COST VOLUME PROFIT ANALYSIS (CVP)

Chapter three

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.

Contribution Margin

• Contribution margin indicates why operating income changes as the number of units sold changes.

= -Total revenues Total variable CostsContribution margin

Contribution Margin

CHAPTER 3 4

Sales revenue ($) 1,000 8,000

Variable cost ( $ ) 600 4800

Contribution margin ($) 400 3200

Fixed Cost ($) 2,000 2,000

Income from operation ($) (1600) 1200

Contribution Income statement for different quantities

A B C D E F G H

1 Number of Units Sold

2 0 1 5 25 40

3 REVENUE $200 Per unit

0 200 1000 5000 8000

4 VARIABLE COST

$120 Per unit

0 120 600 3000 4800

5 Contribution Margin

$80 Per unit

0 80 400 2000 3200

6 Fixed Costs 2000 2000 2000 2000 2000 2000

7 Operating Income

(2000) (1920) (1600) 0 1200

Contribution margin per unit

• = - Contribution

margin per unit Selling price variable cost per unit

Contribution Margin per Unit

Chapter 3 7

Selling price per unit $ 10.00

Variable cost per unit 6.00

Contribution margin per unit 4.00

Contribution margin percentage or (Contribution margin ratio)

=

= ( 4 / 10) x 100 = 40%

Contribution margin percentage or (Contribution

margin ratio)

Contribution margin per unitSelling price

Expressing CVP Relationships

• There are three methods related to CVP relationships:

1- The Equation method2-The contribution margin method3- The graph method

The Equation method

- - - = -

= x = x

Revenuesvariable

costs fixed costs operating income

Revenues selling price (SP)

quantity of units sold(Q)

Variable cost Variable cost per unit(VCU) quantity of units sold

The Equation method

x - x - = Selling price

quantity of units

sold

variable cost per

unit

quantity of units

sold

fixed incom

e

operating income

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

Cost-Volume-Profit Assumptionsand 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.

Cost-Volume-Profit Assumptionsand 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

Break-Even Point Concept(BEP)

Chapter 3 15

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

example1:

Emma Frost sells each unit of product “GAMT”at $ 200. 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.

Solution

By using the three methods

Chapter 3 17

1- The Equation method

x - x - =

Setting operating income equal SR 0. and denoting quantity of output units that must be sold by Q.

Selling price

quantity of units

sold

variable cost per

unit

quantity of units

sold

fixed incom

e

operating income

The Equation method

• per unit: 200X Q )- ($120 X Q) – $2000 = 0 $ 80 X Q= $2000 Q= $2000 / $80 = 25 units• Per revenues: 25 units x $ 200 selling price = $ 5000

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

Quantity of units sold

Fixed costs

Operating income

breakeven number of units

fixed costs contribution margin per unit

contribution margin method

• Per units: breakeven units = 2,000 = 25 units• $80 per unit

• Breakeven revenues= 25 units x $200 per unit = $ 5000

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 = $5000 40%

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?

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

2-contribution margin method

=

Quantity of unites require to be sold= $2000 + $1200 $80 per unit =40 units

Quantity of units to be sold= Fixed costs + Target operating ncome

Contribution Margin per unit

Proof:

• Revenue $200per unit x 40 units = $8,000Variable costs $120 per unit x 40 units= 4800Contribution margin $80 per unit x 40 units = 3200Fixed costs 2000operating income $1200

Target Net Income and Income Taxes

Net Income= Operating Income – Income TaxesFor 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

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 = $ 1600 1 – 0.40Proof: Target operating income $1600 tax at 40% (0.40 x $ 1600) 640 Target net income 960

Target Net Income and Income Taxes

Quantity of units require to be sold = fixed costs + Target operating income contribution margin per unit = $2000 + $1600 = 45 units $80 per unit

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. = -

= -

Margin of safety

Budget revenues Breakeven revenues

Margin of safety in units

Budget sales quantity

Breakeven quantity

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.