ch3.ppt

CHAPTER 3

Cost-Volume-Profit

(CVP)

Analysis

3-2To accompany Cost Accounting 12e, by Horngren/Datar/Foster. Copyright © 2006 by Pearson Education. All rights reserved.

Cost-Volume-Profit Analysis

Cost-volume-profit (CVP) analysis examines the effects of changes of costs and volume on a company’s profits.

CVP analysis illustrates the profits from alternatives, hence guides managers’ planning.


Learning Objective 1

Understand the assumptions

underlying CVP analysis.


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 produced and sold.

2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.



3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range (and time period).

4. The unit selling price, unit variable costs, and fixed costs are known and constant.



5. The analysis either covers a single product or assumes that the sales mix when multiple products are sold will remain constant as the level of total units sold changes.

6. All revenues and costs can be added and compared without taking into account the time value of money.


Basic Formulae

TotalOperating Revenues Variable Fixed

Income from Costs CostsOperations

=

Net Operating IncomeIncome Income Taxes=

Total Cost PretaxOperating Revenues of Operating

Income from Goods ExpensesOperations Sold

=


Contribution Income Statement

A contribution income statement is an income statement with costs classified by behavior, rather than character.

Variable costs are grouped and subtracted from revenues.

Fixed costs are grouped and subtracted from contribution margin.


CVP Income Statement - ExampleCVP Income Statement - ExampleVargo Video Company produces DVD players. Relevant data for June 2008:

Unit selling price of DVD player $500Unit variable costs $300Total monthly fixed costs $200,000Units sold 1,600

LO 5: Indicate what contribution margin is and how it can be expressed.LO 5: Indicate what contribution margin is and how it can be expressed.



Explain the features

of CVP analysis.


Essentials of Cost-Volume-Profit(CVP) Analysis Example

Assume that the Mary can purchase software packages for $120 from a computer software wholesaler with a privilege of returning all unsold packages and receiving a full $120 refund per package within one year.

The average selling price per package is $200 and total fixed costs amount to $2,000.



Case1:How much revenue will the business receive if 5 units are sold?

5 × $200 = $1,000

How much variable costs will the business incur?

5 × $120 = $600

Operating income: $1,000 – 600 – 2,000 = ($1,600)



Case2:How much revenue will the business receive if 40 units are sold?

40 × $200 = $8,000

How much variable costs will the business incur?

40 × $120 = $4,800

Operating income: $8,000 – 4,800 – 2,000 = $1,200


Essentials of Cost-Volume-Profit(CVP) Analysis ExampleCompare Case1 and Case2: The only numbers that change from selling different quantities are total revenues and total variable costs.

Contribution margin: the difference between total revenues and total variable costs.

Contribution margin per unit: the difference between selling price and variable cost per unit.(or, Total contribution margin divided by total quantity)



Case 1: Contribution margin=1,000 –600=400

Contribution margin per unit=400 / 5=80

Case 2:Contribution margin=8,000–4,800 =3,200

Contribution margin per unit=3,200 /40 =80



Contribution margin percentage (contribution margin ratio) is the contribution margin per unit divided by the selling price (or, contribution margin divided by revenues).

Case 1: 400/1,000=40%

Case 2: 3,200/8,000=40%



If the business sells 50 packages, revenues will be $10,000 and contribution margin would equal 40% × $10,000 = $4,000

Contribution margin = Contribution margin per unit × Number of units sold

= Contribution margin percentage × Revenues



Determine the breakeven point

and output level needed to achieve

a target operating income using

the equation, contribution margin,

and graph methods.


Breakeven Point

Sales Variablecosts

Fixedcosts– =

Total revenues = Total costs

Breakeven point (BEP): quantity of output sold at which total revenues equal total costs, i.e. operating income is $0.


Breakeven Analysis

Breakeven analysis: Process to find the Breakeven analysis: Process to find the break-even point

Breakeven point can be expressed either in sales units or in sales dollars


Abbreviations

SP = Selling price

VCU = Variable cost per unit

CMU = Contribution margin per unit

CMR = Contribution margin percentage

FC = Fixed costs

Q = Quantity of output units sold(and manufactured)


Contribution Margin

Contribution Margin equals sales less variable costs CM = S – VC

Contribution Margin per unit equals unit selling price less variable cost per unit CMU = SP – VCU

or CMU=CM / Q


Contribution Margin

Contribution Margin also equals contribution margin per unit multiplied by the number of units sold CM = CMU x Q

Contribution Margin Ratio (percentage) equals contribution margin per unit divided by selling price CMR = CMU ÷ SP

or CMR=CM / S


Abbreviations

OI = Operating income

TOI = Target operating income

TNI = Target net income


Breakeven Analysis: Equation Method

$200Q – $120Q – $2,000 = 0$80Q = $2,000

Q = $2,000 ÷ $80 = 25 units

Let Q = number of units to be sold to break even

SP × Q– VCU× Q – FC = OI


Breakeven Analysis: Contribution Margin Method

A simple manipulation of the last equation, and setting OI to zero will result in the Breakeven Point (quantity): BEQ = FC ÷ CMU

At this point, a firm has no profit or loss.



Sales – VC – FC = OI (SP x Q) – (VCU x Q) – FC = OI Q (SP – VCU) – FC = OI Q (CMU) – FC = OI


Breakeven Analysis: Contribution Margin Method If per-unit values are not available, the

Breakeven Point may be restated in its alternate format:

BE Sales = FC ÷ CMR (Breakeven point in dollar)

The break-even point can be computed using either contribution margin per unit (breakeven units) or contribution margin ratio (breakeven dollars).



$2,000 ÷ $80 = 25 units

$2,000 ÷ 40% = $5,000


A CVP graph shows costs, volume and profits.Used to visually find the break-even pointTo construct a CVP graph:

1.Plot the total sales line starting at the zero activity level

2.Plot the total fixed cost using a horizontal line 3.Plot the total cost line (starts at the fixed-cost

line at zero activity

4.Determine the break-even point from the intersection of the total cost line and the total sales line

Breakeven Analysis: Graph Method


Breakeven Analysis: Graph Method

Total costs line

Operating loss area

Breakeven point = 25 units

$10,000y

$8,000

$6,000

$5,000

$4,000

$2,000

Dol

lars

10 20 25 30 40 50

x

Units Sold

Total costs line

Operating loss area

Operating income area

Breakeven point = 25 units

Total revenues line

Operating income

Variable costs

Fixed costs


Gossen Company is planning to sell 200,000 pliers for $4 per unit. The contribution margin ratio is 25%. If Gossen will break even at this level of sales, what are the fixed costs?

a. $100,000.

b. $160,000.

c. $200,000.

d. $300,000.

Review


CVP Analysis: Profit Planning

Level of sales necessary to achieve a specified income, This level can be expressed either in sales units or in sales dollars.

With a simple adjustment, the Breakeven Point formula can be modified to become a Profit Planning tool Profit is now reinstated to the BE formula, changing it

to a simple sales volume equation Q = (FC + OI)

CMU

or S = (FC+OI)/CMR


CVP Analysis: Target Operating Income

Assume that Mary wants to have anoperating income of $1,200.

How many packages must be sold?

($2,000 + $1,200) ÷ $80 = 40

What dollar sales are needed to achieve this income?

($2,000 + $1,200) ÷ 40% = $8,000



Understand how income

taxes affect CVP analysis.


CVP and Income Taxes

After-tax profit can be calculated by: OI x (1-Tax Rate) = NI

NI can substitute into the profit planning equation through this form: OI = I I NI I

(1-Tax Rate)


Target Net Incomeand Income Taxes Example

Mary would like to earnnet income of $960.

The tax rate is 40%.

What is the target operating income?

Target operating income= Target net income ÷ (1 – tax rate)

TOI = $960 ÷ (1 – 0.40) = $1,600



How many units must be sold?

Revenues – Variable costs – Fixed costs= Target net income ÷ (1 – tax rate)

$200Q – $120Q – $2,000 = $960 ÷ 0.60

$80Q = $1,600 + $2,000

Q = $3,600 ÷ $80 = 45 packages



Proof:Revenues: 45× $200 $9,000Variable costs: 45× $120 5,400Contribution margin $3,600Fixed costs 2,000Operating income 1,600Income taxes: $1,600 × 40% 640Net income $ 960


The mathematical equation for computing required sales to obtain target net income is:

Required sales =

a. Variable costs + Target net income.

b. Variable costs + Fixed costs + Target net income.

c. Fixed costs + Target net income.

d. No correct answer is given.

Review



Explain CVP analysis

in decision making and

how sensitivity analysis helps

managers cope with uncertainty.


Using CVP Analysis Example: Advertising Decision

Suppose the Mary anticipates selling 40 packages.

Mary is considering an advertising campaign that would cost $500.

It is anticipated that the advertising will increase sales by 10% to 44 units.

Should the business advertise?


Using CVP Analysis Example: Advertising Decision

40 units sold with no advertising:

Contribution margin $3,200Fixed costs 2,000Operating income $ 1,200

44 units sold with advertising:

Contribution margin $3,520Fixed costs 2,500Operating income $ 1,020


Using CVP Analysis Example: Reducing Selling Price

Instead of advertising, Mary is considering reducing the selling price to $175 per package.

It is anticipated that this will increase sales to 50 units, and at this quantity, the purchase price will decrease to $115.

Should Mary decrease the selling price per package to $175?


Using CVP Analysis Example: Reducing Selling Price

40 packages sold with no change in the selling price:

Operating income = $1,200

50 packages sold at a reduced selling price:

Contribution margin: (50 × $60) $3,000Fixed costs 2,000Operating income $ 1,000


Sensitivity Analysis

A “what-if” technique that managers use to examine how the outcome will change if the original predicted data are not achieved or if an underlying assumption changes.

“What” happens to profit “if”: Selling price changes Volume changes Cost structure changes

Variable cost per unit changes Fixed cost changes


Margin of Safety

Margin of safety: the amount by which budgeted (actual) revenues exceed breakeven revenues.

An indicator of risk “what-if” question: if budgeted revenues are above

breakeven and drop, how far can they fall below budget before the breakeven point is reached.

The higher the margin of safety, the less likely it is to suffer a loss.

Margin of safety percentage=

Margin of safety/ budgeted (actual) revenues


Sensitivity Analysis andUncertainty: Margin of Safety

Assume that Mary can sell 40 packages. Fixed costs are $2,000

Contribution margin ratio is 40%.

Revenues at breakeven $2,000 ÷ .40 = $5,000.

Margin of safety= 40 ×200-5,000=3,000Margin of safety percentage = 3,000/8,000=37.5%


Marshall Company had actual sales of $600,000 when break-even sales were $420,000. What is the margin of safety ratio?

a. 25%.

b. 30%.

c. 33 1/3%.

d. 45%.

Review



Use CVP analysis to plan

fixed and variable costs.


Alternative Fixed/Variable CostStructures

CVP sensitivity analysis highlights the risks and returns as fixed costs are substituted for variable costs in cost structure.


Alternative Fixed/Variable CostStructures Example

If 40 units are sold, no difference in operating income.If 20 units are sold, option 1 leads to a loss.If 60 units are sold, option 1 shows an operating income of $2,800, greater than option 2 and 3.

Suppose that Mary has the following options:Option 1: $2,000 fixed costOption 2: $800 fixed cost plus 15% of revenuesOption 3: 25% of revenues with no fixed cost


Alternative Fixed/Variable CostStructures Example

Risks and returns among option 1 to 3:Option1: highest risk and return.Option3: lowest risk and return.

Implication to managers’ decision of cost structure: Managers’ confidence in level of demandManagers’ willingness to risk loss


Operating Leverage

Operating leverage describes the effects thatfixed costs have on changes in operatingincome as changes occur in units sold.

Organizations with a high proportion of fixedcosts have high operating leverage.

Degree of operating leverage= Contribution margin ÷ Operating income


Operating Leverage Example

What is the degree of operating leverageat the sales of 40 units for the 3 options?

Option 1 2 3Contribution margin $3,200 $2,000 $1,200Operating income $ 1,200 $1,200 $1,200

Degree of operating leverage 2.67 1.67 1



What is the degree of operating leverageat the sales of 60 units for the 3 options?

Option 1 2 3Contribution margin $4,800 $3,000 $1,800Operating income $ 2,800 $2,200 $1,800

Degree of operating leverage 1.71 1.36 1



Managers must monitor their operating leverage carefully. e.g. U.S. Airways, United Airlines

How to avoid the risk:Fixed cost: a double-edged sword



Apply CVP analysis to a company

producing different products.


Effects of Sales-Mix on CVP

The formulae presented to this point have assumed a single product is produced and sold

A more realistic scenario involves multiple products sold, in different volumes, with different costs

For simplicity’s sake, only two products will be presented, but this could easily be extended to even more products

Sales mix: the quantities of various products or services that make up the total sales of a company.



Breakeven units

Weighted CMU1 x Q1 + CMU2 x Q2 Average CMU

=Total Units Sold (Q) for Both Products

Multi-Product Fixed CostsBEP Weighted Average CMU

=



Break even revenues

Weighted

Average CMR=

Total Revenues

Total CM

Multi-Product Fixed CostsBER Weighted Average CMR

=


Effects of Sales Mix on Income

Sales mix :

1 2Sales price $200 $100Variable costs/unit 120 70Contribution margin/unit $80 $30Contribution margin ratio 40% 30%Units sold 60 40Fixed cost $4,500



What is the weighted-average budgeted contribution margin per unit?

(80 ×60 + 30 ×40)/(60+40) =$60

What is the breakeven point?

$4,500/60=75 units



What is the breakeven in dollars?

Total CM:$80*60+$30*40=$6000Total revenues: $200*60+$100*40=$16,000Weighted-average CMR=37.5%Breakeven revenues: $4,500/37.5%=$12,000

There is no unique breakeven point if sales mix changes



Adapt CVP analysis to situations

in which a product has more

than one cost driver.


Multiple Cost Drivers

Variable costs may arise from multiple cost drivers or activities. A separate variable cost needs to be calculated for each driver.


Multiple Cost Drivers Example

Suppose that Mary will incur an additionalcost of $10 for preparing documents associated

with the sale of software to customers.

Assume that the business sells 40packages to 15 different customers.

The cost structure depends on two cost drivers:

1. Number of units 2. Number of customers



Revenues: 40 × $200 $8,000Variable costs:

Software: 40 × $120 4,800Documents: 15 × $10 150Total 4,950

Contribution margin 3,050Fixed costs 2,000Operating income $ 1,050

What is the operating income from this sale?



Assume 40 packages are sold to 40 different customers.

Revenues: 40 × $200 $8,000Variable costs:

Software: 40 × $120 4,800Documents: 40 × $10 400Total 5,200

Contribution margin 2,800Fixed costs 2,000Operating income $ 800


Multiple Cost Drivers

There is no unique breakeven point when there are multiple cost drivers.



Distinguish between

contribution margin

and gross margin.


Contribution Margin versusGross Margin

Contribution income statement emphasizescontribution margin.

Financial accounting income statementemphasizes gross margin.

Contribution margin=Revenues – All variable costsGross margin=Revenues – Costs of goods sold


Contribution Margin vs.Gross Margin

Revenues: $200Less: Variable Cost of Goods Sold $120 Variable Operating Costs 45 165Contribution Margin 35Fixed Operating Costs 20Operating Income $15

Contribution Margin Income Statement(Internal-Use Only)

Revenues: $200Less: Cost of Goods Sold $120

Gross Margin (Profit) 80Fixed & Variable Operating Costs 65Operating Income $15

Financial Accounting Income StatementGAAP - Based

Merchandising sector


Contribution Margin versusGross Margin

Revenues: $1,000Less: Variable manufacturing costs $250Variable nonmanufacturing costs 270 520Contribution Margin 480Fixed manufacturing Costs 160Fixed nonmanufacturing Costs 138 298Operating Income $182

Contribution Margin Income Statement(Internal-Use Only)

Revenues: $1,000Less: Cost of Goods Sold(250+160) $410

Gross Margin (Profit) 590Nonmanufacturing costs(270+138) 408Operating Income $182

Financial Accounting Income StatementGAAP - Based

Manufacturing sector