1. Fundamentals of Cost Analysis
for Decision Making
Chapter 3

2. Learning Objectives
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).

3. V ? C P Cost-Volume-Profit Analysis What is Cost Volume Profit
L.O. 1 Use cost-volume-profit (CVP) analysis to analyze decisions. V ? C P
What is
Cost
Volume
Profit
CVP studies the relations among revenue, cost, and volume and their effect on profit.

4. The Profit Equation The Income Statement
Operating profit equals total revenue less total costs.
Operating profit
Total revenues
Total costs
The Profit Equation
It’s the income statement written horizontally.
Operating profit
Total revenues
Total costs p TR TC

5. Profit Equation ContinuedTR
Price
Units of output produced and sold P X TR PX TC
Variable costs per unit
Units of output
Fixed costs X F V VX F TC

6. Profit Equation ContinuedTR TC p PX VX F p P F V X [ ]

7. Developed 12,000 prints in March
U-Develop; an Example
U-Develop
Income Statement
Month of March 200X
Total
Per Unit
Sales
$7,200
$0.60
Less Variable cost of goods sold
3,600
0.30
720
Less Variable selling cost
0.06
2,880
Contribution margin
0.24
Less Fixed costs
1,500
Developed 12,000 prints in March
Operating profit
$1,380

8. Profit Equation Example
U-Develop p P V F X
$1,380
$.60
$.36
$1,500
12,000 units [ ]
$.30 + $.06
$1,380
$2,880
$1,500
$1,380 p

9. Contribution Margin Total contribution margin
The difference between total revenue and total variable costs. P V X P V X
Unit contribution margin
CM unit
The difference between sales price and variable costs per unit.
CM unit P V

10. Contribution Margin Example
CVP studies the relations among revenue, cost, and volume and their effect on profit.
U-Develop CM P V X
Total CM
$.60
$.36
12,000 units CM CM
$2,880
$.30 + $.06
CM Unit
CM unit P V
$.60
$.36
CM unit
$.24
CM unit

11. Contribution Margin Continued
U-Develop ?
$.24
CM unit
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.

12. [ ] Target Volume in Units P V F X Target Profit Target Volume (Units)
Fixed costs
Target profit
Unit contribution margin F p X P V

13. Target Volume Units Example
U-Develop
Target Profit of $1,800 p F X
CM unit
$1,800
$1,500 X
$.24 X
13,750 units

14. 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. P X V
Unit contribution margin ratio P V
Contribution margin per unit as a percent of sales price per unit.
CMR unit

15. CMR Example U-Develop CMR P V X $.60 $.36 12,000 .60 CMR $2,880 $7,200
.40
CMR unit
$.24
$.60
.40

16. Target Volume in Sales Dollars=
Fixed costs +
Target profit
Contribution margin ratio
Target volume sales dollars TR F TR p +
CMR =

17. Target Sales Dollars Example
U-Develop F TR p +
CMR = TR
.40
$1,800
$1,500 TR
$8,250
13,750 x $.60 = $8,250

18. 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) F X p +
CM unit =
p = 0
Break-even volume (units) =
Fixed costs
CMunit

19. Break-Even Units Example
U-Develop F X p
CM unit X
$.24
1,500 X
6,250 prints

20. Total revenues = Total costs
Break-Even in Sales Dollars
The total sales dollars at which profits equal zero.
p = 0
Total revenues = Total costs F TR
CMR TR F
CMR

21. Break-Even Sales Dollars Example
U-Develop F TR p
CMR TR
.40
$1500 TR
$3,750
6,250 prints X $.60 = $3,750

22. CVP Summary Summary of Target Volume and Break-Even Formulas
Target volume (units) =
Fixed costs +
Target profit
Unit contribution margin
Target volume sales dollars =
Fixed costs +
Target profit
Contribution margin ratio

23. CVP Summary Continued Summary of Target Volume and Break-Even Formulas
Break-even volume (units) =
Fixed costs
Unit contribution margin
Break-even volume (sales dollars) =
Fixed costs
Contribution margin ratio

24. Graphic Presentation U-Develop Break-Even $3,750 6,250 prints
Total revenue
Total cost
$3,750
6,250 prints

25. 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.
Contribution margin
Net income
The higher the organization’s operating leverage, the higher the break-even point.

26. Comparison of Cost Structures
Lo-Lev Company
Hi-Lev Company
(1,000,000 units)
Amount
Percentage
Sales
$1,000,000
100%
Variable Costs
$750,000
75%
$250,000
25%
Contribution margin
$250,000
25%
$750,000
75%
Fixed costs
$50,000 5%
$550,000
55%
Operating profit
$200,000
20%
Break-even point
200,000 units
733,334 units
Contribution margin per unit
$0.25
$0.75
Degree of Operating Leverage
1.25
3.75

27. Operating Leverage Example
Suppose Lo-Lev & Hi-Lev both increase sales 10% or $100,000.
Why do I care?
Lo-Lev
Hi-Lev
Sales
CMR
Increase in Profit
Prior NI
NI with sales increase of 10%
$100,000
.25
$25,000
$200,000
$225,000
$100,000
.75
$75,000
$200,000
$275,000

28. Operating Leverage Continued
Lo-Lev
Hi-Lev
Percent Increase in sales
Degree of Operating Leverage
Percent increase in NI
Prior NI
NI with sales increase of 10%
10%
1.25
12.5%
$200,000
$225,000
10%
1.75
17.5%
$200,000
$275,000

29. Margin of Safety
The excess of projected or actual sales volume over break-even volume. or
The excess of projected or actual sales revenue over break-even revenue.
Suppose U-Develop sells 8,000 prints
8,000
6,250
1,750 prints
$4,800
$3,750
$1,050
1750 x $.60 = $1,050

30. Extending CVP: Taxes p Profit of $3,000 But this means taxes.
What if U-Develop is in the 15% tax bracket and wants profit after taxes of $3,000?
CM unit F
1 - t p
Target Volume
.85 X
$1,500
$3,000
$.24 X
20,956 units

31. CVP and Taxes Continued
Check it out
20,956
$.60
$12,574
Sales VC
20,956
$.36
7,544 CM
$5,030 FC
1,500
NIBT
$3,530
Taxes
530
3,530
15%
Net Income
$3,000

32. Extending CVP: Multiple Products
What if:
U-Develop does prints and enlargements?
Prints
Enlargements
Selling price
$.60
$1.00
Variable cost
.36
.56
Contribution margin
$. 24
$. 44
Total Fixed Costs
$1,820

33. Product Mix For every 9 prints sold U-Develop sells 1 enlargement.
Weighted Average Contribution Margin
9/10
$.24
1/10
$.44
$ .26
6,300 prints
9/10
Breakeven
$1,820
$.26
7,000
700 enlargements
1/10

34. Differential Analysis
L.O. 3 Use differential analysis to analyze decisions.
Differential Analysis
The process of estimating revenues and costs of alternative actions available to decision makers and of comparing these estimates to the status quo.
Short Run
The period of time over which capacity will be unchanged, usually one year.

35. Differential Costs Alternative A Alternative B
Costs that change in response to an alternative course of action.
Differential costs differ between actions.
Alternative A
Alternative B

36. Sunk Costs IT’S GONE TOO BAD SO SAD
Costs incurred in the past that cannot be changed by present or future decisions.
IT’S GONE
TOO BAD
SO SAD
A sunk cost is NOT relevant.

37. 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

38. 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.

39. 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

40. Short-run vs Long-run Pricing Decisions
Year 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?

41. Short-run Pricing Decisions: Special Orders
An order that will not affect other sales and is usually a one-time occurrence.
Value of Option 1
Accept Special Order?
Is Option > Option 2?
Status Quo: Reject special offer
Alternative: Accept special offer
Value of Option 2
Option 1
Option 2

42. Special Order Example Analysis of Special Order U-Develop Status Quo:
Alternative:
Reject Special Order
Accept Special Order
Difference
Comparison of Totals
Variable costs
(1,000)
(1,100)
(100)
Fixed costs
(1,200)
Operating profit
$300
$400
$100
Sales revenue
$2,500
$2,700
$200
Total contribution
1,500
1,600
100
Alternative Presentation: Differential Analysis
Differential operating profit (before taxes)
$100
Differential sales, 500 at 40¢
$200
Less differential costs, 500 at 20¢
100

43. 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

44. 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.
R&D
Design
Manufacturing
Marketing
Distribution
&
Customer
Service
(Disposal)
Take Back
Cradle
Grave To
Life-cycle Costing
Concerned with covering costs in all categories of the life cycle.

45. 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?
Desired profit
How much profit do I need?
Target cost
The maximum amount of cost allowed.
Can I make it at this cost?

46. 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.
Make or buy?
Decision to add or drop a product line or close a business unit.
Add or drop a segment?
Decision on what products or services to offer.
Product Mix

47. Make or Buy Example Make or buy?
Decision to make goods or services internally or externally.
100,000 prints
Per Unit
100,000 prints
Cost directly traceable
Direct materials
$0.05
$5,000
Direct labor
0.12
12,000
Variable manufacturing overhead
0.03
3,000
Fixed manufacturing overhead
4,000
Common costs allocated to this product line
10,000
$34,000

48. Make or Buy Continued Make or Buy Analysis, U-Develop Status Quo:
Alternative:
Process Prints
Outsource Processing
Difference
100,000 prints
Direct costs
5,000
$25,000 a
20,000
Direct materials
higher
Labor
12,000
lower
Variable overhead
3,000
lower
Fixed overhead
4,000
lower
Common costs
10,000 b
Total costs
$34,000
$35,000
$1,000
higher
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.

49. Make or Buy Continued Make or Buy Analysis, U-Develop Status Quo:
Alternative:
Process Prints
Outsource Processing
Difference
50,000 prints
Direct costs
2,500 c
$12,500 d
10,000
Direct materials
higher
Labor
6,000
lower
Variable overhead
1,500
lower
Fixed overhead
4,000
lower
Common costs
10,000 b
Total costs
$24,000
$22,500
$1,500
lower
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.

50. Opportunity Costs of Making
Make-or-Buy Analysis with Opportunity Cost of U-Develop
Status Quo
Alternative
Process Prints
Outsource Processing
Difference
Total cost of 100,000 prints
$34,000
$35,000
1,000
Higher a
Opportunity cost of using facilities to make covers
2,000
Lower a
Total costs, including opportunity costs
$36,000
$35,000
1,000
Lower a
Differential costs decrease by $1,000 so accept the alternative.
a These indicate whether the alternative is higher or lower than the status quo.

51. Add or Drop Example Add or drop a segment?
Decision to add or drop a product line or close a business unit.
Fourth Quarter Product Line Income Statement, U-Develop
Less fixed costs:
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
$5,000
Rent
4,000
1,000
2,000
Salaries
5,000
2,500
1,500
Marketing and administrative
_3,000
__500
_1,500
_1,000
Operating profit (loss)
$15,000
$(500)
$14,000
$1,500

52. Add or Drop Continued Differential Analysis U-Develop
Status Quo:
Alternative:
Keep Prints
Drop Prints
Difference
Less fixed costs:
Sales revenue
$80,000
$70,000
$10,000
decrease
Cost of sales (all variables)
53,000
45,000
_8,000
Contribution margin
$27,000
$25,000
$2,000
Salaries
5,000
4,000
1,000
Marketing and administrative
_3,000
_2,750
__250
Operating profit (loss)
$15,000
$14,250
$750
Rent
Profits decrease $750 so keep prints.

53. 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.

54. Product Choice Decisions Example
Revenue and Cost Information, U-Develop
Metal Frames
Wood Frames
Price
$50
$80
Less variable costs per unit
Material 8 22
Labor 8 24
Overhead 4
Contribution margin per unit
$30
Fixed manufacturing costs: $3,000 per month
Fixed marketing and administrative costs: $1,500 per month

55. Product Choice Decisions Example
Revenue and Cost Information, U-Develop
Per Unit
Metal Frames
Wood Frames
Contribution margin
$30
Machine hours required .5 1
Contribution margin per machine hour
$60
$30
Metal Frames have a higher contribution margin per machine hour.

56. Product Choice Decisions Example
Suppose U-Develop has 200 machine hours per month available.
Capacity
400
200
Contribution margin per unit
$30
Total contribution margin
$12,000
$6,000
Metal Frames
Wood Frames
Less fixed manufacturing costs
3,000
Less fixed M&A costs
1,500
Operating profit
$7,500
$1,500
Selling metal frames results in higher profits than selling wooden frames.

57. Theory of Constraints 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.

58. Chapter 3
The End