CVP Analysis- "A Total Manager's Guide".

Cost-Volume-Profit (CVP)
Analysis

Profit planning is a function of :
• the selling price of a unit of product ,
• the variable cost of making and selling the
product ,
• the volume of product units sold , and
• in the case of multi-product companies , sales
mix and
• finally total product cost.

The cost-volume-profit (CVP) analysis is a :
• management accounting tool
• to show the relationship between these
ingredients of profit planning
• The entire gamut of profit planning is
associated with CVP inter-relationships.
• A widely – used technique to study CVP
relationships is break-even analysis

A break even analysis is concerned with :
• the study of revenues and
• costs
• in relation to sales volume and particularly ,
• the determination of that volume of sales at which the
firm`s revenues and total costs will be exactly equal (
or net income = zero) .
Thus, the Break-Even Point (BEP) may be defined as
a point at which the firm`s total revenues are
equal to total costs, yielding zero income .
This is a no-profit , no-loss point.

Break even analysis , as a technique ,seeks to provide
answers to the following questions:
• What sales volume is necessary to produce an X amount of
operating profit ?
• What will be the operating profit or loss at X sales volume?
• What profit will result from an X per cent increase in sales
volume?
• What additional sales volume is required to make good an
X percent reduction in selling prices so as to maintain the
current profit level?
• What will be the effect on operating profit if the company's
fixed cost have increased ?

BREAK EVEN ANALYSIS
A BEP analysis shows the relationship between the
costs and profits with sales volume.
The sales volume which equates total revenue with
related costs and results in neither profit or loss is
called Break Even Volume or Point (BEP) .

Illustration 1 :
How many ice-creams having a unit cost of Rs.2 and
a selling price of Rs.3, must a vendor sell in a fair to
recover the Rs.800 fees paid by him for getting the
stall and additional cost of Rs.400 to set up the stall .

BEP (units) = Fixed Cost ÷ Contribution
Margin per unit
BEP (units) = (Entry Fee + Stall Expense) ÷
(Sales Price – Unit Variable Cost)
= (Rs 800 + Rs 400) ÷ ( Rs 3 – Rs 2)
= 1,200 units
BEP (amount) = Fixed Cost ÷ Profit Volume
Ratio (P/V or C/S ratio)
P/V Ratio or C/S Ratio
= Contribution Margin per unit ÷ Selling Price per unit
= Re.1 ÷ Rs. 3 = O.3333 or 33.33 %
= Rs1,200 ÷ 0.3333 = Rs.3,600

Variable Cost to Volume Ratio ( V/V ratio)
= 1- C/S ratio
= 1- 0.3333
= 0.6667 or 66.67 %
V/V ratio = Variable Cost ÷ Sales Revenue
= Rs.2 ÷ Rs. 3
= 66.67%
Therefore
P/V or C/S ratio (+) V/V ratio = 100% i.e. 1

Margin of Safety Ratio (M/S Ratio)
=( (ASR – BESR) ÷ ASR ) x 100
where ,
ASR = actual sales revenue
BESR = break even sales revenue
If the actual sale in this case is 2,000 units (Rs 6,000)
then
M/S ratio = ((Rs 6,000 - Rs 3,600) ÷ Rs 6,000)*100
= 40 %

Profit = [ Margin of safety (amount)] * P/V or C/S ratio
= [ Rs.6,000- Rs 3,600 ] * 0.3333
= [ Rs.2,400 ] * 0.3333
= Rs.800
Profit = [ Margin of Safety (units) ] * Contribution
Margin per unit
= [ 2,000 units – 1,200 units ] * Re.1
= [ 800 units ] * Re.1
= Rs.800

Illustration 2:
Sales = 4,000 units @ Rs 10 per unit
Break-even point = 1,500 units
Fixed Cost = Rs 3,000
What is the amount of (a) variable cost (b) profit ?

Solution :
BEP (in units) = Fixed Cost ÷ Contribution per unit [C]
1,500 = 3,000 ÷ C
C = 3,000 ÷ 1,500
= Rs 2 per unit
(a) Variable Cost = Selling Price – Contribution
= Rs10 – Rs 2
= Rs 8 per unit
(b) Contribution at sales of 4,000 units is Rs 8,000
Profit = Contribution – Fixed Cost
= Rs 8,000 – Rs 3,000
= Rs 5,000

Illustration 3:
Selling Price = Rs 150 per unit
Variable cost = Rs 90 per unit
Fixed Cost = Rs 6,00,000
What is the break even point ?
What is the selling price per unit if break – even
point is 12,000 units ?

Solution :
Break even point = Fixed Cost ÷ Contribution per unit
= Rs 6,00,000 ÷ (Rs150- Rs 90)
= 10,000 units
When BEP is at 12,000 the contribution will be :
12,000 = 6,00,000 ÷ C
C = 6,00,000 ÷ 12,000 = Rs 50 per unit
Contribution = Selling Price –Variable Cost
Rs 50= Selling Price – Rs 90
Selling Price =Rs 90+ Rs 50
= Rs 140 per unit

Illustration 4:
During the current year, Superhouse Ltd. showed a
profit of Rs.1,80,000 on sale of Rs. 30,00,000. The
variable expenses were Rs. 21,00,000.
You are required to work out :
a) The break even sales at present
b) The break even sale if variable cost increases by
5 per cent.
c) The break even sale to maintain the profit as at
present , if the selling price is reduced by 5 per
cent.

Solution:
Sale = VC + FC + Profit
Rs 30,00,000 = Rs 21,00,000 + FC + Rs 1,80,000
Therefore ,
FC = Sales - [ VC + Profit ]
= Rs 30,00,000 - [ Rs 21,00,000 + Rs 1,80,000 ]
= Rs. 7,20,000

a) BEP = FC ÷ PV or CS ratio
PV or CS ratio = Contribution ÷ Sales
= (Sales – Variable Cost) ÷ Sales
= [Rs 30,00,000 – Rs 21,00,000] ÷ Rs
30,00,000
= Rs 9,00,000 ÷ Rs 30,00,000
= 0.30
BEP = FC / PV or CS Ratio
= Rs 7,20,000 ÷ 0.30
= Rs. 24,00,000

b) Revised BEP = FC ÷ New PV ratio
New PV Ratio = [ Sales – (Variable Cost + 5 %) ] ÷
Sales
New PV Ratio = [Rs 30,00,000 – Rs 22,05,000 ] ÷
Rs 30,00,000
= Rs 7,95,000 ÷ Rs 30,00,000
= 0.265
Revised BEP = Rs 7,20,000 ÷ 0.265
= Rs. 27,16,981

c) If sale is reduced by 5 % = Rs 30,00,000 [ 1 - 0.05]
= Rs 30,00,000 [ 0.95 ]
= Rs. 28,50,000
New PV ratio = [ Rs 28,50,000 – Rs 21,00,000 ] ÷
Rs 28,50,000
= Rs 7,50,000 ÷ Rs 28,50,000
= 0.26316
Desired Volume of Sales
= [FC + Desired Profit] ÷ New PV or New CS ratio
= [Rs 7,20,000 + Rs 1,80,000 ] ÷ 0.26316
= Rs. 34,19,973

CVP Analysis- "A Total Manager's Guide".

Garden
Tools
Outdoor
Furniture
Barbecues Outdoor
Lighting
Total
Sales $ 950,000 $ 2,500,000 $ 1,400,000 $ 1,600,000 $ 6,450,000
Less Variable Cost:
Cost of Goods Sold $ 665,000 $ 1,800,000 $ 910,000 $ 640,000 $ 4,015,000
Incentive
Compensation to the
Sales team
$ 95,000 $ 250,000 $ 140,000 $ 160,000 $ 645,000
Miscellaneous
Variable
$ 12,000 $ 13,000 $ 11,000 $ 10,000 $ 46,000
Total VC $ 772,000 $2,063,000 $ 1,061,000 $ 810,000 $ 4,706,000
Less Direct Fixed
Cost:
Sales and Staff
Salaries
$ 75,000 $ 120,000 $ 96,000 $ 103,000 $ 394,000
Product-line Specific
Advertising
$ 20,000 $ 35,000 $ 25,000 $ 10,000 $ 90,000
Total Direct FC $ 95,000 $ 155,000 $ 121,000 $ 113,000 $ 484,000
Illustration 5:
Gilbert and Gibbs, a store sells outdoor products and is interested in using CVP
analysis to analyze its four product lines which include garden tools, outdoor
furniture barbecues and outdoor lightings. The company has done the following
profitability analysis:

Product Line Profit $ 83,000 $ 282,000 $ 218,000 $ 677,000 $ 1,260,000
Less Common
Fixed Cost:
Advertising $ 220,000
Utilities $ 35,000
Rent $ 185,000
Management
Salaries
$ 625,000
Other Fixed Costs $ 55,000
Total Common FC $ 1,120,000
Profit $ 140,000
a) What sales should Gilbert and Gibbs attain to reach the break even?
b) Suppose in the coming year management believes that the total sales will increase by 20% ,
what will the impact on over all profitability of the company?
c) Suppose the company believes sales will increase by $ 1,290,000 but expects the increase in
garden tools by $ 258,000, outdoor furniture $ 387,000 , barbecues by $ 516,000 and outdoor
lighting by $ 129,000.Will there be any change in the impact on the company`s over all profitability?
Incase there is a change in the over all profitability of the company give reasons for the same.
d) Suppose Sarah Williams , the store manager , is considering ways to increase profits in the coming
year. Which product-line do you think she should emphasize?

Garden
Tools
Outdoor
Furniture
Barbecues Outdoor
Lighting
Total
Sales
Less Total VC
Contribution
P/V Ratio or C/S Ratio = Contribution ÷ Sales
BEP Sales = TFC ÷ Contribution Margin
a)

Garden
Tools
Outdoor
Furniture
Barbecues Outdoor
Lighting
Total
Sales $ 950,000 $ 2,500,000 $ 1,400,000 $ 1,600,000 $ 6,450,000
P/V Ratio or C/S Ratio = Contribution÷ Sales
= ($ 1,744,000 ÷ $ 6,450,000) = $ 0.2704
BEP Sales = TFC ÷ Contribution Margin
= [$ 484,000+$ 1,120,000]÷ 0.2704
=$ 1,604,000 ÷ 0.2704 = $ 5,931,953
a)
Less Total VC $ 772,000 $2,063,000 $ 1,061,000 $ 810,000 $ 4,706,000
Contribution $ 178,000 $ 437,000 $ 339,000 $ 790,000 $ 1,744,000

Suppose in the coming year management believes that the total sales
will increase by 20% , what will the impact on over all profitability of
the company?
Expected Increase in Sales = Current Sales x % Increase in Sales
Expected Increase in Profits =Increase in Sales x C/S Ratio
b)

Suppose in the coming year management believes that the total sales
will increase by 20% , what will the impact on over all profitability of
the company?
Expected Increase in Sales = $ 6,450,000 x 0.20 = $ 1,290,000
Expected Increase in Profits =$ 1,290,000 x 0.2704 = $ 348,816
b)

Garden
Tools
Outdoor
Furniture
Barbecues Outdoor
Lighting
Total
Expected
Increase in
Sales
Contribution
Margin
Ratio
Increase in
Profit
c) Suppose the company believes sales will increase by $ 1,290,000 but expects
the increase in garden tools by $ 258,000, outdoor furniture $ 387,000 , barbecues
by $ 516,000 and outdoor lighting by $ 129,000.Will there be any change in the
impact on the company`s over all profitability? Incase there is a change in the over
all profitability of the company give reasons for the same.

Garden
Tools
Outdoor
Furniture
Barbecues Outdoor
Lighting
Total
Expected
Increase in
Sales
$ 258,000 $ 387,000 $ 516,000 $ 129,000 $ 1,290,000
c) Suppose the company believes sales will increase by $ 1,290,000 but expects
the increase in garden tools by $ 258,000, outdoor furniture $ 387,000 , barbecues
by $ 516,000 and outdoor lighting by $ 129,000.Will there be any change in the
impact on the company`s over all profitability? Incase there is a change in the over
all profitability of the company give reasons for the same.
Contribution
Margin
Ratio
0.1874 0.1748 0.2421 0.4938 -
Increase in
Profit
$ 48,349 $ 67,648 $ 124,924 $ 63,700 $ 304,621

OPERATING LEVERAGE AND RISK
Operating Leverage is a relative change in profits due to a change in sales.
A high degree of leverage implies that a large change in profits occurs due
to a relatively small change in sales.
Two types :
Financial Leverage : borrowed funds
Operating Leverage : use of fixed cost in
operation of business

• A firm will have no operating leverage if its ratio of fixed cost to total
cost is nil.
• For such a firm , a given change in sales would produce same percentage
change in the operating profit or EBIT.
• If a firm which has fixed costs ,would have operating leverage :
A) higher operating leverage if the total cost have higher percentage of fixed
costs.
B) operating leverage increases with fixed cost.
C) operating profit of a highly leveraged (operating) firm would increase at a
faster rate for any given increase in sales .
D) if sales fall , the firm with a high operating leverage would suffer more loss
than the firm with no or low operating leverage.

• Airline Industry: high fixed cost – profit is highly sensitive to the number
of passengers carried.
• Retail Firm: very high variable cost and negligible fixed cost.
• Profit fluctuation occurring due to high fixed costs are referred to as
operating risk.

• Degree of Operating Leverage is the % change in operating profits
resulting from a % change in sales.
• DOL= % change in operating profit ÷ % change in sales
• DOL= ∆EBIT/ EBIT ÷ ∆Sales/ Sales
here EBIT = operating profit

CVP Analysis- "A Total Manager's Guide".

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