This document discusses cost-volume-profit analysis and break-even analysis. It defines key terms like contribution margin, variable costs, fixed costs, and sales mix. It provides examples of using the equation method and contribution margin method to calculate break-even points. It also discusses how to calculate target profit, margin of safety, operating leverage, and deals with break-even analysis for situations with multiple products or a sales mix.

1. Cost-Volume-Profit
Relationships

2. COST VOLUME PROFIT ANALYSIS
• HELPFUL TO UNDERSTAND THE RELATIONSHIP
AMONG VARIABLE COSTS, FIXED COSTS AND PROFIT
• BASIC ASSUMPTIONS:
– SELLING PRICE IS CONSTANT
– COSTS ARE LINEAR; AND CAN BE DIVIDED INTO
FIXED AND VARIABLE; FIXED ELEMENT
CONSTANT OVER THE RELEVANT RANGE; UNIT
VARIABLE COST CONSTANT OVER RELEVANT
RANGE
– SALES MIX IS CONSTANT
– INVENTORIES STAY AT THE SAME LEVEL

3. •Contribution Margin (CM) is the amount remaining
from sales revenue after variable expenses have
been deducted
•CM goes to cover fixed expenses.
•After covering fixed costs, any remaining CM
contributes to income

4. The Contribution Approach
For each additional unit Wind sells, $200 more
in contribution margin will help to cover
fixed expenses and profit.

5. The Contribution Approach
Each month Wind must generate at least
$80,000 in total CM to break even.

6. The Contribution Approach
The break-even point can be defined either as:
The point where total sales revenue equals total
expenses (variable and fixed).
The point where total contribution margin equals total
fixed expenses.

7. CONTRIBUTION MARGIN RATIO
CMR= CONTRIBUTION MARGIN RATIO
= CM / SALES OR cmu/p
VCR = VARIABLE COST RATIO
= VC/SALES OR vcu/p
CMR +VCR= 1
EFFECT OF CHANGE IN FIXED COSTS?
EFFECT OF CHANGE IN VARIABLE COSTS?
EFFECT OF CHANGE IN SELLING PRICE?

8. PROFIT ANALYSIS
• AT BREAKEVEN PROFIT = 0
• BEFORE BREAKEVEN LOSS; AFTER BREAKEVEN
PROFIT
• CM COVERS FIXED COST UPTO BREAKEVEN
POINT
• AFTER BREAKEVEN POINT INCREASE IN CM WILL
INCREASE NET INCOME
• CM = FC + INCOME BEFORE TAX

9. Changes in Fixed Costs and Sales
Volume
Wind is currently selling 500 bikes per month. Selling price per
bike is $500, variable cost per bike is $300 and the fixed costs
are $80,000 per month. The company’s sales manager
believes that an increase of $10,000 in the monthly
advertising budget would increase bike sales to 540 units.
• Should we authorize the requested increase in the advertising budget?
• If sales increase by $50,000, what will be the increase in total contributionIf sales increase by $50,000, what will be the increase in total contribution
margin?margin?

10. Current Sales
(500 bikes)
Projected Sales
(540 bikes)
Sales 250,000$ 270,000$
Less: variable expenses 150,000 162,000
Contribution margin 100,000 108,000
Less: fixed expenses 80,000 90,000
Net income 20,000$ 18,000$
Changes in Fixed Costs and Sales
Volume
Sales increased by $20,000, but net
income decreased by $2,000..
Sales increased by $20,000, but net
income decreased by $2,000..
$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000

11. Changes in Fixed Costs and Sales
Volume
The Shortcut SolutionThe Shortcut Solution
Increase in CM (40 units X $200) 8,000$
Increase in advertising expenses 10,000
Decrease in net income (2,000)$

12. Break-Even Analysis
Break-even analysis can be approached in two
ways:
Equation method
Contribution margin method.

13. Equation Method
Profits(before tax) =
Sales – (Variable expenses + Fixed expenses)
Sales = Variable expenses + Fixed expenses + Profits
(before tax)
OR
At the break-even point
profits equal zero.

14. DERIVATION OF EQUATIONS
SALES= VARIABLE COSTS+FIXED COSTS + PROFIT
p*q= vcu *q + FC + ¶
AT BREAKEVEN PROFIT = 0
p*q=vcu *q +FC
q * (p-vcu) = FC
q= FC / (p - vcu) OR q=FC/ cmu
CM= SALES - TOTAL VC
VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND
SELLING EXPENSES
cmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/q
vcu= VARIABLE COST PER UNIT= VC/ q
q number of units

15. Equation Method
Here is the information from Wind Bicycle Co.:
Total Per Unit Percent
Sales (500 bikes) 250,000$ 500$ 100%
Less: variable expenses 150,000 300 60%
Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000
Net income 20,000$

16. Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500q = $300q + $80,000 + $0
Where:
q = Number of bikes sold
$500 = Unit sales price
$300 = Unit variable expenses
$80,000 = Total fixed expenses

17. Equation Method
We can also use the following equation to compute
the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
Where:
X = Total sales dollars
0.60 = Variable expenses as a
percentage of sales
$80,000 = Total fixed expenses

18. Equation Method
We can also use the following equation to compute
the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80,000 + $0
0.40X = $80,000
X = $200,000

19. Contribution Margin Method
The contribution margin method is a variation
of the equation method.
Fixed expenses
Unit contribution margin
=
Break-even point
in units sold
Fixed expenses
CM ratio
=
Break-even point in
total sales dollars

20. -
50,000
100,000
150,000
200,000
250,000
300,000
350,000
400,000
450,000
- 100 200 300 400 500 600 700 800Units
Dollars
CVP Graph
Break-even point
Loss Area
Profit Area

21. Target Profit Analysis
Suppose Wind Co. wants to know how many
bikes must be sold to earn a profit of
$100,000.
We can use our CVP formula to determine the
sales volume needed to achieve a target net
profit figure.

22. The CVP Equation
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $100,000
$200Q = $180,000
Q = 900 bikes

23. The Contribution Margin Approach
We can determine the number of bikes that must
be sold to earn a profit of $100,000 using the
contribution margin approach.
Fixed expenses + Target profit
Unit contribution margin
=
Units sold to attain
the target profit
$80,000 + $100,000
$200
= 900 bikes

24. The Margin of Safety
Excess of budgeted (or actual) sales over the
break-even volume of sales. The amount by
which sales can drop before losses begin to
be incurred.
Margin of safety = Total sales - Break-even sales
Let’s calculate the margin of safety for Wind.

25. The Margin of Safety
Wind has a break-even point of $200,000. If
actual sales are $250,000, the margin of safety is
$50,000 or 100 bikes.
Break-even
sales
400 units
Actual sales
500 units
Sales 200,000$ 250,000$
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net income -$ 20,000$

26. Break-even
sales
400 units
Actual sales
500 units
Sales 200,000$ 250,000$
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net income -$ 20,000$
The Margin of Safety
The margin of safety can be expressed as 20
percent of sales.
($50,000 ÷ $250,000)

27. MARGIN OF SAFETY
: EXCESS OF SALES (EITHER ACTUAL OR FORECASTED ) OVER
THE BREAKEVEN SALES I.E., THE BUFFER AMOUNT
MoS $= ACTUAL OR BUDGETED SALES - BREAKEVEN SALES $
MoS % = MoS $ / ACTUAL OR BUDGETED SALES
BREAKEVEN SALES IN SINGLE PRODUCT SETTING
SALES $ = VC$ + FC$
WHERE VCR= x% *SALES THEN 1-x% = CMR
SALES $ = x% *SALES +FC
(1-x)* SALES $ = FC THAT IS CMR*SALES = FC
SALES $ AT BREAKEVEN = FC/ CMR

28. Operating Leverage
• A measure of how sensitive net income is to
percentage changes in sales.
• With high leverage, a small percentage increase
in sales can produce a much larger percentage
increase in net income.
Contribution margin
Net income
Degree of
operating leverage =

29. Operating Leverage
Actual sales
500 Bikes
Sales 250,000$
Less: variable expenses 150,000
Contribution margin 100,000
Less: fixed expenses 80,000
Net income 20,000$
$100,000
$20,000
= 5

30. Operating Leverage
With a measure of operating leverage of 5, ifWith a measure of operating leverage of 5, if
Wind increases its sales by 10%, net incomeWind increases its sales by 10%, net income
would increase by 50%.would increase by 50%.
Percent increase in sales 10%
Degree of operating leverage × 5
Percent increase in profits 50%
Here’s the proof!

31. Operating Leverage
10% increase in sales from
$250,000 to $275,000 . . .
10% increase in sales from
$250,000 to $275,000 . . .
. . . results in a 50% increase in
income from $20,000 to $30,000.
. . . results in a 50% increase in
income from $20,000 to $30,000.

32. COST STRUCTURE AND PROFITABILITY
• HIGH VARIABLE COSTS LEAD TO LOWER CM AND LESS
VULNERABLE IN CRISIS TIME
• HIGH FIXED COSTS CAUSE HIGHER BREAKEVEN POINT;
AFTER THE BREAKEVEN POINT PROFITS INCREASE FASTER
THAN THE HIGH VARIABLE COST COMPANY
• DEGREE OF OPERATING LEVERAGE: CONTRIBUTION
MARGIN / NET INCOME
• FOR A GIVEN % CHANGE IN SALES, INCOME WILL
INCREASE BY (% INCREASE IN SALES *DEGREE OF
OPERATING LEVERAGE)
• DEGREE OF OPERATING LEVERAGE DECREASES AS THE
SALES MOVE AWAY FROM THE BREAKEVEN POINT
• IF VARIABLE COSTS ARE HIGH DEGREE OF OPERATING
LEVERAGE LOW; AND VICE VERSA

33. The Concept of Sales Mix
• Sales mix is the relative proportions in which a
company’s products are sold.
• Different products have different selling prices,
cost structures, and contribution margins.
Let’s assume Wind sells bikes and carts and see
how we deal with break-even analysis.

34. The Concept of Sales Mix
Wind Bicycle Co. provides us with the following
information:
Bikes Carts Total
Sales 250,000$ 100% 300,000$ 100% 550,000$ 100%
Var. exp. 150,000 60% 135,000 45% 285,000 52%
Contrib. margin 100,000$ 40% 165,000$ 55% 265,000 48%
Fixed exp. 170,000
Net income 95,000$
$265,000
$550,000 = 48% (rounded)
$170,000$170,000
0.480.48 = $354,167 (rounded)= $354,167 (rounded)
WEIGHTED
CMR

35. SALES MIX= % OF TOTAL SALES FOR EVERY PRODUCT
THREE PRODUCTS A , B, C
% SALES OF a, b , c where a= sales of product a / total sales etc.
CMa = CM OF PRODUCT A, B OR C
WEIGHTED CMR= a * CMR of product A + b * CMR of product B + c * CMR of
product C
BREAKEVEN IN MULTIPLE PRODUCT S= FC/ WEIGHTED CMR
•TO FIND HOW MANY UNITS MUST BE SOLD AT BREAKEVEN (OR FOR
TARGET INCOME):
1.FIND BREAKEVEN IN MULTIPLE PRODUCTS
2.COMPUTE EACH PRODUCTS SALES AMOUNT BY MULTIPLYING THE
SALES RATIO * BREAKEVEN SALES
3.FIND THE BREAKEVEN SALE SHARE OF EACH PRODUCT;
4.DIVIDE EACH PRODUCTS SHARE OF BREAKEVEN SALES BY THE UNIT
PRICE OF EACH PRODUCT TO GET THE NUMBER OF UNITS TO BE SOLD OF
EACH PRODUCT IN ORDER TO BREAKEVEN OR FOR TARGET INCOME