Chapter 3

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Fundamentals of Cost Analysis. Chapter 3. for Decision Making. Use cost-volume-profit (CVP) analysis to analyze decisions. 2. Understand the effect of cost structure on decisions. 3. Use differential analysis to analyze decisions.

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Use cost-volume-profit (CVP) analysis to analyze decisions.

2. Understand the effect of cost structure on decisions.

3. Use differential analysis to analyze decisions.

• Understand how to apply differential analysis to pricing decisions.
• Understand several approaches for establishing prices based on costs for long-run pricing decisions.
• Understand how to apply differential analysis to production decisions.

7. Understand the theory of constraints (Appendix).

Learning Objectives

Cost

Volume

Profit

CVP studies the relations among revenue, cost, and volume and their effect on profit.

Cost-Volume-Profit Analysis

V

?

C

P

What is

The Income Statement

Total revenues

Total costs

Operating profit

The Profit Equation

Operating profit

Total revenues

Total costs

p

TR

TC

The Profit Equation

Operating profit equals total revenue less total costs.

It’s the income statement written horizontally.

Units of output produced and sold

Price

TR

P

X

TR

PX

Fixed costs

Variable costs per unit

Units of output

TC

X

F

V

TC

VX

F

Profit Equation Continued

p

TR

TC

p

PX

VX

F

[

]

p

P

V

X

F

Profit Equation Continued

Developed 12,000 prints in March

Total

PerUnit

Sales

\$7,200

\$0.60

Less Variable cost of goods sold

3,600

0.30

Less Variable selling cost

720

0.06

Contribution margin

2,880

0.24

Less Fixed costs

1,500

Operating profit

\$1,380

U-Develop; an Example

U-Develop

Income Statement

Month of March 200X

U-Develop

p

P

V

X

F

[

]

\$1,380

\$.60

\$.36

12,000 units

\$1,500

\$.30 + \$.06

\$1,380

\$2,880

\$1,500

p

\$1,380

Profit Equation Example

Total contribution margin

P

X

V

X

P

V

X

Unit contribution margin

CM unit

CM unit

P

V

Contribution Margin

The difference between total revenue and total variable costs.

The difference between sales price and variable costs per unit.

CM

P

V

X

Total CM

CM

\$.60

\$.36

12,000 units

CM

\$2,880

\$.30 + \$.06

CM unit

CM Unit

P

V

CM unit

\$.60

\$.36

CM unit

\$.24

Contribution Margin Example

CVP studies the relations among revenue, cost, and volume and their effect on profit.

U-Develop

CM unit

\$.24

?

Why do I care?

For every \$1.00 in sales, U-Develop has \$.24 available to first cover fixed costs and then to increase profits.

Contribution Margin Continued

U-Develop

[

]

Target Profit

P

V

X

F

Target Volume (Units)

Fixed costs

Target profit

F

p

X

P

V

Target Volume in Units

Unit contribution margin

p

F

X

\$1,500

\$1,800

X

X

13,750 units

Target Volume Units Example

U-Develop

Target Profit of \$1,800

CM unit

\$.24

P

V

X

P

X

P

V

P

Contribution Margin Ratio

Contribution Margin Ratio

Contribution margin as a percentage of sales revenue.

Total contribution margin ratio

Total contribution margin as a percent of total sales revenue.

Unit contribution margin ratio

Contribution margin per unit as a percent of sales price per unit.

CMR unit

P

V

X

\$.60

\$.36

12,000

CMR

P

X

.60

12,000

\$2,880

CMR

.40

\$7,200

\$.24

CMR unit

.40

\$.60

CMR Example

U-Develop

Target volume sales dollars

Fixed costs

+

Target profit

=

Contribution margin ratio

TR

F

+

p

TR

=

CMR

Target Volume in Sales Dollars

\$1,500

\$1,800

F

+

p

TR

TR

=

.40

CMR

TR

\$8,250

Target Sales Dollars Example

U-Develop

13,750 x \$.60 = \$8,250

F

+

p

X

=

CM unit

Fixed costs

Break-even volume (units)

=

CMunit

Break-Even

The sales volume level at which profits equal zero.

Total revenues = Total costs

Use the target volume formulas to find the break-even point.

Set target profit to zero (p = 0)

p = 0

F

p

X

CM unit

1,500

0

X

\$.24

X

6,250 prints

Break-Even Units Example

U-Develop

F

0

TR

CMR

F

TR

CMR

Break-Even in Sales Dollars

The total sales dollars at which profits equal zero.

p = 0

Total revenues = Total costs

F

p

TR

CMR

\$1500

TR

.40

TR

\$3,750

Break-Even Sales Dollars Example

U-Develop

6,250 prints X \$.60 = \$3,750

Fixed costs

Target profit

+

Target volume (units)

=

Unit contribution margin

Fixed costs

+

Target profit

Target volume sales dollars

=

Contribution margin ratio

CVP Summary

Summary of Target Volume and Break-Even Formulas

Target Volume

Fixed costs

Break-even volume (units)

=

Unit contribution margin

Fixed costs

Break-even volume (sales dollars)

=

Contribution margin ratio

CVP Summary Continued

Summary of Target Volume and Break-Even Formulas

Break even

Total revenue

\$3,750

Total cost

6,250 prints

Graphic Presentation

U-Develop Break-Even

Contribution margin

Net income

The higher the organization’s operating leverage, the higher the break-even point.

CVP and the Effect of Different Cost Structures

L.O. 2 Understand the effect of cost structure on decisions.

Cost structure

Operating leverage

The proportion of fixed and variable costs to total costs.

The extent to which the cost structure is made up of fixed costs.

Why do I care?

Lo-Lev

Hi-Lev

Sales

\$100,000

\$100,000

CMR

.25

.75

Increase in Profit

\$25,000

\$75,000

Prior NI

\$200,000

\$200,000

NI with sales increase of 10%

\$225,000

\$275,000

Operating Leverage Example

Suppose Lo-Lev & Hi-Lev both increase sales 10% or \$100,000.

Lo-Lev

Hi-Lev

10%

10%

Percent Increase in sales

1.25

1.75

Degree of Operating Leverage

12.5%

17.5%

Percent increase in NI

\$200,000

\$200,000

Prior NI

12.5%

17.5%

Percent increase in NI

\$225,000

\$275,000

NI with sales increase of 10%

Operating Leverage Continued

The excess of projected or actual sales volume over break-even volume.

The excess of projected or actual sales revenue over break-even revenue.

8,000

6,250

1,750 prints

\$4,800

\$3,750

\$1,050

Margin of Safety

or

Suppose U-Develop sells 8,000 prints

1750 x \$.60 = \$1,050

What if U-Develop is in the 15% tax bracket and wants profit after taxes of \$3,000?

p

F

1 - t

CM unit

\$3,000

\$1,500

.85

X

\$.24

X

20,956 units

Extending CVP: Taxes

Profit of \$3,000

But this means taxes.

Target Volume

Sales

20,956

\$.60

\$12,574

VC

20,956

\$.36

7,544

CM

\$5,030

FC

1,500

NIBT

\$3,530

Taxes

3,530

15%

530

Net Income

\$3,000

CVP and Taxes Continued

Check it out

Prints

Enlargements

Selling price

\$.60

\$1.00

.36

.56

Variable cost

Contribution margin

\$. 24

\$. 44

Total Fixed Costs

\$1,820

Extending CVP: Multiple Products

What if:

U-Develop does prints and enlargements?

9/10

\$.24

1/10

\$.44

9/10

6,300 prints

\$1,820

7,000

1/10

\$.26

700 enlargements

Product Mix

For every 9 prints sold U-Develop sells 1 enlargement.

Weighted Average Contribution Margin

\$ .26

Breakeven

The process of estimating revenues and costs of alternative actions available to decision makers and of comparing these estimates to the status quo.

The period of time over which capacity will be unchanged, usually one year.

Differential Analysis

L.O. 3 Use differential analysis to analyze decisions.

Differential Analysis

Short Run

Differential costs differ between actions.

Alternative A

Alternative B

Differential Costs

Costs incurred in the past that cannot be changed by present or future decisions.

IT’S GONE

A sunk cost is NOT relevant.

Sunk Costs

Differential Analysis and Pricing Decisions

L.O. 4 Understand how to apply differential analysis to pricing decisions.

Variable costs

Must always be covered.

Cost (\$)

Activity level

Fixed costs

Must be covered in the long run.

Costs (\$)

Activity level

Full Cost and Pricing Decisions

Full cost of manufacturing and selling a product.

Variable costs

Necessary to manufacture and sell the product.

and

Fixed costs

Share of organization’s fixed costs.

Ultimately full costs must be recovered.

Short-run vs Long-run

Variable costs

Must always be covered.

Short-run Pricing Decisions

Fixed costs

Must be covered in the long run.

Long-run Pricing Decisions

Short-run vs Long-run Pricing Decisions

Year

0

1

Short-run Pricing Decision

Long-run Pricing Decision

Shorter than one year

Longer than one year

Pricing a one-time special order.

Pricing a new product.

How much material is required?

Do I need a new plant?

Option 1

Value of Option 1

Status Quo: Reject special offer

Accept Special Order?

Is Option 1 > Option 2?

Alternative: Accept special offer

Value of Option 2

Option 2

Short-run Pricing Decisions: Special Orders

Special order

An order that will not affect other sales and is usually a one-time occurrence.

Comparison of Totals

Reject Special Order

Accept Special Order

Difference

\$2,700

\$200

Sales revenue

\$2,500

(1,100)

(100)

Variable costs

(1,000)

1,600

100

Total contribution

1,500

(1,200)

0

Fixed costs

(1,200)

\$400

\$100

Operating profit

\$300

\$200

Differential sales, 500 at 40¢

100

Less differential costs, 500 at 20¢

\$100

Differential operating profit (before taxes)

Special Order Example

Analysis of Special Order U-Develop

Status Quo:

Alternative:

Alternative Presentation: Differential Analysis

Long-run Pricing Decisions

L.O. 5 Understand several approaches for establishing prices based on costs for long-run pricing decisions.

In the long run an organization must cover variable and fixed costs.

Life-cycle product costing and pricing

Target costing for Target pricing

Manufacturing

Customer

Take Back

R&D

Service

(Disposal)

Design

Marketing

&

Distribution

Grave

To

Life-cycle Product Costing and Pricing

Product life-cycle

The time from initial research and development to the time that support to the customer ends.

Life-cycle Costing

Concerned with covering costs in all categories of the life cycle.

Desired profit

Target cost

Target Costing from Target Pricing

Target price

The price based on customers’ perceived value for the product and the price that competitors charge.

What would a customer pay?

How much profit do I need?

The maximum amount of cost allowed.

Can I make it at this cost?

Differential Analysis for Production Decisions

L.O. 6 Understand how to apply differential analysis to production decisions.

Decision to make goods or services internally or purchase them externally.

Decision to add or drop a product line or close a business unit.

Decision on what products or services to offer.

Product Mix

Per Unit

100,000 prints

Direct materials

\$0.05

\$5,000

Direct labor

0.12

12,000

0.03

3,000

4,000

Common costs allocated to this product line

10,000

Decision to make goods or services internally or externally.

100,000 prints

Cost directly traceable

\$34,000

20,000

higher

5,000

\$25,000 a

Direct materials

Labor

12,000

0

12,000

lower

3,000

0

3,000

lower

4,000

0

4,000

lower

Common costs

10,000 b

10,000 b

0

Total costs

\$34,000

\$35,000

\$1,000

higher

Status Quo:

Alternative:

Process Prints

Outsource Processing

Difference

100,000 prints

Direct costs

Differential costs increase by \$1,000, so reject alternative to buy.

a 100,000 units purchased at \$.25 = \$25,000.

b These common costs remain unchanged for these volumes. Because they do not change, they could be omitted from the analysis.

10,000

higher

2,500 c

\$12,500 d

Direct materials

Labor

6,000

0

6,000

lower

1,500

0

1,500

lower

4,000

0

4,000

lower

Common costs

10,000 b

10,000 b

0

Total costs

\$24,000

\$22,500

\$1,500

lower

Status Quo:

Alternative:

Process Prints

Outsource Processing

Difference

50,000 prints

Direct costs

Differential costs decrease by \$1,500, so accept alternative to buy.

b These common costs remain unchanged for these volumes. Because they do not change, they could be omitted from the analysis.

c Total variable costs reduced by half because volume was reduced by half.

d 50,000 units purchased at \$.25 =\$12,500.

Total cost of 100,000 prints

\$35,000

\$34,000

1,000

Higher a

Opportunity cost of using facilities to make covers

2,000

0

2,000

Lower a

Total costs, including opportunity costs

\$36,000

\$35,000

1,000

Lower a

Opportunity Costs of Making

Make-or-Buy Analysis with Opportunity Cost of U-Develop

Status Quo

Alternative

Process Prints

Outsource Processing

Difference

Differential costs decrease by \$1,000 so accept the alternative.

a These indicate whether the alternative is higher or lower than the status quo.

Total

Prints

Cameras

Frames

Sales revenue

\$80,000

\$10,000

\$50,000

\$20,000

Cost of sales (all variables)

53,000

_ 8,000

30,000

15,000

Contribution margin

\$27,000

\$2,000

\$20,000

\$5,000

Less fixed costs:

Rent

4,000

1,000

2,000

1,000

Salaries

5,000

1,000

2,500

1,500

_3,000

__500

_1,500

_1,000

Operating profit (loss)

\$15,000

\$(500)

\$14,000

\$1,500

Decision to add or drop a product line or close a business unit.

Fourth Quarter Product Line Income Statement, U-Develop

Sales revenue

\$80,000

\$70,000

\$10,000

decrease

Cost of sales (all variables)

53,000

45,000

_8,000

decrease

Contribution margin

\$27,000

\$25,000

\$2,000

decrease

Less fixed costs:

Rent

0

4,000

4,000

Salaries

5,000

4,000

1,000

decrease

_3,000

_2,750

__250

decrease

Operating profit (loss)

\$15,000

\$14,250

\$750

decrease

Differential Analysis U-Develop

Status Quo:

Alternative:

Keep Prints

Drop Prints

Difference

Profits decrease \$750 so keep prints.

Product Choice Decisions

Constraints

Activities, resources, or policies that limit the attainment of an objective.

Contribution margin per unit of scarce resource

Contribution margin per unit of a particular input with limited availability.

Metal Frames

WoodFrames

Price

\$50

\$80

Material

8

22

Labor

8

24

4

4

Contribution margin per unit

\$30

\$30

Product Choice Decisions Example

Revenue and Cost Information, U-Develop

Less variable costs per unit

Fixed manufacturing costs: \$3,000 per month

Fixed marketing and administrative costs: \$1,500 per month

Per Unit

Metal Frames

WoodFrames

Contribution margin

\$30

\$30

Machine hours required

.5

1

Contribution margin per machine hour

\$60

\$30

Product Choice Decisions Example

Revenue and Cost Information, U-Develop

Metal Frames have a higher contribution margin per machine hour.

Metal Frames

WoodFrames

Capacity

400

200

Contribution margin per unit

\$30

\$30

Total contribution margin

\$12,000

\$6,000

Less fixed manufacturing costs

3,000

3,000

Less fixed M&A costs

1,500

1,500

Operating profit

\$7,500

\$1,500

Product Choice Decisions Example

Suppose U-Develop has 200 machine hours per month available.

Selling metal frames results in higher profits than selling wooden frames.

Theory of Constraints

L.O. 7 Understand the theory of constraints (Appendix).

Theory of Constraints

Focuses on revenue and cost management when faced with bottlenecks.

Bottleneck

Operation where the work required limits production.

The bottleneck is a constraining resource.

Chapter 3

The End