0. Differential Analysis: The Key to Decision Making
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Differential Analysis: The Key to Decision Making
Chapter 14: Differential Analysis: The Key to Decision Making
Making decisions is one of the basic functions of a manager. To be successful in decision making, managers must be able to tell the difference between relevant and irrelevant data and must be able to correctly use the relevant data in analyzing alternatives. The purpose of this chapter is to develop these skills by illustrating their use in a wide range of decision-making situations.
Chapter 14

1. Identify relevant and irrelevant costs and benefits in a decision.
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Identify relevant and irrelevant costs and benefits in a decision.
Learning objective number 1 is to identify relevant and irrelevant costs and benefits in a decision.

2. Cost Concepts for Decision Making
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Cost Concepts for Decision Making
A relevant cost is a cost that differs between alternatives. 1 2
A relevant cost is a cost that differs between alternatives.

3. Identifying Relevant Costs
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Identifying Relevant Costs
An avoidable cost is a cost that can be eliminated, in whole or in part, by choosing one alternative over another. Avoidable costs are relevant costs. Unavoidable costs are irrelevant costs.
Two broad categories of costs are never relevant in any decision. They include:
Sunk costs.
Future costs that do not differ between the alternatives.
An avoidable cost is a cost that can be eliminated, in whole or in part, by choosing one alternative over another. Avoidable costs are relevant costs. Unavoidable costs are irrelevant costs.
Two broad categories of costs are never relevant in any decision:
A sunk cost is a cost that has already been incurred and cannot be avoided regardless of what a manager decides to do.
A future cost that does not differ between alternatives is never a relevant cost.

4. Relevant Cost Analysis: A Two-Step Process
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Relevant Cost Analysis: A Two-Step Process
Eliminate costs and benefits that do not differ between alternatives.
Use the remaining costs and benefits that differ between alternatives in making the decision. The costs that remain are the differential, or avoidable, costs.
Step 1
Step 2
Relevant cost analysis is a two-step process.
The first step is to eliminate costs and benefits that do not differ between alternatives. These irrelevant costs consist of sunk costs and future costs that do not differ between alternatives.
The second step is to use the remaining costs and benefits that do differ between alternatives in making the decision. The costs that remain are the differential, or avoidable, costs.

5. Different Costs for Different Purposes
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Different Costs for Different Purposes
Costs that are relevant in one decision situation may not be relevant in another context. Thus, in each decision situation, the manager must examine the data at hand and isolate the relevant costs.
Costs that are relevant in one decision situation may not be relevant in another context. Thus, in each decision situation, the manager must examine the data at hand and isolate the relevant costs.

6. Identifying Relevant Costs
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Identifying Relevant Costs
Cynthia, a Malaysian student studying in Penang, is considering visiting her friend in Kuala Lumpur. She can drive or take the budget airline. By car, it is 230 miles to her friend’s apartment. She is trying to decide which alternative is less expensive and has gathered the following information:
$24,000 cost – $10,000 salvage value ÷ 5 years
$2.70 per gallon ÷ 27 MPG
Part I
Assume the following information with respect to Cynthia, a Penang student who is considering visiting her friend in Kuala Lumpur. Cynthia is trying to decide whether it would be less expensive to drive or take the plane to Kuala Lumpur. She has compiled the following information with respect to her automobile.
Part II
The straight-line depreciation is calculated as cost minus salvage value divided by useful life.
Part III
Gasoline per mile is calculated by taking the price per gallon of gasoline and dividing it by the number of miles per gallon of the car. The annual cost of insurance and license and maintenance and repairs are also included to arrive at the average cost per mile.
Part IV
The parking fee at school is $45 a month. Cynthia attends school only eight months out of the year.
$45 per month × 8 months

7. Identifying Relevant Costs
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Identifying Relevant Costs
She has also gathered additional information to aid in her decision, such as the reduction in resale value per mile driven, round-trip airfare, benefits of relaxing on the plane, cost of putting her dog in the kennel, benefits of having a car in Kuala Lumpur, hassle of parking in Kuala Lumpur, and the per day cost of parking in Kuala Lumpur. Some of these items can be measured in dollars and some can’t.

8. Identifying Relevant Costs
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Identifying Relevant Costs
Which costs and benefits are relevant in Cynthia’s decision?
The cost of the car is a sunk cost and is not relevant to the current decision.
The annual cost of insurance is not relevant. It will remain the same if she drives or takes the plane.
Part I
Which costs are relevant to her decision?
The cost of the car is irrelevant to the decision because it is a sunk cost.
The annual cost of auto insurance is irrelevant because it does not differ between alternatives.
Part II
The cost of the gasoline is relevant because it is avoidable if she takes the plane.
However, the cost of gasoline is clearly relevant if she decides to drive. If she takes the plane, the cost would not be incurred, so it varies depending on the decision.

9. Identifying Relevant Costs
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Identifying Relevant Costs
Which costs and benefits are relevant in Cynthia’s decision?
The cost of maintenance and repairs is relevant. In the long-run these costs depend upon miles driven.
The monthly school parking fee is not relevant because it must be paid if Cynthia drives or takes the plane.
Part I
The cost of maintenance and repairs is relevant because in the long-run these costs depend upon miles driven.
The parking fee at school is irrelevant because it is not a differential cost.
Part II
At this point, we can see that some of the average cost of $0.619 per mile are relevant and others are not.
At this point, we can see that some of the average cost of $0.619 per mile are relevant and others are not.

10. Identifying Relevant Costs
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Identifying Relevant Costs
Which costs and benefits are relevant in Cynthia’s decision?
The decline in resale value due to additional miles is a relevant cost.
The round-trip airfare is clearly relevant. If she drives the cost can be avoided.
Relaxing on the plane is relevant even though it is difficult to assign a dollar value to the benefit.
The kennel cost is not relevant because Cynthia will incur the cost if she drives or takes the plane.
Part I
The decline in resale value is relevant due to the additional miles driven.
The round trip airfare is relevant because it is avoidable if she drives her car.
Relaxing on the plane is relevant, but difficult to quantify.
Part II
The kennel cost is irrelevant because it is not a differential cost.

11. Identifying Relevant Costs
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Identifying Relevant Costs
Which costs and benefits are relevant in Cynthia’s decision?
The cost of parking in Kuala Lumpur is relevant because it can be avoided if she takes the plane.
The benefits of having a car in Kuala Lumpur and the problems of finding a parking space are both relevant but are difficult to assign a dollar amount.
The cost of parking in Kuala Lumpur is relevant because it is avoidable if she takes the plane.
The benefits of having a car in Kuala Lumpur and the problem of finding a parking space are both relevant, but difficult to quantify.

12. Identifying Relevant Costs
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Identifying Relevant Costs
From a financial standpoint, Cynthia would be better off taking the plane to visit her friend. Some of the non-financial factor may influence her final decision.
From a financial standpoint, Cynthia would be better off taking the plane. But, as with any decision we may face, it may be the non-financial or non-quantitative factors that have the most impact on our decision.

13. Total and Differential Cost Approaches
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Total and Differential Cost Approaches
The management of a company is considering a new labor saving machine that rents for $3,000 per year. Data about the company’s annual sales and costs with and without the new machine are:
Assume the following information for a company considering a new labor-saving machine that rents for $3,000 per year.
The total approach requires constructing two contribution format income statements – one for each alternative.
The difference between the two income statements of $12,000 equals the differential benefits shown at the bottom of the right-hand column.

14. Total and Differential Cost Approaches
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Total and Differential Cost Approaches
As you can see, the only costs that differ between the alternatives are the direct labor costs savings and the increase in fixed rental costs.
We can efficiently analyze the decision by looking at the different costs and revenues and arrive at the same solution.
The most efficient means of analyzing this decision is to use the differential approach to isolate the relevant costs and benefits as shown.

15. Total and Differential Cost Approaches
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Total and Differential Cost Approaches
Using the differential approach is desirable for two reasons:
Only rarely will enough information be available to prepare detailed income statements for both alternatives.
Mingling irrelevant costs with relevant costs may cause confusion and distract attention away from the information that is really critical.
Using the differential approach is desirable for two reasons:
First, only rarely will enough information be available to prepare detailed income statements for both alternatives.
Second, mingling irrelevant costs with relevant costs may cause confusion and distract attention away from the information that is really critical.

16. 13-16
Prepare an analysis showing whether a product line or other business segment should be dropped or retained.
Learning objective number 2 is to prepare an analysis showing whether a product line or other business segment should be dropped or retained.

17. Adding/Dropping Segments
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Adding/Dropping Segments
One of the most important decisions managers make is whether to add or drop a business segment. Ultimately, a decision to drop an old segment or add a new one is going to hinge primarily on the impact the decision will have on net operating income.
To assess this impact, it is necessary to carefully analyze the costs.
One of the most important decisions managers make is whether to add or drop a business segment. Ultimately, a decision to drop an old segment or add a new one is going to hinge primarily on the impact the decision will have on net operating income. To assess this impact it is necessary to carefully analyze the costs.

18. Adding/Dropping Segments
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Adding/Dropping Segments
Due to the declining popularity of digital watches, Lovell Company’s digital watch line has not reported a profit for several years. Lovell is considering discontinuing this product line.
Assume that Lovell Company’s digital watch line has not reported a profit for several years; accordingly, Lovell is considering discontinuing this product line.

19. A Contribution Margin Approach
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A Contribution Margin Approach
DECISION RULE
Lovell should drop the digital watch segment only if its profit would increase.
Lovell will compare the contribution margin that would be lost to the costs that would be avoided if the line was to be dropped.
Let’s look at this solution.
To determine how dropping this line will affect the overall profits of the company, Lovell will compare the contribution margin that would be lost to the costs that would be avoided if the line was to be dropped.
Lovell should drop the digital watch segment only if its profit would increase. This would only happen if the fixed cost savings exceed the lost contribution margin.

20. Adding/Dropping Segments
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Adding/Dropping Segments
Assume a segmented income statement for the digital watches line is as shown.

21. Adding/Dropping Segments
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Adding/Dropping Segments
An investigation has revealed that the fixed general factory overhead and fixed general
administrative expenses will not be affected by dropping the digital watch line. The fixed general factory overhead and general administrative expenses assigned to this product would be reallocated to other product lines.
An investigation has revealed that the fixed general factory overhead and fixed general administrative expenses will not be affected by dropping the digital watch line. The fixed general factory overhead and general administrative expenses assigned to this product would be reallocated to other product lines.

22. Adding/Dropping Segments
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Adding/Dropping Segments
The equipment used to manufacture
digital watches has no resale
value or alternative use.
Should Lovell retain or drop
the digital watch segment?
Part I
The equipment used to manufacture digital watches has no resale value or alternative use.
Part II
Should Lovell retain or drop the digital watch segment?

23. A Contribution Margin Approach
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A Contribution Margin Approach
Retain
A contribution margin approach reveals that the contribution margin lost ($300,000) exceeds the fixed costs avoided ($260,000) by $40,000. Therefore, Lovell should retain the digital watch segment.

24. Comparative Income Approach
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Comparative Income Approach
The Lovell solution can also be obtained by preparing comparative income statements showing results with and without the digital watch segment.
Let’s look at this second approach.
Comparative income statements can also be prepared to help make the decision.
Let’s look at this second approach.

25. 13-25
If the digital watch line is dropped, the company loses $300,000 in contribution margin.
These income statements show that if the digital watch line is dropped, the company loses $300,000 in contribution margin.

26. 13-26
On the other hand, the general factory overhead would be the same under both alternatives, so it is irrelevant.
The general factory overhead would be the same under both alternatives, so it is irrelevant.

27. 13-27
The salary of the product line manager would disappear, so it is relevant to the decision.
The salary of the product line manager would disappear, so it is relevant to the decision.

28. 13-28
The depreciation is a sunk cost. Also, remember that the equipment has no resale value or alternative use, so the equipment and the depreciation expense associated with it are irrelevant to the decision.
The depreciation is a sunk cost. Also, remember that the equipment has no resale value or alternative use, so the equipment and the depreciation expense associated with it are irrelevant to the decision.

29. 13-29
The complete comparative income statements reveal that Lovell would earn $40,000 of additional profit by retaining the digital watch line.
The complete comparative income statements reveal that Lovell would earn $40,000 of additional profit by retaining the digital watch line.

30. Beware of Allocated Fixed Costs
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Beware of Allocated Fixed Costs
Why should we keep the digital watch segment when it’s showing a $100,000 loss?
Lovell’s allocated fixed costs can distort the keep/drop decision.
Lovell’s managers may ask “why keep the digital watch segment when its segmented income statement shows a $100,000 loss?”

31. Beware of Allocated Fixed Costs
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Beware of Allocated Fixed Costs
The answer lies in the way we allocate common fixed costs to our products.
The answer lies in the way common fixed costs are allocated to products.

32. Beware of Allocated Fixed Costs
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Beware of Allocated Fixed Costs
Including unavoidable common fixed costs makes the product line appear to be unprofitable.
Our allocations can make a segment look less profitable than it really is.
Including unavoidable common fixed costs in the segmented income statement makes the digital watch product line appear to be unprofitable, when in fact, dropping the product line would decrease the company’s overall net operating income.

33. Prepare a make or buy analysis.
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Prepare a make or buy analysis.
Learning objective number 3 is to prepare a make or buy analysis.

34. The Make or Buy Decision
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The Make or Buy Decision
When a company is involved in more than one activity in the entire value chain, it is vertically integrated. A decision to carry out one of the activities in the value chain internally, rather than to buy externally from a supplier is called a “make or buy” decision.
When a company is involved in more than one activity in the entire value chain, it is vertically integrated.
A decision to carry out one of the activities in the value chain internally, rather than to buy externally from a supplier, is called a make or buy decision.

35. Vertical Integration- Advantages
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Vertical Integration- Advantages
Smoother flow of parts and materials
Better quality control
Vertical integration provides certain advantages.
An integrated company may be able to ensure a smoother flow of parts and materials for production than a nonintegrated company.
Some companies feel that they can control quality better by producing their own parts and materials.
Integrated companies realize profits from the parts and materials that they choose to make instead of buy.
Realize profits

36. Vertical Integration- Disadvantage
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Vertical Integration- Disadvantage
Companies may fail to take advantage of suppliers who can create economies of scale advantage by pooling demand from numerous companies.
While the economics of scale factor can be appealing, a company must be careful to retain control over activities that are essential to maintaining its competitive position.
The primary disadvantage of vertical integration is that a company may fail to take advantage of suppliers who can create an economies of scale advantage by pooling demand from numerous companies.
While the economies of scale factor can be appealing, a company must be careful to retain control over activities that are essential to maintaining its competitive position.

37. The Make or Buy Decision: An Example
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The Make or Buy Decision: An Example
Essex Company manufactures part 4A that is used in one of its products.
The unit product cost of this part is:
Assume that Essex Company manufactures part 4A with a unit product cost as shown.

38. The Make or Buy Decision
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The Make or Buy Decision
The special equipment used to manufacture part 4A has no resale value.
The total amount of general factory overhead, which is allocated on the basis of direct labor hours, would be unaffected by this decision.
The $30 unit product cost is based on 20,000 parts produced each year.
An outside supplier has offered to provide the 20,000 parts at a cost of $25 per part.
Should we accept the supplier’s offer?
Also, assume the following information as shown with respect to part 4A.
Given these additional assumptions, should Essex make or buy part 4A?

39. The Make or Buy Decision
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The Make or Buy Decision
The avoidable costs associated with making part 4A include direct materials, direct labor, variable overhead, and the supervisor’s salary.
The avoidable costs associated with making part 4A include direct materials, direct labor, variable overhead, and the supervisor’s salary.

40. The Make or Buy Decision
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The Make or Buy Decision
The depreciation of special equipment represents a sunk cost. Furthermore, the equipment has no resale value, thus the special equipment and its associated depreciation expense are irrelevant to the decision.
The depreciation of the special equipment represents a sunk cost. The equipment has no resale value, thus its cost and associated depreciation are irrelevant to the decision.

41. The Make or Buy Decision
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The Make or Buy Decision
The general factory overhead represents future costs that will be incurred regardless of whether Essex makes or buys part 4A; hence, it is also irrelevant to the decision.
Not avoidable; irrelevant. If the product is dropped, it will be reallocated to other products.

42. The Make or Buy Decision
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The Make or Buy Decision
The total avoidable costs of $340,000 are less than the $500,000 cost of buying the part, thereby suggesting that Essex should continue to make the part.
Should we make or buy part 4A? Given that the total avoidable costs are less than the cost of buying the part, Essex should continue to make the part.

43. How would this concept potentially relate to the Essex Company?
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Opportunity Cost
An opportunity cost is the benefit that is foregone as a result of pursuing some course of action.
Opportunity costs are not actual cash outlays and are not recorded in the formal accounts of an organization.
How would this concept potentially relate to the Essex Company?
An opportunity cost is the benefit that is foregone as a result of pursuing a course of action. These costs do not represent actual cash outlays and they are not recorded in the formal accounts of an organization.
In the Essex Company example that we just completed, if Essex had an alternative use for the capacity that it used to make part 4A, there would have been an opportunity cost to factor into the analysis.
The opportunity cost would have been equal to the segment margin that could have been derived from the best alternative use of the space.

44. Value to Business (Deprival Value)
Recoverable Value (RV)
= Higher of
Replacement Cost (RC)
Deprival value
= Lower of
Net Realizable Value (NRV)
Value in Use (VIU)
Economic Value (EV) or Present Value (PV)
The Opportunity Cost can be derived by using the deprival value model (also known as Value to Business and Value to Owner).
It is often asked why inventories are not valued at the opportunity cost foregone during the decision making process.
The deprival value of any asset is the lower of its replacement cost and recoverable value, and the recoverable value is the higher of net realizable value and value in use, i.e. the amount that can be generated from the asset.
The rationale of this definition is that if the recoverable value exceeds the replacement cost, the company would go out and buy another one to replace it and make the best use of the asset by selling it or using it. The real cost to the company is the replacement cost. On the other hand, if the replacement cost exceeds the recoverable value, the company would be deprived of owning or using the asset in the long run, and it would not make sense to replace the asset when it would cost the company too much to replace it. In this case, the asset becomes a scarce resource to the company hence the recoverable value of using the asset will be the maximum benefit foregone between the two options, net realizable value and value in use.
The deprival value model summarizes the above neatly and clearly in the simple diagram shown in the slide.

45. Opportunity Costs: An Example
Fed Co. Ltd. is considering the publication of a limited edition of a book, bound in a special grade of leather.
The leather was bought some year ago for $500.
The current price for the same quantity of leather would be $1,200
Fed Co. Ltd. Can use the leather to cover desk furnishings, in replacement for other material which would cost $400
Fed Co. Ltd. can sell it with a net disposal proceeds of $300
How much should the leather be valued for the use of book bounding?
In this example, without the deprival value model, some students cannot differentiate the maximum foregone and the irrelevant information.
With the deprival value model, almost all students can find the opportunity cost of this scenario.
The example can be used with change of the figures to test students understanding.
What if the current price of the leather is only $350?
The relevant value of the leather for the decision making purpose should be $350 in this case! This can be resolved by using the deprival value model on the following slide. The valuation chosen also matches with the financial accounting requirement of inventory being valued at lower of inventory cost or market value.

46. Opportunity Cost: Deprival Value Approach
Recoverable Value (RV)
= Higher of
Replacement Cost
(RC)
$1,200
Deprival value
= Lower of
Net Realizable Value
(NRV)
$300
Value in Use (VIU) (Economic Value (EV))
$400
$400
$400
Fit the figures into the deprival value model can help students to identify the true value including the opportunity cost of using the leather for book bounding.
If we change the market replacement cost to $350, then the deprival value will change to $350 as the leather cannot be valued over its market value based on the basic accounting rule: lower of inventory cost or market value. Furthermore, a trading opportunity may exist to buy and sell the leather to compete with the desk covering material. All inventories for trading are valued based on lower of cost or market value!

47. 13-47
Prepare an analysis showing whether a special order should be accepted.
Learning objective number 4 is to prepare an analysis showing whether a special order should be accepted.

48. 13-48
Key Terms and Concepts
A special order is a one-time order that is not considered part of the company’s normal ongoing business.
When analyzing a special order, only the incremental costs and benefits are relevant.
Since the existing fixed manufacturing overhead costs would not be affected by the order, they are not relevant.
A special order is a one-time order that is not considered part of the company’s normal ongoing business.
When analyzing a special order, only the incremental costs and benefits are relevant. Since the existing fixed manufacturing overhead costs would not be affected by the order, they are not relevant.

49. Should Jet accept the offer?
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Special Orders
Jet Corporation. makes a single product whose normal selling price is $20 per unit.
A foreign distributor offers to purchase 3,000 units for $10 per unit.
This is a one-time order that would not affect the company’s regular business.
Annual capacity is 10,000 units, but Jet Corporation is currently producing and selling only 5,000 units.
Assume the following information with respect to a special order opportunity for Jet Corporation
Should Jet accept the offer?
Should Jet accept the offer?

50. Special Orders $8 variable cost 13-50 Part I
A contribution format income statement for Jet’s normal sales of 5,000 units is as shown.
Part II
Assume variable cost is $8 a unit. Total variable cost would be 5,000 units times $8 a unit.

51. 13-51
Special Orders
If Jet accepts the special order, the incremental revenue will exceed the incremental costs. In other words, net operating income will increase by $6,000. This suggests that Jet should accept the order.
If Jet accepts the special order, the incremental revenue of $30,000 will exceed the incremental costs of $24,000 by $6,000. This suggests that Jet should accept the order. Notice that this answer assumes that the fixed costs are unavoidable and that variable marketing costs must be incurred on the special order.
Note: This answer assumes that the fixed costs are unavoidable and that variable marketing costs must be incurred on the special order.

52. 13-52
Quick Check 
Northern Optical ordinarily sells the X-lens for $50. The variable production cost is $10, the fixed production cost is $18 per unit, and the variable selling cost is $1. A customer has requested a special order for 10,000 units of the X-lens to be imprinted with the customer’s logo. This special order would not involve any selling costs, but Northern Optical would have to purchase an imprinting machine for $50,000.
(see the next page)
Northern Optical ordinarily sells the X-lens for $50. The variable production cost is $10, the fixed production cost is $18 per unit, and the variable selling cost is $1. A customer has requested a special order for 10,000 units of the X-lens to be imprinted with the customer’s logo. This special order would not involve any selling costs, but Northern Optical would have to purchase an imprinting machine for $50,000.

53. 13-53
Quick Check 
What is the rock bottom minimum price below which Northern Optical should not go in its negotiations with the customer? In other words, below what price would Northern Optical actually be losing money on the sale? There is ample idle capacity to fulfill the order and the imprinting machine has no further use after this order.
a. $50
b. $10
c. $15
d. $29
What is the rock bottom minimum price below which Northern Optical should not go in its negotiations with the customer? In other words, below what price would Northern Optical actually be losing money on the sale? There is ample idle capacity to fulfill the order and the imprinting machine has no further use after this order.

54. 13-54
Determine the most profitable use of a constrained resource and the value of obtaining more of the constrained resource.
Learning objective number 5 is to determine the most profitable use of a constrained resource and the value of obtaining more of the constrained resource.

55. 13-55
Key Terms and Concepts
When a limited resource of some type restricts the company’s ability to satisfy demand, the company is said to have a constraint.
The machine or process that is limiting overall output is called the bottleneck – it is the constraint.
When a limited resource of some type restricts the company’s ability to satisfy demand, the company is said to have a constraint. The machine or process that is limiting overall output is called the bottleneck – it is the constraint.

56. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
Fixed costs are usually unaffected in these situations, so the product mix that maximizes the company’s total contribution margin should ordinarily be selected.
A company should not necessarily promote those products that have the highest unit contribution margins.
Rather, total contribution margin will be maximized by promoting those products or accepting those orders that provide the highest contribution margin in relation to the constraining resource.
Fixed costs are usually unaffected in these situations, so the product mix that maximizes the company’s total contribution margin should ordinarily be selected.
A company should not necessarily promote those products that have the highest unit contribution margin.
Rather, total contribution margin will be maximized by promoting those products or accepting those orders that provide the highest contribution margin in relation to the constraining resource.

57. Utilization of a Constrained Resource: An Example
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Utilization of a Constrained Resource: An Example
Ensign Company produces two products and selected data are shown below:
Assume that Ensign Company produces two products and selected data are as shown.

58. Utilization of a Constrained Resource: An Example
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Utilization of a Constrained Resource: An Example
Machine A1 is the constrained resource and is being used at 100% of its capacity.
There is excess capacity on all other machines.
Machine A1 has a capacity of 2,400 minutes per week.
Should Ensign focus its efforts on Product 1 or Product 2?
In addition, assume that Machine A1 is the constraint, and there is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per week.
Should Ensign focus its efforts on Product 1 or Product 2?

59. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
The key is the contribution margin per unit of the constrained resource.
Ensign should emphasize Product 2 because it generates a contribution margin of $30 per minute of the constrained resource relative to $24 per minute for Product 1.
As suggested by the answer to the Quick Check question, Ensign should emphasize Product 2 because it generates a contribution margin of $30 per minute of the constrained resource relative to $24 per minute for Product 1.

60. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
The key is the contribution margin per unit of the constrained resource.
Ensign can maximize its contribution margin by first producing Product 2 to meet customer demand and then using any remaining capacity to produce Product 1. The calculations would be performed as follows.
Ensign can maximize its contribution margin by first producing Product 2 to meet customer demand and then using any remaining capacity to produce Product 1.

61. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
Let’s see how this plan would work.
Satisfying the weekly demand of 2,200 units for Product 2 would consume 1,100 minutes of available capacity on machine A1.

62. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
Let’s see how this plan would work.
This implies that 1,300 constraint minutes would still be available to satisfy demand for Product 1.

63. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
Let’s see how this plan would work.
Since each unit of Product 1 requires one minute of A1 machine time, Ensign could produce 1,300 units of Product 1 with its remaining capacity.

64. Utilization of a Constrained Resource
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Utilization of a Constrained Resource
According to the plan, we will produce 2,200 units of Product 2 and 1,300 of Product 1. Our contribution margin looks like this.
This mix of production would yield a total contribution margin of $64,200.
The total contribution margin for Ensign is $64,200.

65. 13-65
Quick Check 
Colonial Heritage makes reproduction colonial furniture from select hardwoods.
The company’s supplier of hardwood will only be able to supply 2,000 board feet this month. Is this enough hardwood to satisfy demand?
a. Yes
b. No
Review the information provided about Colonial Heritage. Is this enough hardwood to satisfy demand?

66. Quick Check  a. 500 chairs and 100 tables b. 600 chairs and 80 tables
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Quick Check 
The company’s supplier of hardwood will only be able to supply 2,000 board feet this month. What plan would maximize profits?
a. 500 chairs and 100 tables
b. 600 chairs and 80 tables
c. 500 chairs and 80 tables
d. 600 chairs and 100 tables
The company’s supplier of hardwood will only be able to supply 2,000 board feet this month. What plan would maximize profits?

67. 13-67
Quick Check 
As before, Colonial Heritage’s supplier of hardwood will only be able to supply 2,000 board feet this month. Assume the company follows the plan we have proposed. Up to how much should Colonial Heritage be willing to pay above the usual price to obtain more hardwood?
a. $40 per board foot
b. $25 per board foot
c. $20 per board foot
d. Zero
Read this information about Colonial Heritage. Up to how much should Colonial Heritage be willing to pay above the usual price to obtain more hardwood?

68. 13-68
Managing Constraints
It is often possible for a manager to increase the capacity of a bottleneck, which is called relaxing (or elevating) the constraint, in numerous ways such as:
Working overtime on the bottleneck.
Subcontracting some of the processing that would be done at the bottleneck.
Investing in additional machines at the bottleneck.
Shifting workers from non-bottleneck processes to the bottleneck.
Focusing business process improvement efforts on the bottleneck.
Reducing defective units processed through the bottleneck.
It is often possible for a manager to increase the capacity of a bottleneck, which is called relaxing (or elevating) the constraint, in numerous ways such as:
Working overtime on the bottleneck.
Subcontracting some of the processing that would be done at the bottleneck.
Investing in additional machines at the bottleneck.
Shifting workers from non-bottleneck processes to the bottleneck.
Focusing business process improvement efforts on the bottleneck.
Reducing defective units processed through the bottleneck.
These methods and ideas are all consistent with the Theory of Constraints, which was introduced in Chapter 1.
If a company has more than one potential constraint, the proper “mix” of products can be found using a quantitative method known as linear programming, which is covered in quantitative methods and operations management courses.
These methods and ideas are all consistent with the Theory of Constraints, which was introduced in Chapter 1.

69. 13-69
Prepare an analysis showing whether joint products should be sold at the split-off point or processed further.
Learning objective number 6 is to prepare an analysis showing whether joint products should be sold at the split-off point or processed further.

70. 13-70
Joint Costs
In some industries, a number of end products are produced from a single raw material input.
Two or more products produced from a common input are called joint products.
The point in the manufacturing process where each joint product can be recognized as a separate product is called the split-off point.
In some industries, a number of end products are produced from a single raw material input. When two or more products are produced from a common input these products are known as joint products. The split-off point is the point in the manufacturing process at which the joint products can be recognized as separate products.

71. Joint Products Split-Off Point
13-71
Joint Products
For example, in the petroleum refining industry, a large number of products are extracted from crude oil, including gasoline, jet fuel, home heating oil, lubricants, asphalt, and various organic chemicals.
Oil
Common
Production
Process
Joint
Input
Gasoline
Chemicals
For example, in the petroleum refining industry a large number of products are extracted from crude oil, including gasoline, jet fuel, home heating oil, lubricants, asphalt, and various organic chemicals.
Split-Off
Point

72. Joint Products Final Sale Final Sale Separate Split-Off Product Point
13-72
Joint Products
Joint costs
are incurred
up to the
split-off point
Separate
Processing
Final
Sale
Oil
Common
Production
Process
Joint
Input
Final
Sale
Gasoline
Separate
Processing
Final
Sale
Chemicals
The term joint cost is used to describe costs incurred up to the split-off point. Joint costs are common costs incurred to simultaneously produce a variety of end products.
Separate
Product
Costs
Split-Off
Point

73. The Pitfalls of Allocation
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The Pitfalls of Allocation
Joint costs are traditionally allocated among different products at the split-off point. A typical approach is to allocate joint costs according to the relative sales value of the end products.
Although allocation is needed for some purposes such as balance sheet inventory valuation, allocations of this kind are very dangerous for decision making.
Joint costs are traditionally allocated among different products at the split-off point. A typical approach is to allocate joint costs according to the relative sales value of the end products.
Although allocation is needed for some purposes such as balance sheet inventory valuation, allocations of this kind are very dangerous for decision making.

74. Sell or Process Further
13-74
Sell or Process Further
Joint costs are irrelevant in decisions regarding what to do with a product from the split-off point forward. Therefore, these costs should not be allocated to end products for decision-making purposes.
With respect to sell or process further decisions, it is profitable to continue processing a joint product after the split-off point so long as the incremental revenue from such processing exceeds the incremental processing costs incurred after the split-off point.
Joint costs are irrelevant in decisions regarding what to do with a product from the split-off point forward. Therefore, these costs should not be allocated to end products for decision making purposes.
With respect to sell or process further decisions, it is profitable to continue processing a joint product after the split-off point so long as the incremental revenue from such processing exceeds the incremental processing costs incurred after the split-off point.

75. Sell or Process Further: An Example
13-75
Sell or Process Further: An Example
Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the immediate joint products.
Unfinished lumber is sold “as is” or processed further into finished lumber.
Sawdust can also be sold “as is” to gardening wholesalers or processed further into “presto- logs.”
Assume the facts as shown with respect to Sawmill, Inc.

76. Sell or Process Further
13-76
Sell or Process Further
Data about Sawmill’s joint products includes:
Sawmill has two joint products – lumber and sawdust. Selected financial information is shown for each joint product.

77. Sell or Process Further
13-77
Sell or Process Further
The incremental revenue from further processing of the lumber and sawdust is $130 and $10, respectively.

78. Sell or Process Further
13-78
Sell or Process Further
The profit (loss) from further processing is $80 for the lumber and ($10) for the sawdust.

79. Sell or Process Further
13-79
Sell or Process Further
The lumber should be processed further and the sawdust should be sold at the split-off point.
The lumber should be processed further and the sawdust should be sold at the split-off point.

80. 13-80
End of Chapter 14
End of chapter 14.