1. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin Relevant Costs for Decision Making

2. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-2 Cost Concepts for Decision Making Decision making is to choose the best alternative among many alternatives. A relevant cost or benefit is a cost or benefit that differs between alternatives. 1 2

3. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-3 Identifying Relevant Costs Only those costs and benefits that differ between alternatives are relevant in a decision. All the other costs and benefits can and should be ignored. Two broad categories of costs are never relevant in any decision. They include:  Sunk costs.  Future costs that do not differ between the alternatives. Only those costs and benefits that differ between alternatives are relevant in a decision. All the other costs and benefits can and should be ignored. Two broad categories of costs are never relevant in any decision. They include:  Sunk costs.  Future costs that do not differ between the alternatives.

4. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-4 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 and benefits that remain are differential costs and benefits. Step 1 Step 2

5. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-5 Sunk Costs Sunk costs have already been incurred and cannot be changed now or in the future. They should be ignored when making decisions. Example: You bought an automobile that cost $10,000 two years ago. The $10,000 cost is sunk because whether you drive it, park it, trade it, or sell it, you cannot change the $10,000 cost.

6. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-6 Differential Cost and Revenue Costs and revenues that differ among alternatives. Example: You have a job paying $1,500 per month in your hometown. You have a job offer in a neighboring city that pays $2,000 per month. The commuting cost to the city is $300 per month. Differential revenue is: $2,000 – $1,500 = $500 Differential cost is: $300

7. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-7 Opportunity Cost The potential benefit that is given up when one alternative is selected over another. Example: If you were not attending college, you could be earning $15,000 per year. Your opportunity cost of attending college for one year is $15,000.

8. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-8 Different Costs for Different Purposes Costs that are relevant in one decision situation may not be relevant in another context.

9. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-9 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:

10. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-10 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 more efficiently analyze the decision by looking at the different costs and revenues and arrive at the same solution.

11. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-11 Learning Objective 2 Prepare an analysis showing whether a product line or other business segment should be dropped or retained.

12. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-12 Adding/Dropping Segments One of the most important decisions managers make is whether to add or drop a business segment, such as a product or a store. Let’s see how relevant costs should be used in this type of decision. One of the most important decisions managers make is whether to add or drop a business segment, such as a product or a store. Let’s see how relevant costs should be used in this type of decision.

13. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-13 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 dropping this product line.

14. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-14 Adding/Dropping Segments

15. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-15 A Contribution Margin Approach DECISION RULE Lovell should drop the digital watch segment only when doing so increases its profit. This would only happen if the fixed cost savings exceed the lost contribution margin. Let’s look at this solution. DECISION RULE Lovell should drop the digital watch segment only when doing so increases its profit. This would only happen if the fixed cost savings exceed the lost contribution margin. Let’s look at this solution.

16. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-16 Adding/Dropping Segments

17. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-17 Adding/Dropping Segments Investigation has revealed that total fixed general factory overhead and general administrative expenses would not be affected if the digital watch line is dropped. The fixed general factory overhead and general administrative expenses assigned to this product would be reallocated to other product lines. Investigation has revealed that total fixed general factory overhead and general administrative expenses would not be affected if the digital watch line is dropped. The fixed general factory overhead and general administrative expenses assigned to this product would be reallocated to other product lines.

18. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-18 Adding/Dropping Segments The equipment used to manufacture digital watches has no resale value or alternative use. The equipment used to manufacture digital watches has no resale value or alternative use. Should Lovell retain or drop the digital watch segment? Should Lovell retain or drop the digital watch segment?

19. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-19 A Contribution Margin Approach Retain

20. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-20 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. 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.

21. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-21 If the digital watch line is dropped, the company gives up its contribution margin.

22. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-22 On the other hand, the general factory overhead would be the same. So this cost really isn’t relevant.

23. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-23 But we wouldn’t need a manager for the product line anymore.

24. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-24 If the digital watch line is dropped, the net book value of the equipment would be written off. The depreciation that would have been taken will flow through the income statement as a loss instead.

25. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-25

26. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-26 Beware of Allocated Fixed Costs Why should we keep the digital watch segment when it’s showing a $100,000 loss?

27. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-27 Beware of Allocated Fixed Costs The answer lies in the way we allocate common fixed costs to our products.

28. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-28 Beware of Allocated Fixed Costs Our allocations can make a segment look less profitable than it really is.

29. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-29 Learning Objective 3 Prepare a make or buy analysis.

30. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-30 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:

31. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-31 The Make or Buy Decision 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? 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? 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.

32. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-32 The Make or Buy Decision 20,000 × $9 per unit = $180,000

33. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-33 The Make or Buy Decision The special equipment has no resale value and is a sunk cost.

34. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-34 The Make or Buy Decision Not avoidable; irrelevant. If the product is dropped, it will be reallocated to other products.

35. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-35 The Make or Buy Decision Should we make or buy part 4A?

36. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-36 Opportunity Cost An opportunity cost is the benefit that is foregone (i.e., given up) as a result of pursuing some course of action. Opportunity costs are not actual dollar outlays and are not recorded in the formal accounts of an organization. How would this concept potentially relate to the Essex Company? >> Think about the capacity that is no longer used for part 4A. For example, what if $200,000 income is generated from using the facilities for other activities? An opportunity cost is the benefit that is foregone (i.e., given up) as a result of pursuing some course of action. Opportunity costs are not actual dollar outlays and are not recorded in the formal accounts of an organization. How would this concept potentially relate to the Essex Company? >> Think about the capacity that is no longer used for part 4A. For example, what if $200,000 income is generated from using the facilities for other activities?

37. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-37 Learning Objective 4 Prepare an analysis showing whether a special order should be accepted.

38. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-38 Key Terms and Concepts A special order is a one-time order that is not considered part of the company’s normal on-going business. When analyzing a special order, only the incremental costs and benefits are relevant.

39. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-39 Special Orders  Jet, Inc. 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, Inc. is currently producing and selling only 5,000 units.  Jet, Inc. 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, Inc. is currently producing and selling only 5,000 units. Should Jet accept the offer?

40. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-40 Special Orders $8 unit variable cost

41. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-41 Special Orders If Jet accepts the offer, net operating income will increase by $6,000. Note: This answer assumes that fixed costs are unaffected by the order and that all variable costs are the same for the special order.

42. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-42 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. (see the next page)

43. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-43 Quick Check What is the 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

44. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-44 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 Quick Check Variable production cost $100,000 Additional fixed cost + 50,000 Total relevant cost$150,000 Number of units 10,000 Incremental cost per unit = $15 Variable production cost $100,000 Additional fixed cost + 50,000 Total relevant cost$150,000 Number of units 10,000 Incremental cost per unit = $15

45. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-45 Learning Objective 5 Determine the most profitable use of a constrained resource and the value of obtaining more of the constrained resource.

46. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-46 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.

47. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-47 Utilization of a Constrained Resource When a constraint exists, a company should not promote those products that have the highest unit contribution margin. When a constraint exists, a company should not promote those products that have the highest unit contribution margin. Rather, it should promote those products that earn the highest contribution margin in relation to the constraining resource. Rather, it should promote those products that earn the highest contribution margin in relation to the constraining resource. When a constraint exists, a company should not promote those products that have the highest unit contribution margin. When a constraint exists, a company should not promote those products that have the highest unit contribution margin. Rather, it should promote those products that earn the highest contribution margin in relation to the constraining resource. Rather, it should promote those products that earn the highest contribution margin in relation to the constraining resource.

48. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-48 Utilization of a Constrained Resource: An Example Ensign Company produces two products and selected data are shown below:

49. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-49 Utilization of a Constrained Resource Machine A1 is the constrained resource and is being used at 100% of its capacity. Machine A1 is the constrained resource and is being used at 100% of its capacity. There is excess capacity on all other machines. There is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per week. Machine A1 has a capacity of 2,400 minutes per week. Should Ensign focus its efforts on Product 1 or Product 2? Machine A1 is the constrained resource and is being used at 100% of its capacity. Machine A1 is the constrained resource and is being used at 100% of its capacity. There is excess capacity on all other machines. There is excess capacity on all other machines. Machine A1 has a capacity of 2,400 minutes per week. Machine A1 has a capacity of 2,400 minutes per week. Should Ensign focus its efforts on Product 1 or Product 2?

50. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-50 Quick Check How many units of each product can be processed through Machine A1 in one minute? Product 1 Product 2 a. 1 unit 0.5 unit b. 1 unit 2.0 units c. 2 units 1.0 unit d. 2 units 0.5 unit How many units of each product can be processed through Machine A1 in one minute? Product 1 Product 2 a. 1 unit 0.5 unit b. 1 unit 2.0 units c. 2 units 1.0 unit d. 2 units 0.5 unit

51. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-51 How many units of each product can be processed through Machine A1 in one minute? Product 1 Product 2 a. 1 unit 0.5 unit b. 1 unit 2.0 units c. 2 units 1.0 unit d. 2 units 0.5 unit How many units of each product can be processed through Machine A1 in one minute? Product 1 Product 2 a. 1 unit 0.5 unit b. 1 unit 2.0 units c. 2 units 1.0 unit d. 2 units 0.5 unit Quick Check I was just checking to make sure you are with us.

52. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-52 Quick Check What generates more profit for the company, using one minute of machine A1 to process Product 1 or using one minute of machine A1 to process Product 2? a. Product 1 b. Product 2 c. They both would generate the same profit. d. Cannot be determined. What generates more profit for the company, using one minute of machine A1 to process Product 1 or using one minute of machine A1 to process Product 2? a. Product 1 b. Product 2 c. They both would generate the same profit. d. Cannot be determined.

53. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-53 Quick Check What generates more profit for the company, using one minute of machine A1 to process Product 1 or using one minute of machine A1 to process Product 2? a. Product 1 b. Product 2 c. They both would generate the same profit. d. Cannot be determined. What generates more profit for the company, using one minute of machine A1 to process Product 1 or using one minute of machine A1 to process Product 2? a. Product 1 b. Product 2 c. They both would generate the same profit. d. Cannot be determined. With one minute of machine A1, we could make 1 unit of Product 1, with a contribution margin of $24, or 2 units of Product 2, each with a contribution margin of $15. 2 × $15 = $30 > $24 With one minute of machine A1, we could make 1 unit of Product 1, with a contribution margin of $24, or 2 units of Product 2, each with a contribution margin of $15. 2 × $15 = $30 > $24

54. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-54 Utilization of a Constrained Resource The key is the contribution margin per unit of the constrained resource. Product 2 should be emphasized. It provides more valuable use of the constrained resource machine A1, yielding a contribution margin of $30 per minute as opposed to $24 for Product 1.

55. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-55 Utilization of a Constrained Resource If there are no other considerations, the best plan would be to produce to meet current demand for Product 2 and then use remaining capacity to make Product 1. The key is the contribution margin per unit of the constrained resource.

56. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-56 Utilization of a Constrained Resource Let’s see how this plan would work.

57. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-57 Utilization of a Constrained Resource Let’s see how this plan would work.

58. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-58 Utilization of a Constrained Resource Let’s see how this plan would work.

59. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-59 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. The total contribution margin for Ensign is $64,200.

60. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-60 Quick Check Colonial Heritage makes reproduction colonial furniture from select hardwoods. 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

61. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-61 Colonial Heritage makes reproduction colonial furniture from select hardwoods. 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 Quick Check (2  600) + (10  100 ) = 2,200 > 2,000

62. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-62 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

63. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-63 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

64. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-64 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 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

65. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-65 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 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 Quick Check The additional wood would be used to make tables. In this use, each board foot of additional wood will allow the company to earn an additional $20 of contribution margin and profit.

66. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-66 Multiple Constraints Suppose that you are in charge of producing and selling two products. Product 1 requires 3 hours of machine operation while Product 2 requires 6 hours. The total available machine hour is 24000. There is also a constraint on labor hours. Each product requires 2 labor hours, but only 12000 labor hours are available. Assume the following information about the price and unit variable cost, and the total fixed costs $36,000 are unaffected by your decision. Suppose that you are in charge of producing and selling two products. Product 1 requires 3 hours of machine operation while Product 2 requires 6 hours. The total available machine hour is 24000. There is also a constraint on labor hours. Each product requires 2 labor hours, but only 12000 labor hours are available. Assume the following information about the price and unit variable cost, and the total fixed costs $36,000 are unaffected by your decision.

67. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-67 Multiple Constraints # 1# 2Constraint p1015 v47 ucm68 MH3624000 ucm/MH21.333 LH2212000 ucm/LH34

68. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-68 Multiple Constraints Checking the ucm per MH, Product 1 is more profitable. Checking the ucm per LH, Product 2 is more profitable. What is then an optimal output choice? Checking the ucm per MH, Product 1 is more profitable. Checking the ucm per LH, Product 2 is more profitable. What is then an optimal output choice?

69. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-69 Multiple Constraints Max6q 1 + 8q 2 – 36000 s.t.3q 1 + 6q 2  24000  MH constraint 2q 1 + 2q 2  12000  LH constraint q 1, q 2  0. We can solve the problem using Solver in Excel. The optimal solution is q 1 = 4000, q 2 = 2000 and the resulting profit equals $4000. Max6q 1 + 8q 2 – 36000 s.t.3q 1 + 6q 2  24000  MH constraint 2q 1 + 2q 2  12000  LH constraint q 1, q 2  0. We can solve the problem using Solver in Excel. The optimal solution is q 1 = 4000, q 2 = 2000 and the resulting profit equals $4000.

70. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-70 Learning Objective 6 Prepare an analysis showing whether joint products should be sold at the split-off point or processed further.

71. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-71 Joint Costs In some industries, a number of end products are produced from a single raw material input. joint products Two or more products produced from a common input are called joint products. split-off point 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. joint products Two or more products produced from a common input are called joint products. split-off point The point in the manufacturing process where each joint product can be recognized as a separate product is called the split-off point.

72. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-72 Joint Products Joint Input Common Production Process Split-OffPoint Oil Gasoline Chemicals

73. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-73 Joint Products Separate Processing Separate Processing Final Sale Final Sale Final Sale SeparateProductCosts Joint Input Common Production Process Split-OffPoint JointCosts Oil Gasoline Chemicals

74. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-74 The Pitfalls of Allocation Joint costs are often allocated to end products on the basis of the relative sales value of each product or on some other basis. Although allocation is needed for some purposes such as balance sheet inventory valuation, allocations of this kind are very dangerous for decision making.

75. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-75 Joint costs are irrelevant in decisions regarding what to do with a product from the split-off point forward (i.e., stop or process further). It will always be profitable to continue processing a joint product after the split-off point as long as the incremental revenue exceeds the incremental processing costs incurred after the split-off point. Sell or Process Further

76. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-76 Sell or Process Further: An Example Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the immediate joint products. Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the immediate joint products. Unfinished lumber could be sold “as is,” or processed further into finished lumber. Unfinished lumber could be sold “as is,” or processed further into finished lumber. Sawdust could also be sold “as is” to gardening wholesalers, or processed further into “presto- logs.” Sawdust could also be sold “as is” to gardening wholesalers, or processed further into “presto- logs.” Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the immediate joint products. Sawmill, Inc. cuts logs from which unfinished lumber and sawdust are the immediate joint products. Unfinished lumber could be sold “as is,” or processed further into finished lumber. Unfinished lumber could be sold “as is,” or processed further into finished lumber. Sawdust could also be sold “as is” to gardening wholesalers, or processed further into “presto- logs.” Sawdust could also be sold “as is” to gardening wholesalers, or processed further into “presto- logs.”

77. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-77 Sell or Process Further Data about Sawmill’s joint products includes:

78. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-78 Sell or Process Further

79. Copyright © 2008, The McGraw-Hill Companies, Inc.McGraw-Hill/Irwin 13-79 Sell or Process Further