1. COST VOLUME PROFIT ANALYSIS (CVP)
Chapter three

2. Essentials of CVP Analysis
Cost – Volume – Profit (CVP) analysis studies the behavior and relationship among the total revenues , total costs , and income as changes occur in the units sold, the selling price , the variable cost per unit, or the fixed costs of a product.

3. Contribution Margin
Contribution margin indicates why operating income changes as the number of units sold changes. =
Contribution margin
Total revenues
Total variable Costs

4. Contribution Margin Sales revenue ($) 1,000 8,000
Variable cost ( $ )
Contribution margin ($)
Fixed Cost ($) ,000 2,000
Income from operation ($) (1600)
CHAPTER 3

5. Contribution Income statement for different quantitiesG H 1
Number of Units Sold 2 5 25 40 3
REVENUE
$200
Per unit
200
1000
5000
8000 4
VARIABLE COST
$120
120
600
3000
4800
Contribution Margin
$80 80
400
2000
3200 6
Fixed Costs 7
Operating Income
(2000)
(1920)
(1600)
1200

6. Contribution margin per unit=
Contribution margin per unit
Selling price
variable cost per unit

7. Contribution Margin per Unit
Selling price per unit $ 10.00
Variable cost per unit
Contribution margin per unit
Chapter 3

8. Contribution margin percentage or (Contribution margin ratio)
= = ( 4 / 10) x 100 = 40%
Contribution margin percentage or (Contribution margin ratio)
Contribution margin per unit
Selling price

9. Expressing CVP Relationships
There are three methods related to CVP relationships:
1- The Equation method
2-The contribution margin method
3- The graph method

10. quantity of units sold(Q) Variable cost per unit(VCU)
The Equation method
= -
= x
= x
variable costs
fixed costs
operating income
Revenues
Revenues
selling price (SP)
quantity of units sold(Q)
Variable cost
Variable cost per unit(VCU)
quantity of units sold

11. The Equation method x - x - = operating income Selling price
quantity of units sold
variable cost per unit
quantity of units sold
operating income
fixed income
Selling price

12. contribution margin method
Selling - variable cost x quantity of fixed = operating
price per unit units sold costs income
So:
contribution margin x quantity of fixed = operating
per unit units sold costs income

13. Cost-Volume-Profit Assumptions and Terminology
1- Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units sold.
2-Total costs can be separated into two component: a fixed component that does not vary with units sold and a variable component that changes with respect to units sold.

14. Cost-Volume-Profit Assumptions and Terminology
3- When represented graphically, the behaviors of total revenues and total costs are linear (straight-line) in relation to units sold within the relevant range (and time period). 4- selling price, variable cost per unit, and total fixed costs are known and constant

15. Break-Even Point Concept(BEP)
 The break-even point is the second key relationship in CVP analysis and is that quantity of output sold at which total revenues equal total costs – both fixed and variable.
 At break-even point, a business will have neither an income nor loss from operation that results in $0 of operating income.
Chapter 3

16. Emma Frost sells each unit of product “GAMT”
example1:
Emma Frost sells each unit of product “GAMT”
at $ The variable cost per unit is $120. Total fixed cost is $ 2,000 per year.
How many units of “GAMT” must be sold in one year in order to break-even.
Chapter 3

17. By using the three methods
Solution
By using the three methods
Chapter 3

18. 1- The Equation method x - x - =
Setting operating income equal SR 0. and denoting quantity of output units that must be sold by Q.
quantity of units sold
variable cost per unit
quantity of units sold
operating income
fixed income
Selling price

19. The Equation method per unit:
200X Q )- ($120 X Q) – $2000 = $ 80 X Q= $ Q= $2000 / $80
= 25 units
Per revenues:
25 units x $ 200 selling price = $ 5000

20. 2- contribution margin method
x =
At the breakeven point, operating income is by definition $0 and so,
contribution margin per unit x breakeven number of units = fixed costs =
contribution margin per unit
Fixed costs
Operating income
Quantity of units sold
fixed costs
contribution margin per unit
breakeven number of units

21. contribution margin method
Per units:
breakeven units = , = 25 units
$80 per unit
Breakeven revenues= 25 units x $200 per unit
= $ 5000

22. contribution margin percentages method
contribution margin percentages = contribution margin per unit selling price = $80 = o.40 or 40% $ 200 Breakeven revenues = ____fixed costs contribution margin % = $ 2000 = $ %

23. Target operating income in units
Determine the quantity of units Emma must sell to earn an operating income of $1200. selling price is $200 , variable cost per unit $120 , fixed costs are $2000?

24. 1-Equation Method Target operating income in units=
($200 x Q) – ($120XQ)- $2000 =$1200
$80 x q = $2000 =$1200
Q = $3200 = 40 UNITS
$80
Q denotes the number of units required to be sold

25. 2-contribution margin method
Fixed costs + Target operating ncome
Contribution Margin per unit =
Quantity of unites require to be sold= $ $1200
$80 per unit
=40 units
Quantity of units to be sold=

26. Proof: Revenue $200per unit x 40 units = $8,000
Variable costs $120 per unit x 40 units=
Contribution margin $80 per unit x 40 units =
Fixed costs
operating income $1200

27. Target Net Income and Income Taxes
Net Income= Operating Income – Income Taxes
For example Emma me be interested in knwoing the quantity of units she must sell to earn net income of $960 assuming an income tax rate of 40%.
Target net income = target target x tax rate
operating income operating income

28. Target Net Income and Income Taxes
Target net income = (target operating income) x ( 1 – Tax Rate ) target operating income = Target net income 1 – Tax Rate = $ 960 = $ – 0.40 Proof: Target operating income $1600 tax at 40% (0.40 x $ 1600) 640 Target net income 960

29. Target Net Income and Income Taxes
Quantity of units require to be sold = fixed costs + Target operating income contribution margin per unit = $ $1600 = 45 units $80 per unit

30. Sensitivity Analysis and Margin of Safety
Sensitivity Analysis is a ,, what – if ,, technique that managers use to examine how an outcome will change if the original predicted data are not achieved or if an underlying assumption changes. = - = -
Budget revenues
Breakeven revenues
Margin of safety
Margin of safety in units
Breakeven quantity
Budget sales quantity

31. Contribution Margin Versus Gross Margin
Gross Margin = revenues – cost of goods sold
Contribution Margin = revenues – all variables costs
Gross Margin measures how much a company can charge for its products over and above the cost of acquiring or producing them.
Contribution Margin indicates how much of a company’s revenues are available to cover fixed costs.