Cost Volume Profit Analysis

• It is a form of cost accounting. It expands the use of

information provided by breakeven analysis.
• It is a financial decision making aid used to determine
the level of output used to achieve any target profit
level or the financial impact of basic business
activities like changes in costs or pricing.
• It is a management accounting tool that express
relationship between sales volume, cost and profit. It
is a simplified model used for elementary instructions
and short run decisions.
Assumptions of CVP
• Variables included in CVP may be
– Fixed Costs
– Variable Costs
– Profit per unit

Conventional linear cost volume profit analysis is based on five assumptions as

follows:.
Constant sales price
Constant variable cost per unit.
Constant total fixed cost.
Constant sales mix.
Volume is the only cost driver.
The relevant range of volume is specified.
Inventory levels will be unchanged.
The sales mix remains unchanged during the period.
It is a one product business. Effectively deals with only one product.
Uncertainty does not exist.
Units sold is equal to the units produced.
Technology and productive efficiency are constant.
Time value of money is ignored in CVP
• Definitions
– Breakeven Point is the point at which cost or expenses and income are
equal: there is no net loss or gain.
– Mixed Costs contains both fixed and variable elements. There are a
variety of procedures that can be employed to separate the fixed and
variable components.
– Revenue mix is the composition of total revenues in terms of various
products.
– Sensitivity Analysis is the study of how the variation in the output of a
model can be apportioned, qualitatively or quantitatively, to different
sources of variation
– Unit Contribution Margin Unit Revenue minus Unit Variable Cost
• Contribution Margin ratio is the percentage of contribution over
sales, which can be calculated from the unit contribution over unit
price or total contribution over total sales.
• Breakeven is calculated as
– Fixed Cost / Unit Contribution margin
– Unit Contribution Margin = Sales – Variable Cost
• The fixed cost of the company is 4.80,000. Sales Price per unit is
6. Variable cost 10. Calculate Breakeven Point in units
– Break even point = Fixed Cost / Unit Contribution Margin
– Unit Contribution Margin = Sales – Variable Cost
» UCM = (10-6) = 4 Therefore BEP = FC / UCM = 4,80,000
/ 4 = 1,20,000.
• Contribution Income Statement is a statement that organizes cost by
behavior. It shows the relationship of variable costs and fixed costs,
regardless of the functions a given cost item is associated with
– Contribution Income Statement is
– Contribution Margin – Fixed Costs = Operating Incoem
– Contribution Margin = Sales – Variable Cost
• The sales of a company is 45,00,000. The cost may be Cost of
Goods Sold = 2,00,000. Sales Commission = 50,000. Advertising =
25,000, Depreciation = 15,000. Income taxes = 20,000. Prepare
Contribution Income Statement
– Sales 45,00,000
– Less: Variable Costs
– Cost of goods sold 2,00,000
– Sales Commission 50,000 2,50,000
– Contribution margin 42,50,000
– Less: Fixed Costs
– Advertising 25,000
– Income taxes 20,000
– Depreciation 15,000 60,000
– Net Operating Income 41,90,000
 Applications Of CVP

• Operating income is the amount of  profit realized from a business's own

operations, but excluding operating expenses (such as cost of goods
sold) and depreciation from gross income.
• Target Operating Income is the amount of operating income that is
frequently required.
• It can be determined by
– Equation Method
– Contribution Margin Method
– Graph Method
• Target Operating Income is
Target Operating Income = (Fixed Expenses + Operating
Income) / Contribution Margin ( Sales – Variable Cost)
• A company has a operating income of 45,000. The sales price per unit is
100, variable expenses include 70 and the fixed expenses is 90,000.
Calculate the target operating income
– Target Operating Income = (Fixed Expenses + Operating Income) /
Contribution margin (Sales – Variable Cost)
= (45,000 + 90,000) / 30 (100-70)
= 1,35,000 / 30 = 4,500
– Target Net Income it is used when managers want to know the effect of
their decision on income taxes,
– To convert the target net income to target operating income the
formula used is by dividing the target net income by one minus the
income tax rate.
– CVP formula for that adjustment is as
• Revenue = Fixed Costs + Variable Costs + ( Target Net Income /
(1- tax rate)
• Breakeven for multiple products is calculated by finding the weighted
average contribution margin
• Weighted average contribution margin = Total contribution margin of all
products / total units of the products.
A & Co has the following details
Budgeted Units to be sold Cakes Pies Total
Units 2,000 6,000 8,000 (2,000+6,000)
Sales 24,000 36,000 60,000 (24,000+36,000)
Variable Costs 4,500 10,800 15,300 (4,500+10,800)
Contribution Margin
( Sales – VC ) 19,500 25,200 44,700 (19,500+25,200)
Fixed Costs 8,000 5,400 13,400 (8,000+5,400)
Profit (CM – Fixed Cost) 11,500 19,800 31,300 (11,500+19,800)
From the above statement calculate the breakeven point for multiple products
 – WACM = Total Contribution Margin of all products / Total Units of all
Products
Therefore WACM = 44,700 / 8,000 = 5.5875
Breakeven Point = Total Fixed Costs / WACM = 13,400 / 5.5875 = 2398.2
= 2398 units
• Breakeven application assumes that Variable Costing is used
– Variable Costing assigns only variable manufacturing costs to products.
– Variable Costing is for internal use only.
– In variable Costing the breakeven sales do not vary with production.
– Absorption Costing
• Absorption costing assigns all manufacturing costs to products.
• Financial Statements prepared under GAAP uses Absorption
Costing.
• Absorption Costing is an effective tool for long run decision making
since it focuses attention on revenues and total production costs
• From the following problem calculate the Variable Costing and Absorption
Costing
– Direct material unit cost 6.00
– Direct labor unit cost 3.00
– Variable manufacturing overhead 2.00
– Variable marketing 2.50
– Fixed manufacturing overhead per unit 5.00

Ans: Variable Costing is

– Direct materials 6.00
– Direct labor 3.00
– Variable manufacturing overhead 2.00
– Fixed manufacturing overhead -0-
– Total 11.00
 – Absorption Costing is
• Direct materials 6.00
• Direct labor 3.00
• Variable manufacturing overhead 2.00
• Fixed manufacturing overhead 5.00
• Total 16.00
• Degree of Operating Leverage The degree of operating leverage at a given
level of sales is computed as follows:
– Degree of operating Leverage = Contribution Margin / Net Operating
Income
– Degree of Operating Leverage is not constant as the level of sales
changes.
– Degree of Operating Leverage provides a quick way to predict the
percentage effect on profits of a given percentage increase in sales.
– Degree of Operating Leverage points out that the relation between
Operating Leverage and the cost structure is contingent.
The following symbols are used below to illustrate the various
techniques used in cost-volume-profit analysis.
P = Sales price.
V = Variable costs per unit. Note: This is not inventory cost
because it includes both variable manufacturing costs as well as
variable selling and administrative expenses.
X = The number of units produced and sold. A unit is a common
way to describe an output, but an output may be expressed in
pounds, gallons, board feet, cubic feet, etc.
TR = S = Total revenue, or sales dollars.
TVC = Total variable costs = VX
TFC = Total fixed costs.
TC = Total costs = TFC + TVC.
P-V = Contribution margin per unit. This is the amount of sales
revenue that each unit provides towards covering the fixed costs
and providing a profit, i.e., what's left over after the variable costs
associated with the unit have been covered.
TCM = Total contribution margin = (P-V)(X).
CMR = (P-V)÷P = (TR-TVC)÷TR = (PX-VX)÷PX = 1-(V÷P). These
are just different ways to define the contribution margin ratio. They
all work because the functions are linear.
There are many algebraic equations illustrated on the next several
pages that may appear to require memorization. However, every
equation is simply a variation of the following basic concepts:
Total Revenue = Total Cost + Profit
TR = TC + NIBT
TR = TFC + TVC + NIBT
TR - TVC = TFC + NIBT
TCM = TFC + NIBT
Total revenue, or sales dollars, less total variable costs equals
total contribution margin. Contribution margin is the revenue over
and above the variable costs that contributes towards covering the
fixed costs and also towards providing a profit after the fixed costs
have been covered. Practically any cost-volume-profit problem
can be solved with the last equation stated above and an
understanding of the concepts involved.
 SUMMARY EQUATIONS FOR SOLVING
SINGLE PRODUCT CVP PROBLEMS IN UNITS

NUMBER EQUATION USED TO DETERMINE

[1] (P-V)X = TFC Units needed to break-even.

[2] (P-V)X = TFC + NIBT Units needed to generate a target net income
before taxes.

[3] (P-V)X = TFC + [NIAT ÷ (1-T)] Units needed to generate a target net income
after taxes.

[4] (P-V)X = TFC + (R)(PX) Units needed to generate a target NIBT stated as
a proportion (R) of sales dollars (PX).

[5] (P-V)X = TFC + [(R)(PX) ÷ (1-T)] Units needed to generate a target NIAT stated as
a proportion (R) of sales dollars (PX).
UNITS NEEDED TO BREAK-EVEN
Break-even equation is to start with the fact that total revenue
equals total cost at the break-even point. Then the equation is
restated in terms of unit sales, unit prices and unit cost and then
rearranged into the more convenient format presented in Equation
1.
TR = TC
TR = TFC + TVC
PX = TFC + VX
PX - VX = TFC
[1] (P-V)X = TFC or TCM = TFC
X = TFC ÷ (P-V)
Equation 1 shows that the break-even point is where total
contribution margin (P-V)(X) is equal to total fixed costs, i.e., this
level of production and sales provides just enough revenue to
cover all the cost.
UNITS NEEDED FOR TARGET NET INCOME BEFORE TAXES

This equation can be derived from scratch in the same manner

used to develop Equation 1. Notice however that Equation 2 may
be obtained by simply adding the desired amount of net income to
the right hand side of Equation 1.
TR = TFC + TVC + TARGET NIBT
PX = TFC + VX + NIBT
PX - VX = TFC + NIBT
[2] (P-V)X = TFC + NIBT
X = (TFC+NIBT) ÷ (P-V)
UNITS NEEDED FOR TARGET NET INCOME AFTER TAXES
If T = the tax rate, and NIAT = desired net income after taxes,
then
(1-T)(NIBT) = NIAT therefore NIBT = NIAT ÷ (1-T)
Substituting NIAT÷(1-T) for NIBT in Equation 2, provides Equation
3, which allows us to solve for units needed to generate a desired
amount of net income after taxes.
[3] (P-V) X = TFC + [NIAT ÷ (1-T)]
X = [TFC + [NIAT÷(1-T)]] ÷ (P-V)
The after tax relationships are also illustrated graphically in Figure
11-17. The after tax profit function begins at a point equal to (1-T)
(-TFC) assuming the tax benefits of a loss can be used in a prior
period or perhaps in some other segment of the company. The
slope of the after tax profit function is (1-T)(P-V), therefore the
function is not as steep as the before tax profit function. The
break-even point is the same however, and the vertical difference
between the two profit functions is equal to the amount of the tax
WHEN TARGET NET INCOME BEFORE TAXES IS STATED AS
A % OF SALES $

If we use R to define the desired rate of return on sales, i.e., R =

NIBT/TR, then we can substitute R(PX) for the desired net income
before taxes in Equation 3. This provides Equation 4.
[4] (P-V)X = TFC + (R)(PX)
X = [TFC + (R)(PX)] ÷ (P-V)
Since PX equals sales dollars, then R multiplied by PX will provide
the desired profit before taxes.
Although the desired profit is often stated as a percentage, R is a
proportion, i.e, it ranges from 0 to 1.
WHEN TARGET NET INCOME AFTER TAXES IS STATED AS A
PERCENTAGE OF SALES $
If the target rate of return is stated as an after tax rate, i.e., R =
NIAT/TR, then the following approach is used. Substituting
R(PX)÷(1-T) for R(PX) in Equation 4 provides Equation 5.
[5] (P-V)X = TFC + [(R)(PX) ÷ (1-T)]
X = [TFC + [(R)(PX) ÷ (1-T)]] ÷ (P-V)
When solving CVP problems, it is less confusing visually and
more convenient for computational purposes to leave (P-V) on the
left-hand side of the equations initially as indicated in Exhibit 11-1.
It is best to simplify the expressions on both sides of the equation
first, rather than attempt to divide every element on the right-hand
side by P-V.
 SUMMARY EQUATIONS FOR SOLVING
MULTIPLE PRODUCT CVP PROBLEMS IN UNITS
NUMBER EQUATION USED TO DETERMINE

[1] WX = TFC Total mixed units at the BEP.

[2] WX = TFC + NIBT Total mixed units for target NIBT.

[3] WX = TFC + [NIAT ÷ (1-T)] Total mixed units for target NIAT.

[4] WX = TFC + (R)(YX) Total mixed units for target NIBT stated
as a proportion (R) of sales $.

[5] WX = TFC + [(R)(YX) ÷ (1-T)] Total mixed units for target NIAT stated
as a proportion (R) of sales $.

Xi = X(Mi) The number of units of each product

after X is obtained.

 
i = The number designating a particular product.
Pi = The price of product i.
Vi = The variable cost per unit of product i.
X = Total mixed units sold, i.e., includes all products.
Xi = Units of product i sold.
Mi = The mix ratio for product i, i.e., the proportion that
product i represents out of the total number of units sold.
E = Sigma or summation sign which means "the sum of".
W = Weighted average contribution margin per unit = E [(Pi-
Vi)(Mi)]
Y = The weighted average price = E (Pi)(Mi)
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