cost-volume-profit relationships uaa – acct 202 principles of managerial accounting dr. fred...

Cost-Volume-Profit Relationships

UAA – ACCT 202 Principles of Managerial

Accounting Dr. Fred Barbee

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 2

Introduction

• We have learned . . .

– How to identify costs as fixed, variable, and mixed;

– How each of these behave when changes take place; and

– How to separate them into their component parts.

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 3

Introduction

• Understanding these relationships help managers to;

– Predict future conditions (planning); and

– Explain, evaluate, and act on past results (control)

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 4

Introduction

Today we will focus on gaining an understanding of how . . .– Costs

– Volume, and

– Profits

Interact

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 5

Cost-Volume-Profit (CVP)

• CVP is the systematic examination of the relationships among . . .

– Selling prices,

– Volume of Sales and Production

– Cost,

– Expenses, and

– Profits

Output

Sales Price

Variable Costs

Fixed Costs

Total Revenues

TotalCost

OperatingIncome

Total Revenue

Total Cost

Operating Income

What happens here?

As changes occur here.Graphically

4

Output

Sales Price

Variable Costs

Fixed Costs

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 7

CVP - For-Profit Firms

• How many photocopies must the College Avenue Copy Shop produce to earn a profit of $20,000?

• At what sales volume will Burger King’s total costs and total revenues equal?

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 8

CVP - For-Profit Firms

• What will happen to profits in Joe’s Diner if . . .

– There is a 20% increase in the cost of food; and

– A 10% increase in the selling price of meals?

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 9

CVP - Not-For-Profit Firms

• How many meals can the Salvation Army serve with an annual budget of $150,000?

• How many tickets must be sold for the benefit concert to raise $15,000?

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 10

CVP is Useful in . . .

• Choice of product lines

• Pricing of products

• Developing marketing strategies

• Utilization of productive facilities

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 11

Traditional Statement

• Costs are grouped by functional classifications - such as:– Production,– Selling & Administration

• With both fixed and variable costs being included in each category.

Sales $xxx

COGS (xx)

Gross Margin $xxx

Selling Exp. (xx)

Net Income $xxx

Admin. Exp (xx)

ProductionFC & VC

SellingFC & VC

AdministrativeFC & VC

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 13

Contribution Format

• The focus of the contribution format income statement is the contribution margin . . .

Contribution Margin = Net Sales - Variable Costs

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 14

Contribution Format I/S

• Groups costs by behavior:– Fixed, and– Variable

• Rather than into the functional categories of production, marketing and administration.

Sales $xxx

Variable Costs (xx)

Cont. Margin $xxx

Fixed Costs (xx)

Net Income $xxx

Income Statements . . .

Sales $xxx

COGS (xx)

Gross Margin $xxx

Operating Exp (xx)

Traditional Contribution Format

Net Income $xxx

Sales $xxx

Variable Costs (xx)

Cont. Margin $xxx

Fixed Costs (xx)

Net Income $xxx

Sourdough Alaska, Inc.Sourdough Alaska, Inc.

SalesSales $900,000$900,000Cost of SalesCost of Sales Direct Materials Direct Materials $100,000$100,000 Direct Labor Direct Labor 160,000160,000 Mfg. Overhead Mfg. Overhead 100,000100,000 361,000361,000 VC=$55,000 VC=$55,000 FC=$45,000 FC=$45,000Marketing CostsMarketing Costs Variable Variable 18,00018,000 Fixed Fixed 82,00082,000 100,000100,000Admin. Costs (Fixed)Admin. Costs (Fixed) $150,000$150,000

Sourdough Alaska, Inc.Traditional Income Statement

For Year Ended December 31, 2002

Sourdough Alaska, Inc.Traditional Income Statement

For Year Ended December 31, 2002

SalesSales $900,000$900,000 100%100%Cost of SalesCost of Sales Direct Materials Direct Materials $100,000$100,000 Direct Labor Direct Labor 160,000160,000 Mfg. Overhead Mfg. Overhead 100,000100,000 360,000360,000 40%40%Gross MarginGross Margin $540,000$540,000 60%60%Marketing/Admin CostsMarketing/Admin Costs Marketing Costs Marketing Costs $100,000$100,000 Administrative Costs Administrative Costs 150,000150,000 250,000250,000Net IncomeNet Income $290,000$290,000

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 19

What if . . .

• You were asked to project the effect on net income of:

– A 20% increase in sales volume;

– With no change in selling prices.

• How would you go about doing it?

Sourdough Alaska, Inc.Contribution Format Income Statement

For Year Ended December 31, 2002

Sourdough Alaska, Inc.Contribution Format Income Statement

For Year Ended December 31, 2002

SalesSales $900,000$900,000 100%100%Cost of SalesCost of Sales Direct Materials Direct Materials $100,000$100,000 Direct Labor Direct Labor 160,000160,000 Mfg. Overhead Mfg. Overhead 55,00055,000 Variable Mkt. Exp Variable Mkt. Exp 18,00018,000 $333,000$333,000 37%37%Contribution MartinContribution Martin $567,000$567,000 63%63%Fixed CostsFixed Costs Manufacturing Manufacturing 45,00045,000 Marketing Marketing 82,00082,000 Administrative Administrative 150,000150,000 277,000277,000Net IncomeNet Income $290,000$290,000

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 21

NOW . . . What if . . .

• You were asked to project the effect on net income of:

– A 20% increase in sales volume;

– With no change in selling prices.

• How would you go about doing it?

Sourdough Alaska, Inc.Projected Increase in Net Income

For Year Ended December 31, 2002

Sourdough Alaska, Inc.Projected Increase in Net Income

For Year Ended December 31, 2002

Sales ($900,000 x 120%)Sales ($900,000 x 120%) $1,080,000$1,080,000

Contribution MarginContribution Margin 688,400688,400

Projected Net IncomeProjected Net Income 403,400403,400

Less: VC: ($333,000 x 120%)Less: VC: ($333,000 x 120%) 399,600399,600

Less: Fixed CostsLess: Fixed Costs 277,000277,000

Less Original NI ProjectionLess Original NI Projection 290,000290,000

Projected Increase in Net IncomeProjected Increase in Net Income $113,400$113,400

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 23

2• Can be computed two ways:

– The equation method

– The contribution margin method

Breakeven Analysis

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 24

2• Can be computed in two

forms:

Breakeven Analysis

– Number of units required to break even; or

– Sales dollars required to break even.

The Equation Method

Exhaustion Unlimited – An Illustration

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 26

Exhaustion Unlimited

• Exhaustion Unlimited makes and distributes high end exercise equipment.

• One of their best selling products is an exercise bike –Model IMATRD-1

Per Bike Percent SP $500 100%VC 300 60%CM $200 40%Fixed Costs = $80,000

• The equation method centers on the contribution approach to the income statement.

Sales $xxx

Variable Costs (xx)

Contribution Margin $xxx

Fixed Costs (xx)

Net Operating Income $xxx

• At breakeven profit = 0

The equation becomes:The equation becomes:

•Use our BE Equation; and•Let X = BE Point in Bikes

Sales = VC + FC

$500X = $300X + $80,000$200X = $80,000

X = 400 Bikes

Sales FCVC

•Use our BE Equation; and•Let X = BE Point in Sales $

Sales = VC + FC

1X = .6X + $80,000

.4X = $80,000

X = $200,000

Sales FCVC

Exhaustion UnlimitedIncome Statement

For Year Ended 12/31/01

Sales (400 x $500) $200,000

VC (400 x $300) 120,000

CM $80,000

FC 80,000

Net Income $-0-

The Unit Contribution

Method

Exhaustion Unlimited – An Illustration

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 34

Unit-Contribution Method

•Is a variation of the equation method.

•The method may be just a bit more intuitive than the equation method.

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 35

•The approach centers on the idea that each unit sold provides a certain amount of CM that goes toward covering fixed costs.

Unit-Contribution Method

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 36

•The Formula . . .

Unit-Contribution Method

Fixed Expenses= BEPUnit Contribution

Margin

Bikes400200$

000,80$

Fixed Costs

Unit CMBEP in Units

000,200$%40

000,80$

Fixed Costs

CM %BEP in $

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 39

Unit Contribution Method

•Let’s look at a series of income statements that graphically point out the concept of a contribution margin.

Exhaustion UnlimitedIncome Statement

1 Bike 2 Bikes400

Bikes401

Bikes

Sales $500 $1,000$200,00

0$200,50

0

VC 300 600 120,000$120,30

0

CM $200 $400 $80,000 $80,200

FC 80,000 80,000 80,000 80,000

NI($79,800

)($79,600

)$-0- $200

Break-Even Analysis

Target Net Profit Analysis

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 42

Target Net Profit Analysis

•A firm’s targeted NI is the amount of income the firm wishes to make . . .

–Pre-Tax OI; or

–After-Tax NI

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 43

Target Net Profit Analysis

•Recall the BE formula:

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 44

Target Net Profit Analysis

•Using data from Exhaustion Unlimited.

•Assume the firm wants to make a before-tax profit of $40,000.

Per Bike Percent SP $500 100%VC 300 60%CM $200 40%Fixed Costs = $80,000

•Use our BE Equation; and•Let X = BE Point in Bikes

Sales = VC + FC + Profits

$500X = $300X + $80,000 + $40,000

$200X = $120,000

X = 600 Bikes

Sales FCVC

Desired Profit

•Use our BE Equation; and•Let X = BE Point in Sales $

Sales = VC + FC + Profits1X = .6X + $80,000 +

$40,000

.4X = $12,000X = $300,000

Sales FCVC

Desired Profit

Exhaustion UnlimitedIncome Statement

For Year Ended 12/31/01

Sales (600 x $500) $300,000

VC (600 x $300) 180,000

CM $120,000

FC 80,000

Net Income $40,000

Target Before-Tax Profit Analysis

The Unit Contribution Method

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 50

•The Formula . . .

Unit-Contribution Method

Fixed Expenses= BEPUnit Contribution

Margin

Add Targeted Before-Tax OI (TI) to the Fixed

Expenses

Fixed Expenses +TI= BEPUnit Contribution

Margin

Add Targeted Before-Tax OI (TI) to the Fixed

Expenses

Bikes600200$

000,40$000,80$

Fixed Costs

Unit CM BEP in Units

Desired BT OI (TI)

000,300$%40

000,40$000,80$

Fixed Costs

CM % BEP in $

Desired BT OI

Target Net Profit Analysis

What About Taxes?

The equation becomes:The equation becomes:

Remember this?

Profit = Taxes

• At breakeven profit = 0

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 55

Tax Effects . . .

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 56

Net Income OI = ------------------

(1 – TR)

This, then, is our handy-dandy formula to calculate an after-

tax net income (ATNI).

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 57

Target Net Profit Analysis

•Back to Exhaustion Unlimited

•Assume management wants $40,000 after taxes

•Tax Rate = 30%

)30.1(

000,40$000,80$300$500$

XX

Sales = VC + FC + ATNI

Sales FC

VCTargeted ATNI

)30.1(

000,40$000,80$300$500$

XX

)30.1(

000,40$000,80$300$500$

XX

Sales = VC + FC + ATNI

686

143,137$200$

143,57$000,80$300$500$

X

X

XX

686

143,137$200$

143,57$000,80$300$500$

X

X

XX

Bikes

686200$

)30.1(000,40$

000,80$

Bikes

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 61

Limiting Assumptions

• CVP assumes a linear revenue and cost function.

• CVP analysis assumes a relevant range.

• CVP assumes that production equals sales.

Dr. Fred Barbee ACCT 202 - UAA - Fall 2004 62

Limiting Assumptions

• Sales mix remains constant.

• Sales prices and costs are known with certainty.