron used in making steel.
b. Direct Labor
The costs of wages paid to labor that can feasibly be traced to a particular product or jobs.
Examples include wages to workers who assemble furniture or operate melting machine.
c. Factory (Manufacturing) Overhead
All manufacturing costs other than direct materials and direct labor. It includes both fixed and variable costs.
Examples include indirect materials (supplies), indirect labor, repairs and maintenance on machinery, taxes, factory utilities, rent of factory building, insurance, and depreciation on factory equipment and plant.




Other Costs Concepts
* Direct Costs: Costs that can be identified with or traced to a specific cost object
(product, service, or activity). Examples include direct materials and direct labor.
* Indirect Costs: Costs that can not be identified with or traced to a specific cost object
(product, service, or activity). Examples include factory overhead.


2. Nonmanufacturing Costs
All Costs that are not related to the manufacturing activities such as:
* Administrative and office (management) salaries.
* Sales personnel salaries and commissions.
* Advertising
* Freight - out Expense
* Depreciation on management building
* Legal Expenses
* Other selling and administrative Expenses

B) Classification by Variability
1. Variable Costs
* Costs that change in total, directly in proportion to changes in the level of
activities (volume).
* The unit cost remains the same over a wide range of volume
(referred to as the relevant range).
* Relevant Range is the range of activity (production volume) within which variable
unit costs are constant and fixed costs are constant and fixed costs are constant
in total. In this range, the incremental cost of one additional unit of production is
the same.
* Examples include direct materials, direct labor, and part of manufacturing
overhead.


2. Fixed Costs
* Costs that do not change in total regardless of changes in activity.
* The unit cost decreases as volume increases.
* Examples include rent, taxes, and insurance on manufacturing plant.


3. Semivariable (Mixed) Costs
* Costs that contain both variable and fixed costs.
* Examples include: light, heat, and power.


C) Classification by Department
1. Production
* A unit in which operations are performed on a product.
* Example: manufacturing department.


2. Service
* A unit not directly engaged in production and whose costs are ultimately allocated to
a production unit.
* Examples include: maintenance and personnel department.




D) Classification by Inventoriability
1. Inventoriable (product) costs
* Inventoriable (product) costs are included in inventory when the product is produced
and in cost of sales when the product is sold.
* It includes: direct materials, direct labor, and manufacturing overhead.


2. Noninventoriable (Period) Costs
* Costs associated with the passage of time rather than with the product.
* These costs are not inventoried and are charged to income as incurred since no
future benefits are expected.
* Examples include: selling, general, and administrative expenses.


E) Classification by Period Covered
1. Capital Costs
Costs that are expected to benefit future periods and are classified as assets.
2. Revenue Costs
Costs that benefit only the current period and are thus expensed as incurred.


F) Classification by Controllability
1. Controllable Costs
* Costs that directly regulated by management at a given level of production within a
given time span.
* All variable costs such as direct materials, direct labor, and variable overhead, are
usually controllable.
* Fixed costs are not usually controllable.

2. Noncontrollable Costs
* Costs that are not regulated by management at a given level of production within a
given time span.
* All fixed costs are usually not controllable.


IV. Other Costing Concepts
A. Practical Capacity
* The maximum level at which output is produced efficiently.
* Allows for unavoidable delays in production for maintenance, holidays, etc.

B. Theoretical (Ideal) Capacity
* The maximum capacity assuming continuous operations with no holiday, downtime, etc


C. Sunk Cost
* Is a past or historical cost that the entity has irrevocably committed to incur.
* Because it is unavoidable and will therefore not vary with the option chosen, it is not
relevant to future decisions.
* Examples include: research and development costs and fixed assets costs.


D. Opportunity Cost
* Is the maximum benefit foregone by rejecting an alternative.


E. Relevant Costs
* Are those expected future costs that vary between alternatives.
* Examples include: direct materials, direct labor, variable manufacturing overhead,
and variable selling and administrative costs.
* Fixed costs and sunk cost are considered irrelevant to decision making.