CHAPTER ONE

Cost-Volume-Profit Analysis, Absorption, and Variable Costing

Learning Objectives
1. Describe the difference between Absorption and Direct Costing.
2. Describe the assumptions of CVP
3. Determine the breakeven point, contribution margin and margin of safety and output
level needed to achieve a target operating income
4. Explain role of CVP analysis in decision making
5. Illustrate CVP application for multiple products
Absorption versus Direct Costing.
Two general approaches are used for costing products for the purposes of vaulting inventory and
cost of goods sold.
The first approach is absorption costing generally used for external financial reports. Other
approach is variable costing generally used for internal report purpose and income statement
is prepared on contribution approach.

The difference b/n those two approaches is on the income statement that is on the net income.
a) Absorption costing treats of all cost of production as product costs, regardless of whether
they are variable or fixed in nature. The computation of unit product under this costing is
includes direct material, direct labor, and both variable and fixed F.O.H.
Absorption cost allocates a portion of fixed .O.H. to each unit product because in this method they
include all costs of production as product cost, this method in referred to full cost method. In the
absorption costing, all F.O.H. is product cost; it makes no difference whether manufacturing
cost is variable and fixed. They argue that fixed F.O.H. such as deprecation and insurance are
essential in production process and cannot be ignored in costing unit of product. They also argued
that to be fully costed, each unit of product must bear an equitable portion of all manufacturing
cost. Since absorption costing treats fixed manufacturing overhead as a product cost, a portion
fixed H.O is assigned to each unit as it is produced. If the units of product are unsold at the end of
the period, then the F.H.O cost attached to the unit is carried with them in to the inventory account
and deferred to the next period. When these units are sold during the next period, the F.O.H cost
attached to them is released from the inventory account and charged against revenue as part of
CGS. Thus, under absorption costing, it is possible to defer a portion of the F.H.O cost of one
period to the next period through inventory account.
Variable costing – only those production costs that vary with output are treated as product
costs. This includes direct materials, direct labors, and variable overhead. F.O.H cost is treated
as period cost and charged off against revenue as it is incurred, the same as selling
and administrative expenses. Cost of unit of product in inventory or in CGS under variable
costing method contains no element of fixed overhead cost. Variable costing sometime
referred as direct
Costing or Marginal costing. Variable costing is used for the internal reporting purposes.
The selling and administrative expenses are periodic cost under both approach and deduct from
revenue to get net income. Variable costing argue that the F.O.H cost relates to the capacity to
produce rather than the actual production of unit of product in a given year. For example Facilities
and equipment, insurance, supervisor salary and other represent cost of being ready to produce and
therefore will be incurred and treated as periodic cost along with selling and administration cost.
Variable costing used the concept of cost behavior and cost volume profit analysis.
Summary cost classification under absorption and variable costing.
Absorption costing Variable costing
Direct material
Product cost Direct labor Product cost
Variable overhead
Fixed overhead
Periodic cost Selling and administrative expenses Periodic cost
Computation of product cost under both approaches
Example: - The following dates are for XYZ manufacturing company.
Given
Units in banging inventory 0
Units produced 6,000
Units sold 5,000
Unit selling price Br. 20
Variable cost per unit
Direct material Br. 2
Direct labour Br. 4
Variable overhead Br.1
 Variable selling and Adm Expn/ Br. 3
Fixed cost per year
Fixed selling and administrative Br. 10,000
Fixed overhead Br. 30,000

Required
i. Determine product cost under Absorption and variable costing?
ii. Prepare a statement of profit and loss in both approach?
Solution
Absorption costing product cost
Direct material…...................................................Br. 2
Direct labor…………………………………….Br. 4
Variable overhead……………………………….Br.
1 Total variable production cost Br. 7
Fixed. O.H ($ 30,000 / 6,000 unit of product) 5
Unit production cost ……………………….…Br. 12

Variable costing product cost

Direct material…......................................Br. 2
Direct labour…………………………….Br. 4
Variable overhead……………………….Br. 1
Total variable production cost Br. 7
Statement of profit and loss under both approaches.
Absorption costing
Sales (5000 unit*Br. 20)……………………………………………..……….Br. 100,000
Less Cost of goods sold
Beginning inventory………………………………….….Br. 0
Cost of goods manufactured (6000 unit * Br.12) Br.72, 000
Good available for sales……………………………….....Br.
72,000
Less Ending inventory (1000 * Br.12)…......................................(Br.12,000)
Cost of goods sold (Br. 60,000)
Gross margin Br. 40,000
Less selling and adm. Exp (5000 unit x $ 3 variable + 10,000 Fixed) (Br. 25,000)
Net income………………...………………………………………………….Br. 15,000
Variable costing:-
Sales (5000 unit * Br. 20)…..................................................................................100,000
Less cost of goods sold (variable)
Beginning inventory …….…………………………………….Br.
0 Variable manufacturing cost (6000 * Br. 7)…………………...Br.
42,000 Good available for
sales………………………………………..Br. 42,000
Less ending inventory (1000 unit * Br. 7)…......................................(Br. 7000)
Cost of goods sold………………………………………………Br. 35,000
Less variable selling and Adm Expn/ (5000 * 3)…..............................Br. 15,000
Contribution margin………………..Br. 50,000 L e s s fixed expenses
Fixed O.H cost...................................................................................(Br. 30,000)
Fixed selling and Administrative Expenses.....................................(Br. 10,000)
Net income........................................................................................(Br. 10,000)
Note: - The difference in ending inventory, fixed O.H. cost at $ 5 per unit is included under the
Absorption approach. This explains the difference in ending inventory and in net income (1000
units x $ 5 = $ 5000).
Cost behavior and patterns
Cost behavior refers to how a certain cost will behave in response to a change in the level of activity.
level of activity is units produced, units sold, miles driven, beds occupied and hours worked, etc
Variable cost:
A variable cost is a cost that varies, in total, in direct proportion to changes in the level of activity.
Direct material is a good example of a variable cost. The variable cost is constant if expressed on a
per unit basis.
Fixed cost
A fixed cost is a cost that remains constant, in total, regardless of changes in the level of activity.
Rent is a good example of fixed cost. Average fixed cost per unit increases and decreases inversely
with changes in activity.
 Mixed/Semi Variable Cost
A mixed cost contains both variable and fixed cost elements together. Mixed cost is also known as
semi-variable cost. Examples of mixed costs include electricity and telephone bills

Cost-volume-profit (CVP) analysis

Cost-volume-profit (CVP) analysis is a technique that examines changes in profits in response to
changes in sales volumes, costs, and prices. Accountants often perform CVP analysis to plan future
levels of operating activity and provide information about:
🖙 which products or services to emphasize
🖙 the volume of sales needed to achieve a targeted level of profit
🖙 the amount of revenue required to avoid losses
🖙 Whether to increase fixed costs
🖙 Whether fixed costs expose the organization to an unacceptable level of risk
Assumptions
The conditions which are assumed to apply when CVP analysis is used are presented below.
1. Sales prices, unit variable costs, and total fixed expenses will not vary within the relevant
range. This assumption suggests that volume is the only factor/or cost driver that can cause
cost and profits to change.
2. The sales mix remains unchanged during the period. CVP analysis only applies where
one product is being examined or if there are several products then the sales proportions or
combination sold will remain constant as the level of total units sold changes.
3. Total costs and total revenue are linear functions. This assumption suggests that when we
put in a graph, the behavior of total revenue and cost is linear (straight line), i.e. Y = a + bX
holds good which is the equation of a straight line.
4. Profits are calculated using variable costing. Variable costing facilitates profit analysis as
it separates variable and fixed costs and treats fixed costs as a period expense rather than
attempting to allocate them to products.
5. Expenses/or costs can be classified as either variable or fixed.
A. Variable Cost
These costs tend to vary with the volume of activity. Any increase in activity results
in an increase in the variable cost and vice versa.
 For example: Cost of direct labor, direct material, etc
B. Fixed Cost Costs which tend to be unaffected by fluctuations in the levels of activity
(Output). For example: Rent, insurance of factory building etc. remain the same for
different levels of production.

Limitations of Cost-Volume-Profit Analysis

The CVP analysis is generally made under certain limitations and with certain assumed
conditions, some of which may not occur in practice. The following are the main limitations and
assumptions in the cost-volume-profit analysis:
1. It is assumed that the production facilities anticipated for cost-volume-
profit analysis do not undergo any change. Such analysis gives misleading results if
expansion or reduction of capacity takes place.
2. In cases where a variety of products with varying margins of profit are manufactured, it is
difficult to forecast with reasonable accuracy the volume of sales mix which would
optimize the profit.
3. The analysis will be correct only if t h e input price and selling price remain fairly
constant
which in reality is difficult to find. Thus, if a cost reduction program is undertaken or the
selling price is changed, the relationship between cost and profit will not be accurately
depicted.
4. In cost-volume-profit analysis, it is assumed that variable costs are perfectly and
Completely variable at all levels of activity and fixed costs remains constant throughout
the range of volume being considered. However, such situations may not arise in
practical situations.
5. It is assumed that the changes in beginning and ending inventories are not significant,
though sometimes they may be significant.
6. Inventories are valued at variable cost and fixed cost is treated as period cost. Therefore, ending
inventory carried over to the next financial year does not contain any component of fixed cost.
Inventory should be valued at full cost in reality.
Approaches of CVP Analysis
There are three approaches of CVP Analysis,
 1. Equation method
2. Contribution method
3. Graphic method
1. Using Equation method
It is the most general form of break-even analysis that may be adapted to any conceivable cost-
volume-profit situation. This approach is based on the profit equation. Income (or profit) is equal to
sales revenue minus expenses.
Profit = Total revenue -Total costs
By separating costs into variable and fixed categories, we express profit
as: Profit = Total revenue - Total variable costs - Total fixed costs
If we assume that the selling price and variable cost per unit are constant, then total revenue is
equal to price times quantity, and total variable cost is the variable cost per unit time’s quantity.
We then rewrite the profit equation in terms of the contribution margin per unit.
Profit = P * Q - V * Q - F
= (P - V) * Q - F
Where P = Selling price per unit
V = Variable cost per unit
(P - V) = Contribution margin per unit
Q = Quantity of product sold (units of goods or
services) F = Total fixed costs
We use the profit equation to plan for different volumes of operations. CVP analysis can be
performed using either:
Units (quantity) of product sold
Revenues (in dollars)
CVP Analysis in Units
We begin with the preceding profit equation. Assuming that fixed costs remain constant, we
solve for the expected quantity of goods or services that must be sold to achieve a target level of
profit.
Profit equation: Profit = (P - V) * Q - F
Solving for Q: Q = F + Profit
(P- V)
  Q = Quantity (units) required to obtain target profit
 Notice that the denominator in this formula, (P - V), is the contribution margin per unit.
CVP Analysis in Revenues
To analyze CVP in terms of total revenue instead of units, we can obtain the revenue amount by
multiplying the number of units sold times unit price
I.e. Q*SP
Breakeven point
When we at Break Even, our Sales Revenue minus our Total Costs are zero i.e. Breakeven point
is a point where profit becomes zero:
 Sales Revenue – Total Costs = 0
Therefore, If we move our Total Costs to the other side of the equation, we see that our Sales
Revenue equals our Total Costs when we at Break Even:
Sales Revenue = Total Costs
Now, solve for the number of units produced and sold (Q) that satisfies this relationship:
Revenue = Total Costs
PQ = VQ + F
PQ – VQ = F
Q (P - V) = F
Q= F
(P -V)
Example #01
Suppose that ABC Company wants to produce a new mountain bike and has forecast the
following information.
Price per bike =Br. 800
Variable cost per bike = Br. 300
Fixed costs related to bike production = Br. 5,500,000
Target profit =Br. 200,000
Estimated sales = 12,000 bikes
Required: Calculate
1. BEP
i. In units
ii. In dollar amount
 2. Quantity of bikes needed for the target profit
a) In units
b) In dollar amount
A solution to the above question
BEP in Units: To determine the number of bikes needed for breakeven in units as follows:
Q at BEP = F
(P -
V) Q = Br.
5,500,000
(800 -300)
11,000 bikes
BEP in dollar amount: To determine the number of bikes needed for breakeven in dollar
amount use the following formula:
Therefore, BEP in Revenue = Q@BEP X USP
11,000 X 800 = 8,800,000
2 Quantity of bikes needed for the target profit
Using the data from example #01, we find the volume that provides an operating profit of Br.
200,000 as follows:
𝑭𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕𝒔 + 𝑻𝒂𝒓𝒈𝒆𝒕 𝒑𝒓𝒐𝒇𝒊𝒕

𝒑𝒓𝒊𝒄𝒆−𝒖𝒏𝒊𝒕 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆 𝒄𝒐𝒔𝒕

Target volume (units) =

𝑩𝒓.𝟓,𝟎𝟎,𝟎𝟎𝟎 + 𝑩𝒓.𝟐𝟎𝟎,𝟎𝟎𝟎
Target volume (units) =

𝟖𝟎𝟎−𝟑𝟎𝟎
= 11,400 bikes

𝑭c + 𝑻𝒂𝒓𝒈𝒆𝒕
Target volume

𝒑𝒓𝒐𝒇𝒊𝒕
(Birr) =

𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒎𝒂𝒓𝒈𝒊𝒏 𝑹𝒂𝒕𝒊𝒐

𝑩𝒓.𝟓,𝟎𝟎,𝟎𝟎𝟎 + 𝟐𝟎𝟎,𝟎𝟎𝟎
Target volume (Birr) =
 𝟎.𝟔𝟐𝟓
= Br. 9,120,000
Target volume= quantity *price
=11,400*800
=Br 9,120,000
2. Using contribution margin method
This second approach uses a little bit of algebra to rewrite our equation above, concentrating on the
use of the ‘contribution margin’. The contribution margin is total revenue minus total variable
costs. Similarly, the contribution margin per unit is the selling price per unit minus the variable
cost per unit. Both contribution margin and contribution margin per unit are valuable tools when
considering the effects of volume on profit. Contribution margin per unit tells us how
much revenue from each unit sold can be applied toward fixed costs. Once enough units have been
sold to cover all fixed costs, then the contribution margin per unit from all remaining sales
becomes profit.
Therefore, (USP x Q) – (UVC x Q) – FC = P
Q x (USP – UVC) = FC + P
Q x UCM = FC + P
𝐂+𝐏
Quantity required = UCM= p-uc
𝐔𝐂𝐌
So, if P=0 (because we want to find the break-even point), we would simply divide our fixed
costs by our unit contribution margin. We often see the unit contribution margin referred to as
the ‘contribution per unit’.
𝐅𝐂
i.e. BEP in Quantity =
𝐔𝐂𝐌
Computation of Breakeven point in unit using contribution approach
 In order to calculate the BEP in contribution approach from the above example
𝐫.𝟓,𝟓𝟎𝟎,𝟎𝟎𝟎
BEP in Quantity =
𝟓𝟎𝟎
11,000 bikes
The contribution margin ratio (CMR) is the percent by which the selling price (or revenue)
per unit exceeds the variable cost per unit, or contribution margin as a percent of revenue. For a
single product, it is
CMR = P -V
P
To analyze CVP in terms of total revenue instead of units, we substitute the contribution margin
ratio for the contribution margin per unit. We rewrite the equation to solve for the total dollar
amount of revenue we need to cover fixed costs and achieve our target profit as
Revenue= F CMR = P -V
CMR P
Applying this approach to the above example again:
To solve for the new mountain bikes revenues needed for BEP, we first calculate the contribution
margin ratio as follows:
𝑷−𝑼𝑽𝑪
CMR% =

𝑷
=8000-300 = 0.625/or 62.5%, FC =5,500,000 and P = 0.
,𝟓𝟎𝟎,𝟎𝟎𝟎 + 𝟎
800 Breakeven point (in Birr) =
𝟔𝟐.𝟓%
= Br. 8,800,000
A contribution margin ratio of 0.625 means that 62.5% of the revenue from each bike sold
contributes first to fixed costs and then to profit after fixed costs are covered.
NB: The contribution margin ratio can also be written in terms of total revenues (TR) and total
variable costs (TVC). That is, for a single product, the CMR is the same whether we compute it
using per-unit selling price and variable cost or using total revenues and total variable costs.
Thus, we can create the following mathematically equivalent version of the CVP formula.
3. Using graphical method
With the graphical method, the total costs and total revenue lines are plotted on a graph; the
amount in Dollar or Birr is shown on the y axis and units are shown on the x axis. The point
where the total cost and revenue lines intersect is the break-even point. The amount of profit or
loss at different output levels is represented by the distance between the total cost and total
revenue lines. The gap between the fixed costs and the total costs line represents variable costs
and the variable cost line and the total cost line that represents fixed costs

Total Revenue Total Variable Cost

Operating Profit Total Cost Line

Fixed Cost Line

8,800,000 Operating Loss Breakeven Point

11,000 Units
Margin of Safety (MOS)
The margin of safety is the excess of an organization’s expected future sales (in either revenue or
units) above the breakeven point. The margin of safety indicates the amount by which sales
could drop before profits reach the breakeven point:
 It is calculated as the difference between sales or production units at the selected activity and the
breakeven sales or production.
Margin of safety is the difference between the total sales (actual or projected) and the breakeven
sales. It may be expressed in monetary terms (value) or as a number of units (volume). It can be
expressed as profit / CM %. A large margin of safety indicates the soundness and financial
strength of business.
Margin of safety can be improved by lowering fixed and variable costs, increasing volume of
sales or selling price and changing product mix, so as to improve contribution and overall CM %.
Margin of safety = Sales at selected activity – Sales at BEP = Profit at selected
Activity
CM %
Margin of safety is also presented in ratio or Margin of safety (sales) x 100 %
percentage as : = Sales at selected activity

The size of margin of safety is an extremely valuable guide to the strength of a business. If it is large,
there can be substantial falling of sales and yet a profit can be made. On the other hand, if margin is
small, any loss of sales may be a serious matter. If margin of safety is unsatisfactory, possible steps
to rectify the causes of mismanagement of commercial activities as listed below can be undertaken.
 Increasing the selling price-- It may be possible for a company to have higher margin of
safety in order to strengthen the financial health of the business. It should be able to
influence price, provided the demand is elastic. Otherwise, the same quantity will not be
sold.
 Reducing fixed costs
 Reducing variable costs
 Substitution of existing product(s) by more profitable lines e. Increase in the volume of
output
 Modernization of production facilities and the introduction of the most cost effective
technology.
Example#02
A company earned a profit of Br. 30, 000 during the year 2000-01. Variable cost and selling
price of a product are Br. 8 and B. 10 per unit respectively. Find out the margin of safety.
Solution
 Profit
Margin of safety = CM %

CM % = (UCM) Contribution in total x 100

(USP) Sales in total

Example#2
A company producing a single article sells it at Br. 10 each. The marginal cost of production is
Br. 6 each and fixed cost is Br. 400 per annum. You are required to calculate the following:
a) Profits for annual sales of 1 unit, 50 units, 100 units and 400 units
b) CM%
c) Breakeven sales
d) Sales to earn a profit of Br. 500
e) Profit at sales of Br. 3,000
f) New breakeven point if sales price is reduced by 10%
g) Margin of safety at sales of 400 units
Targeted income
CVP analysis is also used when a company is trying to determine what level of sales is necessary
to reach a specific level of income, also called targeted income. To calculate the required sales
level, the targeted income is added to fixed costs, and the total is divided by the contribution
margin ratio to determine required sales dollars, or the total is divided by contribution margin per
unit to determine the required sales level in units.
 Target Volume in Units: To find the target volume, we use the profit equation with the
target profit specified. The formula to find the target volume in units is

𝑭𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕𝒔 + 𝑻𝒂𝒓𝒈𝒆𝒕 𝒑𝒓𝒐𝒇𝒊𝒕

Target volume (units) =

𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒎𝒂𝒓𝒈𝒊𝒏 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕

Using the data from example #01, we find the volume that provides an operating profit of
Br.200, 000 as follows:
𝑩𝒓.𝟓,𝟎𝟎,𝟎𝟎𝟎 + 𝑩𝒓.𝟐𝟎𝟎,𝟎𝟎𝟎
Target volume (units) =

𝟓𝟎𝟎
 = 11,400 bikes
 Target Volume in Sales Dollars: To find the target volume in sales dollars, we use the
contribution margin ratio instead of the contribution margin per unit. The formula to find
the target volume follows:

𝑭𝒊𝒙𝒆𝒅 𝒄𝒐𝒔𝒕𝒔 + 𝑻𝒂𝒓𝒈𝒆𝒕 𝒑𝒓𝒐𝒇𝒊𝒕

Target volume (Birr) =

𝒄𝒐𝒏𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒎𝒂𝒓𝒈𝒊𝒏
𝑹𝒂𝒕𝒊𝒐
𝑩𝒓.𝟓,𝟎𝟎,𝟎𝟎𝟎 + 𝟐𝟎𝟎,𝟎𝟎𝟎
Target volume (Birr) =

𝟎.𝟔𝟐𝟓
= Br. 9,120,000
CVP Calculations for a Sales Mix
Sales mix is the proportion in which two or more products are sold. For the calculation of break-
even point for sales mix, following assumptions are made in addition to those already made for
CVP analysis:
1. The proportion of sales mix must be predetermined.
2. The sales mix must not change within the relevant time period.
The calculation method for the break-even point of sales mix is based on the contribution
approach method. Since we have multiple products in sales mix therefore it is most likely that we
will be dealing with products with different contribution margin per unit and contribution margin
ratios. This problem is overcome by calculating weighted average contribution margin per unit
and contribution margin ratio. These are then used to calculate the break-even point for sales
mix.
The calculation procedure and the formulas are discussed via following example:
Example:
Following information is related to sales mix of product A, B and C.
Product A B C
Sales Price per Unit Br. 15 Br. 21 Br. 36
Variable Cost per Unit Br. 9 Br. 14 Br. 19
 Sales Mix Percentage 20% 20% 60%
Total Fixed Cost Br. 40,000
Calculate the break-even point in units and in dollars.
Calculation
 Step 1: Calculate the contribution margin per unit for each product:
Product A B C
Sales Price per Unit Br. 15 Br. 21 Br. 36
− Variable Cost per Unit Br. 9 Br. 14 Br. 19
Contribution Margin per Unit Br. 6 Br. 7 Br. 17
 Step 2: Calculate the weighted-average contribution margin per unit for the sales mix
using the following formula:

Product A CM per Unit × Product A Sales Mix Percentage

+ Product B CM per Unit × Product B Sales Mix Percentage

+ Product C CM per Unit × Product C Sales Mix Percentage

= Weighted Average Unit Contribution Margin

Product A B C
Sales Price per Unit Br. 15 Br. 21 Br. 36
− Variable Cost per Unit Br. 9 Br. 14 Br. 19
Contribution Margin per Unit Br. 6 Br. 7 Br. 17
× Sales Mix Percentage 20% 20% 60%
Br. 1.2 Br. 1.4 Br. 10.2
Sum: Weighted Average CM per Unit Br. 12.80
 Step 3: Calculate total units of sales mix required to break-even using the formula:

Break-even Point in Units of Sales Mix = Total Fixed Cost ÷ Weighted Average CM per
Unit
Total Fixed Cost Br. 40,000
÷ Weighted Average CM per Unit Br. 12.80

Break-even Point in Units of Sales Mix 3,125

 Step 4: Calculate number units of product A, B and C at break-even point:

Product A B C
Sales Mix Ratio 20% 20% 60%
× Total Break-even Units 3,125 3,125 3,125
Product Units at Break-even Point 625 625 1,875

 Step 5: Calculate Break-even Point in dollars as follows:

Product A B C
Product Units at Break-even Point 625 625 1,875
× Price per Unit Br. 15 Br. 21 Br. 36
Product Sales in Dollars Br. 9,375 Br. 13,125 Br. 67,500
Sum: Break-even Point in Dollars Br. 90,000