emba 5403 fall 2010 cost-volume-profit relationships

EMBA 5403 Fall 2010

Cost-Volume-Profit Relationships

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Cost Estimation 1

Constant 250Std Err of Y Est 299.304749934466R squared 0.944300518134715No. of Observations 5Degrees of Freedom 3

X Coefficient(s) 6.75Std Err of Coef. 0.9464847243

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Estimation (continued)

The results gives rise to the following equation:

Utility Costs = £250 + (£6.75 x # of units produced)

R2 = .944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable.

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Estimation (continued)

Given:

*T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale test and 3 degrees of freedom)

*Standard error of estimate for this sample at the 95% confidence level is 598.6

The confidence interval for 300 units is:

TC = £250 + 6.75 (300) + (3.182 x £598.6)

= £2275 + £1911

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Cost Estimation Example 2 In each month, Exclusive Billiards produces between 4 to

10 pool tables. The plant operates on 40-hr shift to produce up to seven tables. Producing more than seven tables requires the craftsmen to work overtime. Overtime work is paid at a higher hourly wage. The plant can add overtime hours and produce up to 10 tables per month. The following table contains the total cost of producing between 4 and 10 pool tables.

Required: a. compute average cost per pool table for 4 to 10 tables Estimate fixed costs per month.

Pool Tables Total Cost4 628005 660006 692007 724008 758009 79200

10 82600

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Cost-Volume-Profit Analysis Examines the behavior of total revenues, total costs, and

operating income as changes occur in the output level, selling price, variable costs or fixed costs

helpful to understand the relationship among variable costs, fixed costs and profit

Assumptions of CVP Analysis1. revenues change in relation to production and sales2. costs can be divided in variable and fixed categories and fixed

element constant over the relevant range3. revenues and costs behave in a linear fashion4. costs and prices are known 5. if more than one product exists, the sales mix is constant6. inventories stay at the same level7. we can ignore the time value of money

7

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Contribution Margin Contribution margin is equal to the difference between

total revenue and total variable costs

Contribution margin per unit= Selling price - Variable cost per unit

Contribution margin percentage= Contribution margin per unit / selling price per unit

Pages 68 - 69

Revenue $200 $400 100%Variable costs 120 240 60%Contribution margin $80 $160 40%

Total forPer Unit 2 units %

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Contribution Margin Income Statement

Packages Sold0 1 2 25 40

Revenue $0 $200 $400$5,000 $8,000

Variable costs 0 120 240 3,000 4,800

Contribution margin 0 80 160 2,000 3,200

Fixed costs 2,000 2,000 2,000 2,000 2,000

Operating income$(2,000)$(1,920)$(1,840) $0 $1,200

Income statement that groups line items by cost behaviour to highlight the contribution margin

Page 69

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Breakeven Point Quantity of output where total revenues equal total

costs Point where operating income equals zero

Breakeven point in units= Fixed costs / Contribution margin per unit= $2,000 / $80 = 25 units

Breakeven point in dollars= Fixed costs / contribution margin %= $2,000 / 40% = $5,000

Page 71

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Cost-Volume-Profit Graph

$10,000

$8,000

$6,000

$4,000

$2,000

$00 10 20 30 40 50

Units Sold

Total revenuesline

BreakevenPoint

25 units

Operatingincome

Operatingloss

Page 72

Total costsline

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Target Operating Income For most firms in the private sector, the main

objective is not to breakeven Convert after-tax desired net income to its

before-tax equivalent operating income

Target operating income= Target net income / (1 - tax rate)

Target Unit Sales= (Fixed costs + Target operating income)

/ Contribution margin per unitTarget Dollar Sales= (Fixed costs + Target operating income)

/ Contribution margin %

Pages 73 - 75

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Sensitivity Analysis

sensitivity analysis is a “what-if” technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes

What will happen to operating income if volume declines by 5%?

What will happen to operating income if variable costs increase by 10% per unit?

sensitivity analysis broadens management’s perspectives about possible outcomes

Pages 76 - 77

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Alternative Cost Structures

CVP helps managers assess the risks and potential benefits of adopting alternative cost structures

Pages 77 - 78

Example: Alternative rental arrangements

Option 320% Commission

Rev

Cost$

Units

Breakeven = 0 units

Option 2$1,400 Fixed Fee+ 5% Commission

Rev

Cost$

Units

Breakeven = 20 units

Option 1$2,000 Fixed Fee

Rev

Cost$

Units

Breakeven = 25 units

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Basics of Cost-Volume-Profit Analysis

CM is used first to cover fixed expenses. Any remaining CM

contributes to net operating income.

CM is used first to cover fixed expenses. Any remaining CM

contributes to net operating income.

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The Contribution Approach Sales, variable expenses, and contribution margin can

also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be

generated to cover fixed expenses and profit.

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The Contribution Approach

Each month Racing must generate at least $80,000 in total CM to break even.

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The Contribution ApproachIf Racing sells 400 units400 units in a month, it will be

operating at the break-even point.

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The Contribution ApproachIf Racing sells one more bike (401 401

bikesbikes), net operating income will increase by $200.

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The Contribution ApproachWe do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit.

If Racing sells If Racing sells 430 bikes, its 430 bikes, its

net income will net income will be $6,000.be $6,000.

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CVP Relationships in Graphic Form

The relationship among revenue, cost, profit and volume can be expressed graphically by

preparing a CVP graph. Racing developed contribution margin income statements at 300,

400, and 500 units sold. We will use this information to prepare the CVP graph.

Income 300 units

Income 400 units

Income 500 units

Sales 150,000$ 200,000$ 250,000$ Less: variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Less: fixed expenses 80,000 80,000 80,000 Net operating income (20,000)$ -$ 20,000$

Income 300 units

Income 400 units

Income 500 units

Sales 150,000$ 200,000$ 250,000$ Less: variable expenses 90,000 120,000 150,000 Contribution margin 60,000$ 80,000$ 100,000$ Less: fixed expenses 80,000 80,000 80,000 Net operating income (20,000)$ -$ 20,000$

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CVP Graph

Units

Dol

lars

In a CVP graph, In a CVP graph, unit volumeunit volume is is usually represented on the usually represented on the

horizontal (X) axishorizontal (X) axis and and dollarsdollars on on the the vertical (Y) axisvertical (Y) axis. .

In a CVP graph, In a CVP graph, unit volumeunit volume is is usually represented on the usually represented on the

horizontal (X) axishorizontal (X) axis and and dollarsdollars on on the the vertical (Y) axisvertical (Y) axis. .

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CVP Graph

Units

Dol

lars

Fixed Expenses

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CVP GraphD

olla

rs

Units

Fixed Expenses

Total Expenses

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CVP Graph

Fixed Expenses

Dol

lars Total Expenses

Total Sales

Units

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CVP GraphD

olla

rs

Units

Break-even pointBreak-even point(400 units or $200,000 in sales)(400 units or $200,000 in sales)

Break-even pointBreak-even point(400 units or $200,000 in sales)(400 units or $200,000 in sales)

Profit Area

Loss Area

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Contribution Margin Ratio

The contribution margin ratio is:

For Racing Bicycle Company the ratio is:

Total CMTotal sales

CM Ratio =

Each $1.00 increase in sales results in a total contribution margin increase of 40¢.

= 40%$80,000$200,000

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Or, in terms of units, the contribution margin ratio is:

For Racing Bicycle Company the ratio is:$200$500

= 40%

Unit CMUnit selling price

CM Ratio =

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400 Bikes 500 BikesSales 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 operating income -$ 20,000$

400 Bikes 500 BikesSales 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 operating income -$ 20,000$


A $50,000 increase in sales revenue A $50,000 increase in sales revenue results in a $20,000 increase in CM.results in a $20,000 increase in CM.

($50,000 × 40% = $20,000)($50,000 × 40% = $20,000)

A $50,000 increase in sales revenue A $50,000 increase in sales revenue results in a $20,000 increase in CM.results in a $20,000 increase in CM.

($50,000 × 40% = $20,000)($50,000 × 40% = $20,000)

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CONTRIBUTION MARGIN RATIO

CMR= CONTRIBUTION MARGIN RATIO = CM / SALES OR cmu/pVCR = 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?

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Quick Check

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch?

a. 1.319b. 0.758c. 0.242d. 4.139

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Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch?a. 1.319b. 0.758c. 0.242d. 4.139

Quick Check

Unit contribution marginUnit selling price

CM Ratio =

=($1.49-$0.36)

$1.49

=$1.13$1.49

= 0.758

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Changes in Fixed Costs and Sales Volume

What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?

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Changes in Fixed Costs and Sales Volume$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000$80,000 + $10,000 advertising = $90,000

Sales Sales increasedincreased by $20,000, but net operating by $20,000, but net operating income income decreaseddecreased by $2,000 by $2,000..

Sales Sales increasedincreased by $20,000, but net operating by $20,000, but net operating income income decreaseddecreased by $2,000 by $2,000..

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Changes in Fixed Costs and Sales Volume

The Shortcut Solution

Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net operating income (2,000)$

Increase in CM (40 units X $200) 8,000$ Increase in advertising expenses 10,000 Decrease in net operating income (2,000)$

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Change in Variable Costs and Sales VolumeWhat is the profit impact if Racing can use higher quality raw materials, thus

increasing variable costs per unit by $10, to generate an increase in unit sales

from 500 to 580?

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Change in Variable Costs and Sales Volume

580 units 580 units ×× $310 variable cost/unit = $179,800 $310 variable cost/unit = $179,800580 units 580 units ×× $310 variable cost/unit = $179,800 $310 variable cost/unit = $179,800

Sales Sales increaseincrease by $40,000, and net operating income by $40,000, and net operating income increasesincreases by $10,200 by $10,200..

Sales Sales increaseincrease by $40,000, and net operating income by $40,000, and net operating income increasesincreases by $10,200 by $10,200..

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Change in Fixed Cost, Sales Price and Volume

What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its advertising budget

by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month?

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Sales Sales increaseincrease by $62,000, fixed costs increase by by $62,000, fixed costs increase by $15,000, and net operating income $15,000, and net operating income increasesincreases by $2,000 by $2,000..

Sales Sales increaseincrease by $62,000, fixed costs increase by by $62,000, fixed costs increase by $15,000, and net operating income $15,000, and net operating income increasesincreases by $2,000 by $2,000..

Change in Fixed Cost, Sales Price and Volume

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Change in Variable Cost, Fixed Cost and Sales Volume

What is the profit impact if Racing (1) pays a $15 sales commission per bike sold instead of paying salespersons flat

salaries that currently total $6,000 per month, and (2) increases

unit sales from 500 to 575 bikes?

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Change in Variable Cost, Fixed Cost and Sales Volume

Sales Sales increaseincrease by $37,500, variable costs by $37,500, variable costs increaseincrease by by $31,125, but fixed expenses $31,125, but fixed expenses decreasedecrease by $6,000 by $6,000..

Sales Sales increaseincrease by $37,500, variable costs by $37,500, variable costs increaseincrease by by $31,125, but fixed expenses $31,125, but fixed expenses decreasedecrease by $6,000 by $6,000..

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Change in Regular Sales Price

If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers

or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by

$3,000?

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Change in Regular Sales Price

3,000$ ÷ 150 bikes = 20$ per bikeVariable cost per bike = 300 per bikeSelling price required = 320$ per bike

3,000$ ÷ 150 bikes = 20$ per bikeVariable cost per bike = 300 per bikeSelling price required = 320$ per bike

150 bikes × $320 per bike = 48,000$ Total variable costs = 45,000 Increase in net income = 3,000$

150 bikes × $320 per bike = 48,000$ Total variable costs = 45,000 Increase in net income = 3,000$

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Break-Even Analysis

Break-even analysis can be approached in two ways:

1. Equation method2. Contribution margin

method

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Equation Method

Profits = (Sales – Variable expenses) – Fixed expenses

Sales = Variable expenses + Fixed expenses + Profits

OR

At the break-even point At the break-even point profits equal zeroprofits equal zero

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Break-Even Analysis

Here is the information from Racing Bicycle Company:

Total Per Unit PercentSales (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 operating income 20,000$

Total Per Unit PercentSales (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 operating income 20,000$

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Equation Method We calculate the break-even point as follows:

Sales = Variable expenses + Fixed expenses + ProfitsSales = Variable expenses + Fixed expenses + Profits

$500Q = $300Q + $80,000 + $0

Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense

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Equation Method

$500Q = $300Q + $80,000 + $0$200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes

We calculate the break-even point as follows:


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Equation Method

The equation can be modified to calculate the break-even point in sales dollars.


X = 0.60X + $80,000 +X = 0.60X + $80,000 + $0$0

Where: X = Total sales dollars

0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses

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Equation Method

X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000


The equation can be modified to calculate the break-even point in sales dollars.

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Contribution Margin Method

The contribution margin method has two key equations.

Fixed expensesUnit contribution margin

=Break-even point

in units sold

Fixed expenses CM ratio

=Break-even point intotal sales dollars

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Contribution Margin Method

Let’s use the contribution margin method to calculate the break-even point in total

sales dollars at Racing.

Fixed expenses CM ratio

=Break-even point intotal sales dollars

$80,000$80,00040%40% = $200,000 break-even sales= $200,000 break-even sales

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Quick Check Coffee Klatch is an espresso stand in a

downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?

a. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cups

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?

a. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cups

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Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?a. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cups

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?a. 872 cupsb. 3,611 cupsc. 1,200 cupsd. 1,150 cups

Quick Check

Fixed expensesUnit CMBreak-even

= $1,300$1.49/cup - $0.36/cup

=$1,300

$1.13/cup

= 1,150 cups

=

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downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars?a. $1,300b. $1,715c. $1,788d. $3,129

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars?a. $1,300b. $1,715c. $1,788d. $3,129

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Quick Check

Fixed expensesCM Ratio

Break-evensales

$1,3000.758

= $1,715

=

=

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DERIVATION OF EQUATIONS

SALES= VARIABLE COSTS+FIXED COSTS + PROFITp*q= vcu *q + FC + ¶

AT BREAKEVEN PROFIT = 0p*q=vcu *q +FCq * (p-vcu) = FCq= FC / (p - vcu) OR q=FC/ cmu

CM= SALES - TOTAL VC VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND

SELLING EXPENSEScmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/qvcu= VARIABLE COST PER UNIT= VC/ q q number of units

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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

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Target Profit Analysis

The equation and contribution margin methods can be used to determine the

sales volume needed to achieve a target profit.

Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of

$100,000.

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The CVP Equation Method


$500Q = $300Q + $80,000 + $100,000

$200Q = $180,000

Q = 900 bikes

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The Contribution Margin Approach

The contribution margin method can be used to determine that 900 bikes must be sold to

earn the target profit of $100,000.

Fixed expenses + Target profit Unit contribution margin

=Unit sales to attain

the target profit

$80,000 + $100,000 $200/bike

= 900 bikes

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downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month?a. 3,363 cupsb. 2,212 cupsc. 1,150 cupsd. 4,200 cups

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month?a. 3,363 cupsb. 2,212 cupsc. 1,150 cupsd. 4,200 cups

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Quick Check

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Unit breakeven

Fixed expenses + Target profitUnit CM

Unit salesto attain

target profit

= 3,363 cups

=$3,800$1.13

$1,300 + $2,500$1.49 - $0.36 =

=

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The Margin of Safety

The margin of safety is the excess of budgeted (or actual) sales over the

break-even volume of sales.

Margin of safety = Total sales - Break-even salesMargin of safety = Total sales - Break-even sales

Let’s look at Racing Bicycle Company and determine the margin of safety.

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If we assume that Racing Bicycle Company has actual sales of $250,000, given that we have

already determined the break-even sales to be $200,000, the margin of safety is $50,000 as

shownBreak-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 operating income -$ 20,000$

Break-even sales

400 unitsActual sales

500 unitsSales 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 operating income -$ 20,000$

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The margin of safety can be expressed as 20% of sales.

($50,000 ÷ $250,000)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 operating income -$ 20,000$

Break-even sales

400 unitsActual sales

500 unitsSales 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 operating income -$ 20,000$

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The margin of safety can be expressed in terms of the number of units sold. The margin of safety at Racing is $50,000,

and each bike sells for $500.

Margin ofSafety in units

= = 100 bikes$50,000

$500

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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 SETTINGSALES $ = VC$ + FC$ WHERE VCR= x% *SALES THEN 1-x% = CMRSALES $ = x% *SALES +FC(1-x)* SALES $ = FC THAT IS CMR*SALES = FCSALES $ AT BREAKEVEN = FC/ CMR

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downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety?a. 3,250 cupsb. 950 cupsc. 1,150 cupsd. 2,100 cups

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety?a. 3,250 cupsb. 950 cupsc. 1,150 cupsd. 2,100 cups

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Quick Check

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Margin of Safety

Margin of safety = Total sales – Break-even sales

= 950 cups= 2,100 cups – 1,150 cups

or950 cups

2,100 cupsMargin of safety

percentage = = 45%

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Cost Structure and Profit StabilityCost structure refers to the relative proportion of fixed and variable costs in an organization.

Managers often have some latitude in determining their organization’s cost structure.

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Cost Structure and Profit Stability

There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed

cost (or high variable cost) structures.

An advantage of a high fixedcost structure is that incomewill be higher in good years

compared to companieswith lower proportion of

fixed costs.

An advantage of a high fixedcost structure is that incomewill be higher in good years

compared to companieswith lower proportion of

fixed costs.

A disadvantage of a high fixedcost structure is that income

will be lower in bad yearscompared to companieswith lower proportion of

fixed costs.

A disadvantage of a high fixedcost structure is that income

will be lower in bad yearscompared to companieswith lower proportion of

fixed costs.

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Operating Leverage

A measure of how sensitive net operating income is to percentage changes in sales.

Contribution margin Net operating income

Degree ofoperating leverage

=

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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$

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

At Racing, the degree of operating leverage is 5.

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Operating Leverage

With an operating leverage of 5, if Racing With an operating leverage of 5, if Racing increases its sales by 10%, net operating increases its sales by 10%, net operating

income would increase by 50%.income would increase by 50%.

Percent increase in sales 10%Degree of operating leverage × 5Percent increase in profits 50%

Here’s the verification!

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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 inincome from $20,000 to $30,000.. . . results in a 50% increase in

income from $20,000 to $30,000.

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downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?a. 2.21b. 0.45c. 0.34d. 2.92

Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?a. 2.21b. 0.45c. 0.34d. 2.92

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Quick Check

Contribution marginNet operating income

Operating leverage =

$2,373$1,073= = 2.21

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Con’tActual sales2,100 cups

Sales 3,129$ Less: Variable expenses 756 Contribution margin 2,373 Less: Fixed expenses 1,300 Net operating income 1,073$

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Quick Check

At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average.

If sales increase by 20%, by how much should net operating income increase?

a. 30.0%b. 20.0%c. 22.1%d. 44.2%



a. 30.0%b. 20.0%c. 22.1%d. 44.2%

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a. 30.0%b. 20.0%c. 22.1%d. 44.2%



a. 30.0%b. 20.0%c. 22.1%d. 44.2%

Quick Check

Percent increase in sales 20.0%

× Degree of operating leverage 2.21 Percent increase in profit 44.20%

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Cost Structure and Operating Leverage

Operating leverage is greatest in companies that have a high proportion of fixed costs in relation to variable costs.

Operating leverage is greatest in companies that have a high proportion of fixed costs in relation to variable costs.

Company A Company BSales 500.000$ 500.000$ Variable Expense 300.000 50.000 CM 200.000 450.000 Fixed Expenses 150.000 400.000 Net Income 50.000$ 50.000$

Operating Leverage Factor 200.000 450.000 50.000 50.000

4 9

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Operating Leverage Factor

A measure of how a percentage change in sales will affect profits.

The greater the operating leverage, the greater the sensitivity of its profit to changes in volume.

A measure of how a percentage change in sales will affect profits.

The greater the operating leverage, the greater the sensitivity of its profit to changes in volume.

Contribution margin Net income

Operating leveragefactor

=

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Operating Leverage Factor

If Company A and B increases its sales by 10%, which company will have the

greatest change in net income and why?

If Company A and B increases its sales by 10%, which company will have the

greatest change in net income and why?

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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

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Verify Increase in Profit

Actual sales

Increased sales

2,100 cups 2,520 cupsSales 3,129$ 3,755$ Less: Variable expenses 756 907 Contribution margin 2,373 2,848 Less: Fixed expenses 1,300 1,300 Net operating income 1,073$ 1,548$

% change in sales 20.0%% change in net operating income 44.2%

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Structuring Sales CommissionsCompanies generally compensate

salespeople by paying them either a commission based on sales or a salary plus a

sales commission. Commissions based on sales dollars can lead to lower profits in a

company.

Let’s look at an example.Let’s look at an example.

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Structuring Sales CommissionsPipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin

per unit of $18.

The sales force at Pipeline Unlimited is compensated based on sales commissions.

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Structuring Sales CommissionsIf you were on the sales force at Pipeline, you would

push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit.

To eliminate this type of conflict, commissions can be based on contribution margin rather than on

selling price alone.

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The Concept of Sales Mix

Sales mix is the relative proportion in which a company’s products are sold.

Different products have different selling prices, cost structures, and contribution margins.

Let’s assume Racing Bicycle Company sells bikes and carts and that the sales mix between the two products remains the

same.

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Revenue Mix

Revenue mix (or sales mix) is the relative combination of quantities of products or services that make up total revenue

Pages 73 - 75

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Multi-product break-even analysis

Racing Bicycle Co. provides the following information:

$265,000 $550,000

= 48.2% (rounded)

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Multi-product break-even analysis

Fixed expensesCM Ratio

Break-evensales

$170,00048.2%

= $352,697

=

=

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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 CBREAKEVEN 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 SALES3.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

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Key Assumptions of CVP Analysis Selling price is constant. Costs are linear. In multi-product companies, the sales

mix is constant. In manufacturing companies,

inventories do not change (units produced = units sold).

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Multiple Cost Drivers In many cases there may be multiple cost drivers

Do-All Software ExampleVariable costs: $40 per software package sold

$15 per invoice issuedOperating income= Revenue – ($40 x packages sold) – ($15 x invoices

issued) – Fixed costs

In cases where there are multiple cost drivers there are multiple breakeven points

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Examples

Please do the exercises before the next session.

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Contribution Margin & Gross MarginMerchandising Sector

Pages 82 - 83

Contribution MarginFormat

Revenues $200Variable costs:Cost of goods sold $120Other variable 43 163Contribution margin 37Fixed costs:Cost of goods sold 5

Other fixed 19 24Operating income $13

Gross MarginFormat

Revenues $200

Cost of goods sold (120+5) 125

Gross margin 75

Operating costs (43+19) 62

Operating income $13

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Example 1: equation approach

• Movie theater: $48,000 monthly fixed costs

• $8 ticket price.

• $2 variable cost per ticket.

• $6 contribution margin per ticket; 75% cont. margin ratio

• Give breakeven units and revenue

BEunits = $48,000/($8 - $2)

BEunits = 8,000 tickets.

BErevenue = $64,000

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Profit

Loss

-50

2,000 4,000 6,000 8,000 10,000

0

10

20

30

40

$000 (per month)

-10

-20

-30

-40

Fixed expenses = $48,000

Loss area

Profit area

Break-even point: 8,000 tickets

Volume of tickets sold

in one month

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Example 1 Cont’d

• Suppose practical capacity per month is 12,000 tickets and that the movie theater has operated at 60% capacity during December. It is now December 30.

• Has the theater made money in December?

• If they could capture 1,000 customers by lowering the ticket price to $7 for New Year’s Eve, should they do it?

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Example 1 con’t

practical capacity 12000 tickets

operating at 60%

contribution =60% *12000*6= 43200

fixed costs 48000

loss -4800 7 - 2

add'l contribution 1000 5 5000 > 4800200 net income

yes, they should

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Example 2

Data: The Doral Company manufactures and sells pens. Present sales output is 5,000,000 per year at a selling price of $.50 per unit. Fixed costs are $900,000 per year. Variable costs are $.30 per unit.

What is the current yearly operating income?

What is the current breakeven point in sales dollars?

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Example 2 Cont’d –answer part 1

Contribution margin ratio = $.20/$.50= 40%total contribution margin = $1,000,000Fixed Cost $900,000operating income $100,000

Breakeven Sales = 900,000/60%= $2,250,000

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Example 2 Cont’d – question part 2

Compute the new operating income if . . . 1. A $.04 per-unit increase in variable

costs.

2. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable costs, and a 40% increase in units sold.

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1. $0.04 increase in variable costsnew variable cost 0.34new cont. margin per pen 0.16total sales 5,000,000 penstotal cont. margin = $800,000Fixed costs $900,000operating income ($100,000)

new selling price $0.40new variable costs $0.27new units sold 7,000,000 penstotal cont. margin = $1,890,000Fixed costs $900,000operating income $990,000

2. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable costs, and a 40% increase in units sold.

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Example 2 Cont’d-questions part 3

Compute the new breakeven point in units for

each of the following changes. A 10% increase in fixed costs:

A 10% increase in selling price and a $20,000 increase in fixed costs.

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new fixed costs $990,000contribution margin per pen $0.20New BE units 4,950,000 pens

new selling price $0.55 per pennew fixed costs $920,000new contribution margin $0.25 per penNew BE units 3,680,000 pens

new BE units if selling price increase by 10% and fixed cost increase by $20.000.

new BE units if fixed cost increase by 10%

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Example 3

The Rapid Meal has two restaurants that are open 24 hours per day. Fixed costs for the two restaurants together total $450,000 per year. Service varies from a cup of coffee to full meals. The average sales check for each customer is $8.00. The average cost of food and other variable costs for each customer is $3.20. The income tax rate is 30%. Target net income is $105,000.

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Example 3 Cont’d

Compute the total dollar sales needed to obtain the target net income.

How many sales checks are needed to break even?

Compute net income if the number of sales checks is 150,000

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Example 3 - answers

105000/0.7= $150,000approach 1;

average check per customer = 8variable cost per customer = 3.2approach 2:contribution margin per customer = 4.8

0.6$450,000$600,000

$1,000,000 (600.000 /0.60)

Compute the total dollar sales needed to obtain the target net incomebefore tax income=

sales = vc +fc+before tax profitsales = average sales check x no of customersvariable cost= vc per cust x no of customers

Sales to reach target income =fixed cost + target income =fixed costs =contribution margin ratio =

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Example 3 - answers

$600,000contribution margin per customer = $4.80number check (customers) to reach target income 125000

contribution margin per customer = $4.80number of sales checks (customers)= 150000total contribution margin $720,000

$450,000income before tax $270,000income tax 81000net income $189,000

fixed cost + target income =

fixed costs =

How many sales checks are needed to break even?

Compute net income if the number of sales checks is 150,000

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Assume the following:

Regular Deluxe Total PercentUnits sold 400 200 600 ----

Sales price per unit $ 500 $750 ---- ----

Sales $200,000 $150,000 $350,000 100.0%

Less: Variable expenses 120,000 60,000 180,000 51.4

Contribution margin $ 80,000 $ 90,000 $170,000 48.6%

Less: Fixed expenses 130,000

Net income $ 40,000=======

Multiple-Product Example

1. What is the break even point?

2. How much sales revenue of each product must be generated to earn

a before tax profit $50,000?

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Multi product example -answer1. What is the break even point?

fixed costs $130,000weighted cont. margin ratio 48.60%BE sales dollars $267,490

2. How much sales revenue of each product must be generated to earn a before tax profit $50,000?target income $50,000fixed costs $130,000weighted cont. margin ratio 48.60%

fixed cost + target income $180,000sales revenue targeted- total $370,370.37

sales mix (percent)regular (200.000/350.000) 57.14%deluxe (150.000 / 350.000) 42.86%

Sales of regular $211,640.21Sales of deluxe $158,730.16(sales mix % x sales target)

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Multiple product - verify

cmr - regular 40.00%cmr - deluxe 60.00%

contribution margin -regular $84,656.08contribution margin - deluxe $95,238.10total contribution $179,894.18Fixed costs $130,000before tax income $49,894.18

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Example 4 A financial analyst is studying the feasibility of two

alternative assembly methods, manual and automated. The automated method has variable costs of TL 2.10 per unit and annual committed costs of TL 130.000; in contrast, the manual method has variable costs of TL 4.20 per unit and committed costs of TL 60.000. The company sells its products for TL 23 per unit.

What is break-even of each method? Above what volume level will management prefer

the automated method to the manual method?

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Example 4 Answer

Selling price TL23.00Automatedvariable TL2.10 per unitfixed TL130,000 per year

Manualvariable TL4.20 per unitfixed TL60,000 per year

Automated BE units:fixed cost TL130,000cont.per unit TL20.90

BE units 6,220.10 6221 units

Manual BE units:fixed cost TL60,000cont.per unit TL18.80

BE units 3,191.49 3.192 units

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Example 4 answer

2.1q+130000=4.2q+60000change in cost TL70,000change in q 2.1

33333.333 33.334 unitsafter 33.334 units automated is better

Find the indifference point:

at 35.000 units

manual automatedcont. margin per unit TL18.80 TL20.90number of units 35000 35000Contribution Margin TL658,000.00 TL731,500.00

Fixed Costs TL60,000 TL130,000

Operating Income TL598,000 TL601,500

at 30.000 units

manual automatedcont. margin per unit TL18.80 TL20.90number of units 30000 30000Contribution Margin TL564,000.00 TL627,000.00

Fixed Costs TL60,000 TL130,000

Operating Income TL504,000 TL497,000

emba 5403 fall 2010 cost-volume-profit relationships

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