cvp relationship

Introduction to Introduction to Cost-Volume Cost-Volume RelationshipsRelationships

Variable and Fixed Cost Variable and Fixed Cost BehaviorBehavior

A A variable costvariable cost changes in direct changes in direct

proportion to changes proportion to changes in the cost-driver level.in the cost-driver level.

A A fixed costfixed cost is is not immediately not immediately

affected by changes affected by changes in the cost-driver.in the cost-driver.

Think of variable Think of variable costs on a per-unit basis.costs on a per-unit basis.

The per-unit variable The per-unit variable cost remains unchanged cost remains unchanged regardless of changes in regardless of changes in

the cost-driver.the cost-driver.

Think of fixed costs Think of fixed costs on a total-cost basis.on a total-cost basis.

Total fixed costs remain Total fixed costs remain unchanged regardless of unchanged regardless of

changes in the cost-driver.changes in the cost-driver.

Relevant RangeRelevant Range

The relevant range is the limitThe relevant range is the limitof cost-driver activity level within which aof cost-driver activity level within which a

specific relationship between costsspecific relationship between costsand the cost driver is valid.and the cost driver is valid.

Even within the relevant range, a fixed Even within the relevant range, a fixed cost remains fixed only over a given cost remains fixed only over a given

period of time Usually the budget period.period of time Usually the budget period.

Fixed Costs and Relevant RangeFixed Costs and Relevant Range

20 40 60 80 10020 40 60 80 100

$115,000$115,000 100,000100,000

60,00060,000

Total Cost-Driver Activity in Thousands Total Cost-Driver Activity in Thousands of Cases per Monthof Cases per Month

Tota

l Mon

thly

Fix

ed

Tota

l Mon

thly

Fix

ed

Cost

sCo

sts

Relevant rangeRelevant range$115,000$115,000 100,000100,000

60,00060,000

20 40 60 80 10020 40 60 80 100

CVP ScenarioCVP Scenario

Per Unit Percentage of Per Unit Percentage of Sales Sales Selling priceSelling price $1.50 $1.50 100%100%Variable cost of each itemVariable cost of each item 1.20 1.20 8080Selling price less variable costSelling price less variable cost $ .30 $ .30 20%20%

Monthly fixed expenses:Monthly fixed expenses: RentRent $3,000 $3,000 Wages for replenishing andWages for replenishing and servicingservicing 13,500 13,500 Other fixed expenses Other fixed expenses 1,500 1,500Total fixed expenses per month $ 18,000Total fixed expenses per month $ 18,000

Cost-volume-profit (CVP) analysis is the study of the effects of output Cost-volume-profit (CVP) analysis is the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit).volume on revenue (sales), expenses (costs), and net income (net profit).

Break-Even PointBreak-Even Point

The break-even point is the level of sales at which The break-even point is the level of sales at which revenue equals expenses and net income is zero.revenue equals expenses and net income is zero.

Sales Sales - Variable expenses- Variable expenses- Fixed expenses- Fixed expensesZero net income (break-even point)Zero net income (break-even point)

Contribution Margin MethodContribution Margin Method

$18,000 fixed costs ÷ $.30$18,000 fixed costs ÷ $.30= 60,000 units (break even)= 60,000 units (break even)

Contribution marginContribution margin Per UnitPer Unit

Selling priceSelling price $1.50 $1.50 Variable costsVariable costs 1.20 1.20 Contribution marginContribution margin $ .30 $ .30

Contribution margin ratioContribution margin ratioPer UnitPer Unit % %

Selling priceSelling price 100 100 Variable costsVariable costs .80 .80 Contribution marginContribution margin .20 .20

Contribution Margin MethodContribution Margin Method

$18,000 fixed costs$18,000 fixed costs÷ 20% (contribution-margin percentage)÷ 20% (contribution-margin percentage)

= $90,000 of sales to break even= $90,000 of sales to break even

60,000 units × $1.50 = $90,00060,000 units × $1.50 = $90,000in sales to break evenin sales to break even

Equation MethodEquation Method

Sales – variable expenses – fixed expenses = net incomeSales – variable expenses – fixed expenses = net income$1.50N – $1.20N – $18,000 = 0$1.50N – $1.20N – $18,000 = 0

$.30N = $18,000$.30N = $18,000N = $18,000 ÷ $.30N = $18,000 ÷ $.30N = 60,000 UnitsN = 60,000 Units

Let N = number of unitsLet N = number of unitsto be sold to break even.to be sold to break even.

Equation MethodEquation Method

S – .80S – $18,000 = 0S – .80S – $18,000 = 0.20S = $18,000.20S = $18,000

S = $18,000 ÷ .20S = $18,000 ÷ .20S = $90,000S = $90,000

Let S = sales in dollarsLet S = sales in dollarsneeded to break even.needed to break even.

Shortcut formulas:Shortcut formulas:Break-even volume in units = Break-even volume in units = fixed expensesfixed expenses unit contribution marginunit contribution margin

Break-even volume in sales = Break-even volume in sales = fixed expensesfixed expenses contribution margin ratio contribution margin ratio

Cost-Volume-Profit Graph

18,000 30,000

90,000

120,000 138,000

$150,000

0 10 20 30 40 50 60 70 80 90 100

Units (thousands)

Dol

lar

s

60,000 Total

Expenses

SalesNet Income

Area

Break-Even Point 60,000 units or

$90,000Net Loss Area

A

C

D

BFixed

Expenses

Variable Expense

s

Net Income

Target Net ProfitTarget Net Profit

Managers use CVP analysis Managers use CVP analysis to determine the total sales, to determine the total sales, in units and dollars, needed in units and dollars, needed To reach a target net profit.To reach a target net profit.

Target sales Target sales – – variable expenses variable expenses

– – fixed expenses fixed expenses target net incometarget net income

$1,440 per month $1,440 per month is the minimumis the minimum

acceptable net income.acceptable net income.

Target sales volume in units =Target sales volume in units =(Fixed expenses + Target net income)(Fixed expenses + Target net income)

÷ Contribution margin per unit÷ Contribution margin per unit

($18,000 + $1,440) ÷ $.30 = 64,800 units($18,000 + $1,440) ÷ $.30 = 64,800 units


Selling priceSelling price $1.50 $1.50 Variable costsVariable costs 1.20 1.20 Contribution margin per unitContribution margin per unit $ .30 $ .30

Target sales dollars = sales price X sales volume in unitsTarget sales dollars = sales price X sales volume in unitsTarget sales dollars = $1.50 X 64,800 units = $97,200.Target sales dollars = $1.50 X 64,800 units = $97,200.

Sales volume in dollars = Sales volume in dollars = 18,000 + $1,44018,000 + $1,440 = $97,200 = $97,200 .20.20


Target sales volume in dollars = Target sales volume in dollars = Fixed expenses + target net incomeFixed expenses + target net incomecontribution margin ratiocontribution margin ratio

Contribution margin ratioContribution margin ratioPer UnitPer Unit % %

Selling priceSelling price 100 100 Variable costsVariable costs .80 .80 Contribution marginContribution margin .20 .20

Scenario 1: Scenario 1: Break-even Analysis SimplifiedBreak-even Analysis Simplified• When total revenue is equal to total cost When total revenue is equal to total cost

the process is at the break-even point.the process is at the break-even point.

TC = TRTC = TR

Break-even Analysis:Break-even Analysis: Comparing different variables Comparing different variables• Company XYZ has to choose between Company XYZ has to choose between

two machines to purchase. The selling two machines to purchase. The selling price is $10 per unit.price is $10 per unit.

• Machine A: annual cost of $3000 with Machine A: annual cost of $3000 with per unit cost (VC) of $5.per unit cost (VC) of $5.

• Machine B: annual cost of $8000 with Machine B: annual cost of $8000 with per unit cost (VC) of $2.per unit cost (VC) of $2.

Break-even analysis:Break-even analysis:Comparative analysis Part 1Comparative analysis Part 1• Determine break-even point for Machine Determine break-even point for Machine

A and Machine B.A and Machine B.

• Where: V = FCWhere: V = FC SP - VCSP - VC

Break-even analysis:Break-even analysis:Part 1, Cont.Part 1, Cont.Machine A: Machine A:

vv = $3,000= $3,000 $10 - $5$10 - $5= 600 units= 600 units

Machine B:Machine B: vv = $8,000= $8,000 $10 - $2$10 - $2 = 1000 units= 1000 units

Part 1: ComparisonPart 1: Comparison• Compare the two results to determine Compare the two results to determine

minimum quantity sold.minimum quantity sold.

• Part 1 shows:Part 1 shows:– 600 units are the minimum.600 units are the minimum.– Demand of 600 you would choose Demand of 600 you would choose

Machine A. Machine A.

Part 2: ComparisonPart 2: ComparisonFinding point of indifference between Finding point of indifference between

Machine A and Machine B will give the Machine A and Machine B will give the quantity demand required to select quantity demand required to select Machine B over Machine A. Machine B over Machine A.

Machine A Machine A = Machine B= Machine B FC + VCFC + VC == FC + VC FC + VC$3,000 + $5$3,000 + $5 QQ = $8,000 + $2Q= $8,000 + $2Q

$3Q$3Q = $5,000= $5,000 QQ = 1667= 1667

Part 2: ComparisonPart 2: ComparisonCont.Cont.• Knowing the point of indifference we will Knowing the point of indifference we will

choose:choose:

• Machine A when quantity demanded is Machine A when quantity demanded is between 600 between 600 and 1667.and 1667.

• Machine B when quantity demanded Machine B when quantity demanded exceeds 1667.exceeds 1667.

Part 2: ComparisonPart 2: ComparisonGraphically displayedGraphically displayedDolla$Dolla$21,00021,00018,00018,00015,00015,00012,00012,000 9,000 9,000 6,000 6,000 3,000 3,000 00

500 1000 1500 2000 2500 3000500 1000 1500 2000 2500 3000 QuantityQuantity

Machine AMachine A

Machine BMachine B

Part 2: ComparisonPart 2: ComparisonGraphically displayed Cont.Graphically displayed Cont.Dolla$Dolla$21,00021,00018,00018,00015,00015,00012,00012,000 9,000 9,000 6,000 6,000 3,000 3,000 Point of indifferencePoint of indifference 00

500 1000 1500 2000 2500 3000500 1000 1500 2000 2500 3000 QuantityQuantity

Machine AMachine A

Machine BMachine B

Exercise 1:Exercise 1:• Company ABC sell widgets for $30 a Company ABC sell widgets for $30 a

unit. unit.

• Their fixed cost is$100,000Their fixed cost is$100,000

• Their variable cost is $10 per unit. Their variable cost is $10 per unit.

• What is the break-even point using the What is the break-even point using the basic algebraic approach?basic algebraic approach?

Exercise 1:Exercise 1:AnswerAnswer

Revenues – Variable cost - Fixed cost = OIRevenues – Variable cost - Fixed cost = OI

(USP x Q) – (UVC x Q) – FC (USP x Q) – (UVC x Q) – FC = OI= OI $30Q - $10Q – $100,00 $30Q - $10Q – $100,00 = $ 0.00= $ 0.00

$20Q $20Q = $100,000= $100,000 Q Q = 5,000= 5,000

Exercise 2:Exercise 2:• Company DEF has a choice of two Company DEF has a choice of two

machines to purchase. They both make machines to purchase. They both make the same product which sells for $10.the same product which sells for $10.

• Machine A has FC of $5,000 and a per unit Machine A has FC of $5,000 and a per unit cost of $5.cost of $5.

• Machine B has FC of $15,000 and a per Machine B has FC of $15,000 and a per unit cost of $1.unit cost of $1.

• Under what conditions would you select Under what conditions would you select Machine A?Machine A?

Exercise 2:Exercise 2:AnswerAnswerStep 1: Break-even analysis on both options.Step 1: Break-even analysis on both options.Machine A: Machine A:

vv = $5,000= $5,000 $10 - $5$10 - $5= 1000 units= 1000 units

Machine B:Machine B: vv = $15,000= $15,000 $10 - $1$10 - $1 = 1667 units= 1667 units

Exercise 2:Exercise 2:Answer Cont.Answer Cont.

Machine A Machine A = Machine B= Machine B FC + VCFC + VC == FC + VC FC + VC$5,000 + $5$5,000 + $5 QQ = $15,000 + $1Q= $15,000 + $1Q

$4Q$4Q = $10,000= $10,000 QQ = 2500= 2500

• Machine A should be purchased if Machine A should be purchased if expected demand is between 1000 and expected demand is between 1000 and 2500 units per year.2500 units per year.

Operating LeverageOperating Leverage

Operating leverage: a firm’s ratio of fixed costs to variable costs. Operating leverage: a firm’s ratio of fixed costs to variable costs.

Margin of safety = planned unit sales – break-even sales Margin of safety = planned unit sales – break-even sales How far can sales fall below the planned level before losses occur?How far can sales fall below the planned level before losses occur?

Highly leveraged firms have high fixed costs and low variable costs. Highly leveraged firms have high fixed costs and low variable costs. A small change in sales volume = a large change in net income.A small change in sales volume = a large change in net income.

Low leveraged firms have lower fixed costs and higher variable costs. Low leveraged firms have lower fixed costs and higher variable costs. Changes in sales volume will have a smaller effect on net income.Changes in sales volume will have a smaller effect on net income.

Contribution MarginContribution Marginand Gross Marginand Gross Margin

Sales price – Cost of goods sold = Gross marginSales price – Cost of goods sold = Gross margin

Sales price - all variable expenses = Contribution marginSales price - all variable expenses = Contribution margin

Per UnitPer UnitSelling priceSelling price $1.50$1.50Variable costs (acquisition cost)Variable costs (acquisition cost) 1.20 1.20Contribution margin and Contribution margin and gross margin are equalgross margin are equal $ .30$ .30

Contribution Margin and Gross Contribution Margin and Gross MarginMargin

Contribution Gross Contribution Gross Margin MarginMargin Margin Per UnitPer Unit Per Unit Per Unit

SalesSales $1.50$1.50 $1.50 $1.50 Acquisition cost of unit soldAcquisition cost of unit sold 1.201.20 1.20 1.20 Variable commissionVariable commission .12 .12Total variable expense Total variable expense $1.32$1.32Contribution marginContribution margin .18 .18 Gross marginGross margin $.30 $.30

Suppose the firm had to pay a commission of $.12Suppose the firm had to pay a commission of $.12 per unit sold. per unit sold.

Sales Mix AnalysisSales Mix Analysis

Sales mix is the relative proportions orSales mix is the relative proportions orcombinations of quantities of productscombinations of quantities of products

that comprise total sales.that comprise total sales.


Ramos Company ExampleRamos Company Example

Sales in unitsSales in units 300,000300,000 75,000 75,000 375,000 375,000Sales @ $8 and $5Sales @ $8 and $5 $2,400,000 $2,400,000$375,000$375,000 $2,775,000$2,775,000Variable expensesVariable expenses @ $7 and $3@ $7 and $3 2,100,000 2,100,000 225,000 225,000 2,325,000 2,325,000 Contribution marginsContribution margins @ $1 and $2@ $1 and $2 $ 300,000$ 300,000$150,000$150,000 $ 450,000$ 450,000Fixed expensesFixed expenses 180,000 180,000 Net incomeNet income $ 270,000 $ 270,000

WalletsWallets(W)(W)

Key CasesKey Cases(K)(K) TotalTotal


Break-even point for a constant sales mix Break-even point for a constant sales mix of 4 units of W for every unit of K.of 4 units of W for every unit of K.

sales – variable expenses - fixed expenses = zero net incomesales – variable expenses - fixed expenses = zero net income[$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0 [$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0

32K + 5K - 28K - 3K - 180,000 = 032K + 5K - 28K - 3K - 180,000 = 06K = 180,000 6K = 180,000

K = 30,000K = 30,000W = 4K = 120,000 W = 4K = 120,000

Let K = number of units of K to break even, andLet K = number of units of K to break even, and4K = number of units of W to break even.4K = number of units of W to break even.


If the company sells only key cases:If the company sells only key cases:break-even point = break-even point = fixed expensesfixed expenses

contribution margin per unitcontribution margin per unit = = $$180,000180,000

$2$2 = 90,000 key cases = 90,000 key cases

If the company sells only wallets:If the company sells only wallets:break-even point = break-even point = fixed expensesfixed expenses

contribution margin per unitcontribution margin per unit = = $$180,000180,000

$1$1 = 180,000 wallets = 180,000 wallets


Suppose total sales Suppose total sales were equal to the were equal to the

budget of 375,000 units.budget of 375,000 units.

However, Ramos sold However, Ramos sold only 50,000 key casesonly 50,000 key casesAnd 325,000 wallets.And 325,000 wallets.What is net income?What is net income?


Ramos Company ExampleRamos Company Example

Sales in unitsSales in units 325,000 50,000 325,000 50,000 375,000 375,000 Sales @ $8 and $5Sales @ $8 and $5 $2,600,000 $2,600,000 $250,000 $250,000 $2,850,000 $2,850,000 Variable expensesVariable expenses @ $7 and $3@ $7 and $3 2,275,000 2,275,000 150,000 150,000 2,425,000 2,425,000 Contribution marginsContribution margins @ $1 and $2@ $1 and $2 $ 325,000 $ 325,000 $100,000 $100,000 $ 425,000 $ 425,000 Fixed expensesFixed expenses 180,000 180,000 Net incomeNet income $ 245,000 $ 245,000

WalletsWallets(W)(W)

Key CasesKey Cases(K)(K) TotalTotal

cvp relationship

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