Cost Accounting

at lease 400 word each question

no plagiarism please

College of Administration and Finance Sciences
Assignment (2)
Deadline: Saturday 04/05/2024 @ 23:59
Course Name: Cost Accounting
Student’s Name:
Course Code: ACCT 301
Student’s ID Number:
Semester: Second
CRN:
Academic Year: 1445 H
For Instructor’s Use only
Instructor’s Name:
Students’ Grade:
/15
Level of Marks: High/Middle/Low
Instructions – PLEASE READ THEM CAREFULLY
• The Assignment must be submitted on Blackboard (WORD format only) via allocated
folder.
• Assignments submitted through email will not be accepted.
• Students are advised to make their work clear and well presented, marks may be
reduced for poor presentation. This includes filling your information on the cover
page.
• Students must mention question number clearly in their answer.
• Late submission will NOT be accepted.
• Avoid plagiarism, the work should be in your own words, copying from students or
other resources without proper referencing will result in ZERO marks. No exceptions.
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No pictures containing text will be accepted and will be considered plagiarism.
• Submissions without this cover page will NOT be accepted.
College of Administration and Finance Sciences
Assignment Question(s):
(Marks 15)
Q1. What is the process of identifying activities in an organisation and assigning costs under the
Activity Based Costing (ABC) system? Elucidate. You will need to include the right numerical
examples to support your answer.
(2 Marks) (Chapter 7, Week 7)
Answer:
Q2. PPLC Company has two support departments, SD1 and SD2, and two operating
departments, OD1 and OD2. The company decided to use the direct method and allocate
variable SD1 dept. costs based on the number of transactions and fixed SD1 dept. costs based on
the number of employees. SD2 dept. variable costs will be allocated based on the number of
service requests, and fixed costs will be allocated based on the number of computers. The
following information is provided:
(4 Marks) (Chapter 8, Week 10)
Support Departments
Operating Departments
SD1
SD2
OD1
OD2
Total Department variable costs
18,000
19,000
51,000
35,000
Total department fixed costs
20,000
24,000
56,000
30,000
Number of transactions
30
40
200
100
Number of employees
14
18
35
30
Number of service requests
28
18
35
25
Number of computers
15
20
24
28
College of Administration and Finance Sciences
You are required to allocate variable and fixed costs using direct method.
Answer:
Q3. What are an organization’s “outsourcing decisions” and “constrained resource decisions?”
Provide a suitable numerical example of these decisions and explain how quantitative and
qualitative considerations support a company’s decision-making process.
(2 Marks) (Chapter 4, Week 9)
Note: Your answer must include suitable numerical examples. You are required to assume values
of your own, and they should not be copied from any sources.
Answer:
Q4. VBN plastic industry makes three plastic toys: T1, T2, and T3. The joint costs of the three
products in 2017 were SAR 120,000. The total number of units for each product and the selling
price per unit is given below:
(3 Marks) (Chapter 9, Week 11)
Product
Units
Selling Price per unit
T1
45,000
SAR 15
T2
26,000
SAR 14
T3
18,000
SAR 10
You are required to allocate the joint costs to each product using the physical volume method and sales
value at the split-off method.
Answer:
College of Administration and Finance Sciences
Q5. MN&M Corporation is preparing a budget for 2018. The company provides you with the
following details which will help you to prepare the budget:
(4 Marks) (Chapter 10, Week 12)
Budgeted selling price per unit
=
SAR 500 per unit
Total fixed costs
=
SAR 150,000
Variable costs
=
SAR 100 per unit
Required:
You are required to prepare a flexible budget for 1,000, 1,100, 1,200 and 1,300 units.
Answer:
Another way to compute the weighted average contribution margin ratio is to sum the contribution margin ratios for the three products, weighted by revenues as follows: ($2,000,000 ÷
$24,200,000)[($200 − $75) ÷ $200] + ($12,600,000 ÷ $24,200,000)[($700 − $250) ÷ $700] + ($9,600,000 ÷ $24,200,000)[($800 − $300) ÷ $800] = 63.43%.
3
In the Chapter 2 illustration Small Animal Clinic (Part 2), the cost function was calculated as: TC = $119,009 + ($15.20)(Number of animal visits) + (0.04)(Fee revenue). If average fee revenue is
$30 per animal visit, then the last term in the cost function can be rewritten as (0.04)($30)(Number of animal visits), which can be simplified as ($1.20)(Number of animal visits). This substitution
allows the cost function to be rewritten as: TC = $119,009 + ($16.40)(Number of animal visits). This version of the cost function is appropriate for estimating total costs for the clinic, but it would
not be appropriate for estimating total costs for a single animal visit, where the fees vary depending on the services performed.
4
To see the relationship between the two formulas, recall the profit equation: Profit = (P − V) × Q − F, which can be rewritten as F + Profit = Contribution margin. In turn, Degree of operating
leverage = Contribution margin ÷ Profit = (F + Profit) ÷ Profit = (F ÷ Profit) + 1.
5
CHAPTER
4
Relevant Information for Decision Making
In Brief
Managers make a variety of decisions about operations over the next period that include special orders, outsourcing, keeping or dropping a
product line or customer, and constrained resource management. Identifying relevant information such as revenues and costs is an important
part of making these decisions. However, strategic fit and other qualitative factors are also important, sometimes overriding cost
considerations. Managers often weigh the business risk of alternatives when choosing the best course of action.
This Chapter Addresses the Following Questions:
•
•
•
•
•
•
Q1 What is the process for identifying and using relevant information in decision making?
Q2 How is relevant quantitative and qualitative information used in special order decisions?
Q3 How is relevant quantitative and qualitative information used in keep or drop decisions?
Q4 How is relevant quantitative and qualitative information used in outsourcing (make or buy) decisions?
Q5 How is relevant quantitative and qualitative information used in product emphasis and constrained resource decisions?
Q6 What factors affect the quality of operating decisions?
INTERNATIONAL OUTSOURCING: THE GOOD, THE BAD, AND THE
CONTROVERSIAL
I
n recent years, many companies around the world have contracted with other organizations to perform manufacturing tasks or provide
services that had previously been performed internally. This practice is referred to as outsourcing. Outsourcing often involves laying off
employees, which is controversial because of the consequences of lost jobs and lost income for the families of laid-off employees. Following
are examples of recent news stories.
•
•
•
•
•
A report issued by The Hackett Group estimated that Fortune 500 companies could save $20 billion per year by outsourcing 650,000
procurement and finance jobs internationally.
LEGO Group, a Danish toy maker, announced a plan to outsource most of its remaining production to a Singapore company. LEGO
eliminated over 5,000 jobs in the United States and Denmark during a three-year period.
Airport workers for Air New Zealand sought a court injunction to prevent outsourcing their jobs to a Spanish company. The airline’s
plan was expected to save $20 million per year.
Tripos, a chemistry services, software, and analytics services company with operations in the United States and United Kingdom,
announced a 40% decline in revenues and net loss of over $9 million for the first nine months of 2006. The company had lost major
contracts with Pfizer and other pharmaceutical companies to lower-cost competitors in Asia and Eastern Europe.
Business process services companies in India faced profit declines. Increased demand caused labor costs to increase by 15% in one
year. At the same time, competition increased, and customers demanded higher quality and greater productivity.
If you were a manager thinking about outsourcing a business activity, what business risks or other issues would you consider? You would
need to evaluate the expected financial costs and benefits. But as the preceding examples illustrate, these decisions can lead to labor
problems or financial catastrophe for existing suppliers. In this chapter we develop problem-solving methods for a variety of decisions that
arise periodically. We will examine several different organizations, including a basketball manufacturer, a nonprofit service provider, a
publisher, and others. We will also consider strategies for dealing with constrained resources.
SOURCES: S. Johnson, “Offshoring Finance Jobs Saves Billions?” CFO.com, November 9, 2006; D. Ibison, “Lego to Outsource and Cut
1,200 Jobs,” Financial Times, June 21, 2006; R. Van Den Bergh and A. Janes, “Union Sues Air NZ over Outsourcing,” The Press,
November 29, 2006; and R. Melcer, “Trips Falls Victim to Indian Outsourcing,” St. Louis Post-Dispatch, November 19, 2006.
RELEVANT INFORMATION FOR DECISION MAKING
Q1 What is the process for identifying and using relevant information in decision making?
Relevant information is important to each of us when we make decisions. A decision as simple as choosing a restaurant for dinner involves
analysis of relevant information. What is the estimated cost? What is the quality of the food? Is the atmosphere pleasing? What are the
opportunity costs (e.g., foregone experiences at other restaurants and money used in other ways)?
This chapter focuses on identifying and analyzing relevant information for making sound business decisions. As we learned in Chapter 1,
accounting systems often include irrelevant information. Managers and accountants must identify information that is relevant for a particular
decision. They also consider a variety of factors, including organizational strategies and business risks, before choosing a course of action.
CHAPTER REFERENCE
Chapter 12 focuses on the analysis of relevant information for long-term decisions such as capital expenditures.
The concepts introduced in this chapter apply to a wide range of business decisions. However, we will concentrate on the following types of
operating decisions that require the use of judgment when identifying and analyzing relevant information:
•
•
•
•
Whether to commit resources for a special order
Whether to use internal resources or to outsource some activities
Whether to discontinue a product line or business subunit or segment
How to manage limited resources
PROCESS FOR IDENTIFYING AND ANALYZING RELEVANT INFORMATION
Many management decisions are unique, making it impossible to create a “cookbook” approach that can be memorized and used. Instead, a
decision-making process is needed. Appendix 1A introduced Steps for Better Thinking, which is an example of a decision-making process
that leads to higher-quality decisions. Exhibit 4.1 demonstrates how Steps for Better Thinking relates specifically to the use of relevant
information for decision making.
Identifying and Envisioning the Problem and Alternatives We do not know whether information is relevant to decision making until we
know the type of decision to be made. We address problems more correctly and efficiently by clarifying the type of problem before jumping
into an analysis. For example, if you need to make a decision about buying a new car or keeping the one you own, some costs are not
relevant to the decision, such as parking fees at the university. To identify the relevant cash flows, however, you need to know the brand,
year, and model of car you are considering. Even among similar types of cars, differences exist among brands and models in gasoline
mileage, insurance rates, license fees, and so on. You might also wish to consider qualitative factors such as color, trunk size, or reliability.
EXHIBIT 4.1
Strategic Use of Relevant
Information for Decision
Making
Until you choose a specific car to consider, you cannot accurately identify relevant cash flows or qualitative factors. You might also want to
envision other options or approaches. Perhaps you dislike the color of your current car. You could consider repainting rather than replacing
it. Or perhaps you could consider leasing rather than purchasing a new car. Higher quality decision making often involves seeking new
approaches by thinking “out of the box.”
Identifying Relevant Quantitative Information Most business decisions require analysis of both quantitative and qualitative
information. Quantitative information is numerical information that is available for addressing a problem. In Chapter 1 we learned about
relevant and irrelevant cash flows. To be relevant, cash flows must (1) arise in the future and (2) vary with the action taken. We identify
relevant cash flows by analyzing the decision alternatives and then selecting cash flows that are unique to each alternative. We ignore
irrelevant (unavoidable) cash flows, those that do not differ among alternatives. Sunk costs (i.e., costs that were incurred in the past) are
always irrelevant.
Where do we find quantitative information? We obtain some relevant information from the accounting system, such as past revenues and
costs. In addition, each decision requires specific kinds of information gathered from outside the accounting system. Such information could
include bids from other companies to provide services such as payroll and telemarketing, or to manufacture parts prior to final assembly. If
some of the quantitative information is unknown, we might need to estimate it. For example, we can use regression analysis as shown
in Chapter 2 to estimate the fixed and variable portions of a mixed cost.
Identifying Relevant Qualitative Information Rarely in the business world do decisions rely solely on the results of quantitative
analysis. Qualitative information—factors that are not valued in numerical terms—is vital to good decision making.
Qualitative factors can be difficult to identify because no formula assures us that we have considered the important issues. Qualitative
information might be identified from experience with similar past decisions, through research into business risks and other factors that might
affect the outcomes of a decision, or by means of discussions with managers or other personnel. When considering a decision to outsource,
several qualitative factors could override quantitative factors, such as the ability of the outside vendor to provide a good or service at the
same level of quality and in a timely manner.
Performing Quantitative and/or Qualitative Analyses Quantitative calculations usually focus on comparing the relevant cash flows across
alternatives. Sometimes we use cost-volume-profit (CVP) analysis learned in Chapter 3. In this chapter we will learn another quantitative
technique, linear programming. We select one or more techniques that provide the appropriate information needed for making a specific
decision. Qualitative factors are incorporated into our analysis using judgment, although sometimes they can be analyzed using simulation or
other quantitative techniques. Occasionally, the qualitative factors are so important that they override the need to perform quantitative
analysis. For example, many students live off-campus, even though it is usually more expensive. The benefits of a sense of independence
and increased freedom in lifestyle choices must outweigh the increased costs in the minds of these students.
Prioritizing Issues to Arrive at a Decision We learned in Chapter 1 that operating decisions should be guided by organizational strategies
in conjunction with the organization’s vision, core competencies, and risk appetite. Before conducting detailed analysis for a decision,
managers should consider whether or how the decision might affect progress toward long-term goals. Sometimes strategic and risk
considerations take priority over other factors. For example, concerns about the reliability of a supplier’s parts might lead managers to
eliminate that vendor from consideration. The managers would then explore alternatives such as purchasing from other vendors or
manufacturing the parts in-house. As shown by the arrows in Exhibit 4.1, strategic concerns can influence all aspects of the decision-making
process.
Each operating decision introduced in this chapter employs a guideline—a quantitative decision rule—to make a decision. Using
quantitative analysis, we identify the decision alternative that maximizes short-term cash flows. However, we do not always choose that
option. Managers often make trade-offs among important issues when deciding on a course of action. In addition, we evaluate the quality of
the information used. We rely more on higher-quality information than on lower-quality information. When decision makers fail to consider
the quality of information, they may make poor decisions. For example, in a study of German firms, researchers Gorzig and Stephan found
that outsourcing improved employee productivity, yet decreased return on sales because transaction costs such as transportation, contracting
and monitoring costs for outside vendors overwhelmed the savings.1 Assuming that the managers expected to achieve cost savings, the
authors concluded that it might be difficult for managers to identify and evaluate the transaction costs that offset savings from purchasing
outsourced products or using offshore labor. These results suggest that the quality of information related to transaction costs is low,
hampering the ability of managers to make optimal decisions.
OPERATING DECISION EXAMPLES
The remainder of the chapter illustrates the following types of nonroutine operating decisions:
•
•
•
•
•
Special orders
Keep or drop decisions
Insource or outsource (make or buy) decisions
Constrained resources
Product emphasis—multiple resource constraints and multiple products
SPECIAL ORDERS
Q2 How is relevant quantitative and qualitative information used in special order decisions?
Managers need to determine whether to accept a customer’s special order, one that is not part of the organization’s normal operations. This
type of decision might have no long-term strategic impact because it involves a one-time sale of a specified quantity of goods or services,
and often at a reduced price. Suppose a print shop has been asked by the local Boys and Girls Club to print postcards inviting potential
donors to a silent auction fundraiser. The club would like a discounted price for the printing. If the print shop has idle capacity—machine
and labor time are not fully occupied with other orders—the incremental (relevant) cost of taking the order is only the variable costs of
postcard paper and ink. Therefore, the print shop is no worse off financially by accepting the order as long as the price at least covers the
cost of the paper and ink.
ALTERNATIVE TERMS
Some people use the term one-time-only order instead of special order.
QUANTITATIVE RULE FOR SPECIAL ORDER DECISIONS
The quantitative decision rule for special orders is that we want to be as well off after accepting the order as we were before we accepted it.
Thus, the decision rule is to accept the special order if:
Price ≥ Relevant Variable Costs + Relevant Fixed Costs + Oppurtunity Cost
The variable costs of delivering the product or service are usually relevant. However, variable selling costs such as commissions are often
irrelevant if the company requesting the special order places it directly. Most fixed costs, such as rent and depreciation on plant and
equipment, are unavoidable, making them irrelevant. Some fixed costs, such as the lease cost for a piece of equipment needed for the special
order, are relevant because they are unique to the special order. Labor costs are relevant if the special order causes them to change. If the
order replaces regular business, then the opportunity cost (i.e., foregone contribution margin) is also relevant. On the other hand, if idle
capacity is available, the special order is acceptable if the organization at least breaks even.
CHAPTER REFERENCE
Chapter 2 defined opportunity costs as the benefits we forgo when we choose one alternative over the next best alternative.
The following Barkley Basketballs illustration provides an opportunity to practice making a special order decision.
BARKLEY BASKETBALLS
SPECIAL ORDER
Barkley Basketballs manufactures high-quality basketballs at its plant, which has a production capacity of 50,000 basketballs per month.
Current production is 35,000 per month. The manufacturing costs of $24 per basketball are categorized as follows:
Jack O’Neil operates not-for-profit basketball camps for disadvantaged youths on Indian reservations and throughout inner cities in large
urban areas. Jack asks Billie Walton, CFO at Barkley Basketballs, to sell him 5,000 basketballs at $23 per ball, or $115,000 for the entire
order.
Billie speaks to the cost accountant and then goes to the production floor to speak to several supervisors to gather information for this
decision. She determines that the direct labor cost is variable. Workers are paid an hourly wage and are sent home when there are no balls to
manufacture. These workers have no guaranteed salary, but demand is stable so they always work at least half-time, and often 40 hours a
week.
Billie asks about the manufacturing overhead and finds that it consists of variable and fixed costs incurred to run the plant where the
basketballs are manufactured. Overhead includes insurance, property taxes, depreciation, utilities, and various other plant-related costs. She
finds that all of the fixed costs are related to a capacity level of 50,000 and will not change if she uses part of the idle capacity of 15,000
units. The foreman warns her, however, that once production exceeds 40,000 basketballs, bottlenecks occur and the production process will
slow down and cause inventory levels to congest the plant, sometimes causing overtime to be paid.
QUANTITATIVE ANALYSIS
With the 5,000 basketballs produced for Jack, total production for the month would be 40,000 basketballs. Bottlenecks and slowdowns do
not occur until production exceeds 40,000. Therefore, the special order is within the relevant range of production; the fixed costs should
remain fixed. The relevant revenues and costs per basketball are as follows:
Selling price
$23.00
Variable costs (materials, labor, and overhead)
$14.50
In deciding whether to accept this special order, fixed costs are irrelevant because they are unavoidable. They will be incurred whether
35,000 or 40,000 basketballs are produced. The variable cost of $1.00 sales commission per ball is also irrelevant because no sales
representatives are involved in this particular transaction. Therefore, the contribution margin for each special order basketball would be
$23.00 − $14.50 = $8.50. For 5,000 basketballs, the total contribution margin would be $42,500.
QUALITATIVE ANALYSIS
Based on the preceding quantitative analysis, Billie wants to accept the order. However, she first needs to consider the qualitative aspects of
the decision. If she sells the basketballs at this lower price, other customers might demand lower prices too, causing Barkley Basketballs to
get into a pricing war with itself. However, Jack’s organization is not-for-profit; Billie doubts that other customers would object to giving it a
discount.
Billie also believes that the company could enhance its reputation if Jack publicizes Barkley Basketballs’ support of the basketball camps. To
evaluate the value of such publicity, she meets with the marketing manager, Mark Jordan. Mark cannot quantify the value, but he suggests
that the publicity would definitely help promote the Barkley Basketballs brand name. In addition, the company has funded basketball camps
in the past, in keeping with its policy of supporting the community.
STRATEGIC PRIORITIZATION
After considering all of these factors, Billie discusses the special order with Jack. She offers to lower the price even further than $23. Jack is
pleasantly surprised and offers to publicize Barkley Basketballs’ generosity. Billie and Jack settle on a price of $20 per ball. The contribution
margin of the special order is reduced from $42,500 to $27,500 (5,000 balls at $20.00 − $14.50).
In this situation, Billie is willing to reduce the price of the special order even further for several reasons. In the past, the company donated
money to not-for-profit basketball camps, so providing basketballs at a discount fits with management’s desire to act in a socially responsible
manner. She also believes the company will benefit from additional publicity. And the company will still earn a profit from the special order.
Although Billie has agreed to a lower price than usual, the special order meets the general decision rule: ample capacity is available, and the
price is greater than the relevant costs (variable production costs).
Later that week, Billie is reviewing the decision to sell Jack O’Neil basketballs at $20 each. She visits with Mark Jordan, who insists that the
value of the publicity exceeds the reduction of $15,000 in contribution margin. Billie concludes that the decision to sell the balls at a
discount was appropriate.
STRATEGIC RISK MANAGEMENT Barkley Basketballs
SPECIAL ORDER DECISION PROCESS
Note the process used to make the Barkley Basketballs decision. Billie first identified the type of decision (special order). To identify
relevant costs, she (1) determined whether enough capacity was available for the special order without causing fixed and variable costs to
change, and (2) categorized costs as fixed and variable. In this case, all of the variable production costs and none of the fixed costs or sales
commissions were relevant. In manufacturing settings such as this one, where the same product is made repeatedly, manufacturing costs can
be estimated with high accuracy. Billie had good reason to be confident in her quantitative analysis. She then identified qualitative factors
related to the decision and summarized the relevant information, as shown in Exhibit 4.2. How did Billie reach a conclusion that the special
order was appropriate? She determined that the benefits of the special order included earning incremental profit, gaining publicity, and
contributing to the community. Billie weighed these benefits against the cost of offering a discount from the company’s usual selling price.
SPECIAL ORDERS AND PRICING POLICIES
CHAPTER REFERENCE
Chapter 13 addresses general pricing policies.
Under the quantitative decision rule, managers are willing to accept a special order as long as the selling price is at least equal to incremental
costs—in other words, as long as the incremental contribution margin is zero or positive. If excess capacity exists, the minimum acceptable
selling price is the sum of the per unit relevant variable and fixed costs. Typical prices charged by most organizations are higher than this
minimum price. Prices are usually set so that the organization will earn a profit. Why would an organization be willing to accept a special
order at a price that covers only incremental costs? By definition, a special order is not part of the organization’s normal operations. If excess
capacity exists and if the price on a special order will not affect prices on regular business, then the organization is better off accepting
special orders that generate at least some incremental profit.
EXHIBIT 4.2 Relevant Costs and Qualitative Factors for Barkley Basketballs
CURRENT PRACTICE
It’s Show Time!
What is the minimum acceptable price for a seat at a Broadway show on the day of the performance? Regular ticket prices are set to cover
fixed and variable costs plus provide profit to the show’s investors. However, on the day of a performance seats often cannot be sold at
regular prices. Almost all of the costs for a Broadway performance are fixed, so the incremental cost to seat another patron is very small,
probably near zero. As the time of a performance approaches, the opportunity cost becomes zero because an unsold seat would provide no
revenue. Thus, tickets sold at any price provide an incremental contribution.
Broadway shows use several methods to sell discounted tickets on the day of a performance. Theater-goers can purchase same-day tickets
for many Broadway shows at TKTS ticket booths from 3 to 8 p.m. at discounts of 25 to 50%. Lines for these tickets are often very
long. Student Rush offers tickets only to students with ID at the box office at a specified time. In addition, show box offices might sell
tickets on a first-come, first-served basis or using a lottery system immediately before a show begins. After all seats are sold, theaters
sometimes sell discounted standing-room-only (SRO) tickets, which allow patrons to stand in a numbered space.
SOURCE: From the Web site at www.nyu.edu/ticketcentral/discount.finder/broadway.discounts.html.
QUALITATIVE AND RISK FACTORS FOR SPECIAL ORDER DECISIONS
Relevant qualitative factors for a special order include any nonquantitative issues that managers should consider before making a decision.
These factors vary across organizations and across orders. Here are examples of questions managers could ask to identify relevant qualitative
factors, including business risks, for a special order:
•
•
•
•
•
•
•
Does this order help achieve a strategic goal such as improved brand recognition or social responsibility?
Will this order take attention away from orders that are more important strategically?
If we give this customer a discount, will other customers also expect a lower price?
How accurate are our capacity estimates? Can we deliver this order without disrupting schedules for more profitable regular business?
Will this order lead to additional orders from a potential new customer?
Will this order help retain the business of an existing profitable customer?
If we ask employees to work overtime, could this order lead to labor problems?
KEEP OR DROP DECISIONS
Q3 How is relevant quantitative and qualitative information used in keep or drop decisions?
When organizations provide multiple products (goods or services), they periodically review operating results for each product, group of
products (product line), or business segment and decide whether to keep or drop the product or segment. If financial statement data are used
in these calculations, average costs are often mistakenly included as relevant information. However, managers need to separate relevant and
irrelevant cash flows. Therefore, they may need to develop distinct cost functions for each product, product line, or segment.
QUANTITATIVE RULE FOR PRODUCT AND BUSINESS SEGMENT KEEP OR DROP
DECISIONS
The quantitative rule is that we want to be at least as well off after we discontinue a product or business segment as we were before we
dropped it. Usually this means that we discontinue a product or segment when the incremental profit from keeping it is negative. Thus, the
decision rule is to drop if:
Contribution Margin < Relevant Fixed Costs + Opportunity Cost To apply this decision rule, we first separate costs into fixed and variable. To identify relevant costs, we consider whether the cost is avoidable or unavoidable if we drop the product or segment. To identify and estimate avoidable costs, we analyze the nature of the cost and its relation to the two alternatives (keep or drop). Variable costs are often avoidable and therefore relevant, whereas fixed costs usually include both avoidable and unavoidable costs. For example, dropping a product might mean that an employee in accounting or marketing could be laid off. The labor costs and fringe benefits for that employee are relevant to the keep or drop decision because they are avoidable if the product is dropped. Alternatively, the lease cost for a manufacturing facility that produces a number of products is unavoidable if only one product is dropped. Therefore, the lease cost is irrelevant. Opportunity costs include the potential contribution margin foregone when resources are devoted to an existing product or segment instead of alternatives. For example, managers of grocery stores continuously monitor the contribution earned by different products to maximize profits earned from limited shelf space. When shelf space is devoted to one product, the company foregoes the potential contribution margin from another product. The following Home Aide Services illustration provides an opportunity to practice making a keep or drop decision. HOME AIDE SERVICES KEEP OR DROP Home Aide Services is a not-for-profit organization that provides a variety of services for people who would prefer to live at home, but need assistance. The organization has several lines of service, including housekeeping, meals, and shopping and transportation services. Lately the organization has suffered a decline in surplus. The manager, Justin Bean, wants to drop one of the services to increase profitability. Following are the monthly cash flows for each service. QUANTITATIVE ANALYSIS When Justin tells Elizabeth Klein, the accountant, that housekeeping services should be dropped to save the organization $5,000, Elizabeth says she needs to analyze costs further. The next day she reports to Justin that instead of having an overall surplus of $5,000, Home Aide Services would incur a deficit of $2,000 if housekeeping were dropped. She presents the following information about the remaining product lines if housekeeping were discontinued: Justin asks how this could be. Elizabeth explains that when she analyzed the costs in more detail, she found that the fixed costs for housekeeping included benefits for the housekeepers. The cost of benefits would be avoided if housekeeping were dropped. These costs are $8,000. Total fixed costs are now $23,000 ($31,000 − $8,000). These fixed costs are unavoidable and are allocated to the remaining departments. They include the cost of depreciation on cars as well as administrative costs for the entire organization that had been allocated to housekeeping. Labor costs are a small part of the meal department's total cost. Only $1,000 of fixed costs would be avoided if meals were dropped; the employees who prepare meals also help with administrative work. Shopping and transportation includes $4,000 in avoidable fixed costs. This amount represents salary and benefits costs for drivers who are available all hours that the service is open. Elizabeth prepares the following report for Justin. With this new information, Justin analyzes the costs again. He realizes that all of the services are contributing to the unavoidable fixed costs and should be continued. QUALITATIVE ANALYSIS Elizabeth observes that competitors provide all three services. Therefore, dropping housekeeping could affect demand for the other services. Clients might not want to deal with two separate organizations, when one could provide all the different services they need. Even if housekeeping were just breaking even, it should not be eliminated if dropping it would alienate current customers and cause demand for the other services to decrease. In addition, employee morale could suffer if a number of workers were laid off. STRATEGIC PRIORITIZATION Given this new cost analysis and the qualitative factors, Justin decides to retain all of the current services. However, he decides to investigate alternative ways that the organization could improve its surplus. First he considers any opportunity costs. If housekeeping were dropped, could Home Aide add nursing or other services instead? Would the surplus added from nursing be higher than housekeeping? STRATEGIC RISK MANAGEMENT Home Aide Services THE BUSINESS RISK OF DROPPING A PRODUCT If one of the services had actually resulted in a loss, would the manager of Home Aide Services make a different decision? Before dropping that service, the manager would need to consider whether some clients might drop all services and find another organization that could provide them. Most likely, the manager would need more information to evaluate this risk. For example, accounting records could be examined to determine the proportion of customers using multiple services. Existing customers could be surveyed about their preferences. Competitor service offerings could be investigated. CUSTOMER PROFITABILITY As the business environment has become increasingly dynamic, organizations often obtain strategic benefit from developing more flexible operations. Customers are increasingly demanding additional services such as timely delivery of small amounts of inventory or large amounts of support. Sometimes the seller's costs to maintain these relationships are larger than the benefits. In addition, changes in the economic environment or strategic goals may require reevaluation of customer relationships. Managers need to decide whether to keep, drop, or add individual customers or groups of customers. For example, Castle Key (formerly Allstate Floridian) decided to reduce its insurance risk in the State of Florida by dropping commercial coverage and 95,000 homeowner policies.2 The process and decision rule for these decisions is similar to other keep or drop decisions. A customer should be dropped if: Customer Contribution Margin < Relevant Fixed Costs + Opportunity cost Relevant cash flows include the revenues that will be foregone if the customer is dropped and the costs to maintain the customer and deliver products or services. Potential relevant costs include: • • • • • • • Avoidable costs of products manufactured or services provided Marketing, sales-order, and delivery costs Cost for equipment or other assets devoted to particular customers Product technical support, warranty costs, and product return handling Inventory carrying costs such as material handling, warehousing, and insurance Avoidable administrative costs for labor, facility, or other resources needed to satisfy customer demands Alternative uses for capacity devoted to customers CHAPTER REFERENCE Many customer-related costs vary with activities that are performed to satisfy customer needs. In Chapter 7, we will learn about identifying these activities, their costs, and cost drivers. For a book publisher, relevant customer costs include costs related to book return policies. The publisher delivers the number of books requested by a book store, but the store typically has the right to return books that do not sell within a specified period of time. If returned books remain in inventory for long periods, the cost of providing the books could easily outweigh the revenues from small book store customers. RISK OF BIASED DECISIONS Confirmation Bias Confirmation bias is a tendency to seek and interpret information to corroborate preconceptions. This bias may cause managers to misidentify or misinterpret relevant quantitative or qualitative information that would support choosing an alternative different than the one they prefer. For example, a manager who favors keeping a product may overlook opportunity costs, underestimate the product's relevant costs, or disregard negative market signals about the product's long-term viability. Considerable judgment is used in many business decisions, making it difficult to detect a manager's confirmation bias. Nevertheless, organizations can reduce the risk of biased decisions by pursuing contrary evidence and by vigorously debating the pros and cons of proposed actions. COSTS OF CARRYING INVENTORY CHAPTER REFERENCE In Chapter 13, we will learn about just-in-time inventory practices, which eliminate most inventory carrying costs. The costs of carrying inventory are often avoidable if a firm drops a customer or product. Thus, these costs can be relevant to keep or drop decisions. As we will learn in the next section of the chapter, inventory carrying costs may also be relevant to make or buy (outsourcing) decisions. When deciding how much inventory to keep on hand, managers consider the cost of carrying additional inventory, along with the order and transportation costs. Inventory carrying costs are sometimes difficult to identify and separate from general overhead costs. However, these costs often include the following. • • • • • • • Costs to process purchase orders Avoidable costs invested in the inventory, such as direct materials, direct labor, variable overhead, or fixed overhead Opportunity cost for alternative uses of cash, such as short-term investments or reductions in debt Costs to handle, warehouse, insure, and maintain inventory Opportunity cost of foregone sales from inventory shortages (stock-outs) Costs for tracking inventory and determining appropriate inventory levels Inventory shrinkage or value decline from breakage, theft, deterioration, or obsolescence For book publishers, carrying costs would include material handling costs of labor, fork-lifts, cranes, and any other equipment needed to handle cases of books in the warehouse; insurance on the warehouse facility and its contents; property taxes; resources devoted to the inventory including direct materials, direct labor, and variable overhead; and costs to handle direct material purchase orders. In this industry, the costs of foregone sales from insufficient inventories of best-seller books can be large. However, the carrying costs of inventory for books that do not become best sellers are also large. QUALITATIVE AND RISK FACTORS FOR KEEP OR DROP DECISIONS Relevant qualitative factors include any nonquantitative issues that managers should consider before making a decision. Here are examples of questions managers could ask to help them identify relevant qualitative factors, including business risks, for a keep or drop decision: • • • • • • How strategically important is this product, segment, or customer? Will dropping one product or customer affect the sales of other products? Will potential layoffs affect worker morale? How achievable are the revenue and cost estimates? What kinds of products and prices are competitors offering? How would dropping this product or customer affect overall organizational risk? INSOURCE OR OUTSOURCE (MAKE OR BUY) DECISIONS Q4 How is relevant quantitative and qualitative information used in outsourcing (make or buy) decisions? Outsourcing, the practice of finding outside vendors to supply products and services, has become an increasingly common practice. Insourcing is the practice of providing the good or service from internal resources. For manufacturers, outsourcing decisions are often called make or buy decisions: Does the company make the product internally, or does it buy it from the outside? Potential cost savings as well as organizational strategies, business risks, and other factors drive such decisions. Some managers outsource any activity they view as unrelated to the organization's core competencies. QUANTITATIVE RULE FOR INSOURCE OR OUTSOURCE DECISIONS The quantitative rule for insource or outsource decisions is to choose the option with the lowest relevant cost. Thus, the decision rule is to outsource (i.e., buy) if: Cost to Outsource < Cost to Insource, or Cost to Outsource < Relevant Variable Costs + Relevant Fixed Costs + Opportunity Cost To apply this decision rule, we first separate costs into fixed and variable. The variable costs are usually relevant. Existing fixed costs are relevant only if they can be avoided through outsourcing. The costs for insourcing also include opportunity costs. Sometimes extra space or capacity from outsourcing can be converted to other uses. Another product could be manufactured or the space rented out. The forgone benefits (contribution margin from the new product or rent payments) are an opportunity cost for insourcing. The following Roadrunner Publishers (Part 1) illustration provides an opportunity to practice making an outsourcing decision. ROADRUNNER PUBLISHERS (PART 1) INSOURCE OR OUTSOURCE Roadrunner Publishers produces the book covers for its hardbound books. Recently, Marliss Book Binders purchased new robotic equipment that cuts, trims, and prints book covers in one process. Marliss offered to provide book covers for Roadrunner at $2.00 per book. Mark Bonaray, the cost accountant for Roadrunner Publishers, analyzes the cost information for internally producing hardbound book covers as follows: After summarizing the costs for producing the book covers in-house, Mark needs to identify costs that are relevant and irrelevant to the decision. First, he gathers more information. He learns from the production manager that the foreman could be laid off if the book covers are outsourced. As a cost accountant, Mark already knows that manufacturing overhead is an indirect cost. In this case, it is allocated to books based on the number of direct labor hours used in each production process. Overhead costs will be incurred even if the book covers are outsourced. However, after examining past utility bills, Mark estimates that closing off the part of the plant where book covers are produced would save about $30,000, or $0.30 per book cover. QUANTITATIVE ANALYSIS Although outsourcing would save $30,000 of the manufacturing overhead, the remaining $70,000 (or $0.70 per book cover) will be incurred under each alternative and is therefore irrelevant to the decision. The relevant production and outsourcing costs for this decision are as follows: Based only on the preceding cost information, Roadrunner would save $5,000 by outsourcing the book covers. However, Mark has not yet considered the potential opportunity costs of continuing to produce the book covers in-house. If Roadrunner Books has an alternative use for the space that houses the book cover operations, the contribution margin from the use of that space would be relevant to the decision. For simplicity, we assume that Roadrunner's management has no alternative use for the space and, therefore, no opportunity costs to consider for this decision. QUALITATIVE ANALYSIS Another factor Mark considers is the quality of the book covers, which is emphasized in Roadrunner's book production process. Roadrunner's sales managers believe that high-quality covers are important to sales. The quality of Marliss's sample covers appears to be high, possibly even higher than Roadrunner's current level of quality. Mark is also concerned about the timeliness of delivery. He speaks with Roadrunner's book cover supervisor, who explains that the department is able to respond to changes in production volumes if given lead time. It has been relatively easy to have Roadrunner's employees work overtime or to hire part-time employees when a book appears to be a best seller, causing production levels to rise. When Mark asks Marliss about its ability to manage a very large order caused by unanticipated demand, the sales representative cannot guarantee that such an order could be produced quickly. This response concerns Mark, who is aware that when books are best sellers, large volumes must be produced quickly. STRATEGIC PRIORITIZATION When Mark summarizes the relevant information for the decision, he concludes that the savings from outsourcing and the quality differences are relatively small. In addition, he decides that being able to meet demand is worth the additional cost. Based on his analysis, he concludes that the risks of outsourcing do not outweigh the benefits. Accordingly, he recommends that the company continue producing its own book covers. QUALITATIVE AND RISK FACTORS FOR OUTSOURCING DECISIONS Product or service quality is often a major factor in outsourcing decisions. To ensure high quality, organizations typically negotiate outsource contracts that stipulate specific performance criteria, such as product specifications and timeliness. For example, the American Institute of Certified Public Accountants and National Association of State Boards of Accountancy negotiated a contract withPrometric to provide computer testing centers for the CPA examination. The contract requires Prometric to accommodate test candidate appointments within a certain number of days and to report on its compliance with contract provisions. Some organizations use multiple outsource vendors to avoid overreliance on any one vendor. However, few outside vendors may be available for some activities, increasing the risk of quality problems. As outsourcing has become increasingly popular, organizations need to consider a variety of qualitative factors. Exhibit 4.3 presents a list of factors that financial institutions would consider in their decisions to outsource information technology. Following are examples of questions managers could ask to help them identify relevant qualitative factors, including business risks, for an outsourcing (make or buy) decision: EXHIBIT 4.3 Examples of Financial Institution Considerations for International IT Outsourcing • • • • • • • • • • Is this activity a core competency? Would outsourcing this activity increase managerial attention devoted to core activities? Does this activity involve highly sensitive information? If we outsource this activity, will our organization lose strategic skills? How important are high quality and timeliness? Is it easier to ensure high quality and timeliness via insourcing or outsourcing? Do reliable measures exist for monitoring the supplier's performance? Will the supplier meet contractual obligations? Can we easily monitor compliance? How would outsourcing affect our labor relations? Will the supplier use acceptable worker conditions and environmental practices? FOCUS ON ETHICAL DECISION MAKING Offshoring Surgery Medical costs in the united States are the highest in the world, and employer medical costs have risen by 75% since 2000 (Grassi, 2006). Seeking ways to reduce escalating employee health-care costs, Blue Ridge Paper Products planned to send one of its employees to India for gall bladder and shoulder surgery. The employee, Carl Garrett, said that he was looking forward to the trip. He had volunteered for the plan in exchange for a share of the cost savings, which were estimated at $50,000, and an opportunity to visit the Taj Mahal and other sites (Rai, 2006). But before the trip took place, the employee's union, United Steelworkers of America (USWA), challenged the plan. USWA president Leo Gerard argued that workers should not bear the risks of international travel for medical procedures. The issue of liability was a major concern. The company had asked Garrett to sign a release from liability, and questions arose about whether or how much liability coverage might exist for procedures performed in India. The union was also concerned that international medical procedures might become mandatory rather than voluntary in the future (Jonsson, 2006). After the union objected, Blue Ridge withdrew its offer. The company planned to find a treatment alternative for Garrett in the United States. However, it also planned to continue offering the international option to salaried (i.e., nonunion) employees. The company, which was self-insured, was also pursuing other ways to reduce medical costs (Jonsson, 2006). SOURCES: D. Grassi, “Offshoring Patients No Cure for Ailing,” The Conservative Voice, November 18, 2006, P. Jonsson; “Union Blocks Foreign Healthcare Plan,” The Christian Science Monitor, September 29, 2006; S. Rai, “Union Disrupts Plan to Send Ailing Workers to India for Cheaper Medical Care,” The New York Times, October 11, 2006. THE ETHICS OF INTERNATIONAL MEDICAL OUTSOURCING This case highlights major conflicts among stakeholder interests related to international outsourcing of medical procedures. Several ethicsrelated questions can be asked. Was it ethical for the company to ask an employee to fly 20 hours for medical procedures and sign a liability release? Was the proposed share of cost savings and sightseeing opportunity sufficient compensation for the employee to assume additional risks? Did the employee adequately understand the risks? Was it ethical for the union to interfere when the employee volunteered to participate? What implications does this case have for other companies and other employee groups? PRODUCT EMPHASIS DECISIONS Q5 How is relevant quantitative and qualitative information used in product emphasis and constrained resource decisions? Instead of simply responding to demand and advertising products that sell well, managers may want to focus customer attention on products that contribute more to profitability. Managers choose to emphasize particular products in their product mix through promotions and advertising campaigns, or by providing incentives for salespersons. Deciding which products to emphasize requires a short-term decision. QUANTITATIVE RULE FOR PRODUCT EMPHASIS DECISIONS The general quantitative rule is to rank products by contribution margin per unit and then emphasize products with higher contribution margins. This approach assumes that fixed costs are unaffected by product mix or customer requirements and that ample excess capacity exists. However, sometimes there are factors that constrain capacity or other resources, and managers need to consider these constraints in their product emphasis decisions. ALTERNATIVE TERMS The following pairs of terms are synonymous: product-mix decision and product emphasis decision; scarce resources and constrained resources. THEORY OF CONSTRAINTS AND CONSTRAINED RESOURCES According to the Theory of Constraints, managers always face a constraint in their operations.Constraints are resource limitations and can be shortages of direct material or labor, or bottlenecks in the manufacturing process. A bottleneck is any resource or process that limits overall capacity. Constraints can be managed through a sequential four-step process.3 First, managers identify the constraint. If the constraint is materials or labor, managers may need to acquire additional resources and may need to pay more for them. If the constraint is a bottleneck, it must be identified. Because manufacturing and service delivery processes include a number of dependent events, it can sometimes be difficult to find the bottleneck. Second, the pace of manufacturing throughput or service delivery is set at the same pace as the bottleneck. This step usually means slowing down the production process. The slowdown reduces the costs of congestion that arise when product or services are waiting for the next step in production. Third, managers need to find improvements for the bottleneck to increase throughput. Fourth, when this link is no longer a constraint, managers identify the next constraint and repeat the process. This process considers demand as setting the throughput pace. When production is balanced with demand and no more bottlenecks exist, demand becomes the constraint. Then, managers should focus on increasing demand until a new constraint arises within the system. According to the Theory of Constraints, managers will always face a constraint. CHAPTER REFERENCE Chapter 14 discusses increasing throughput, the rate at which product moves through the manufacturing process to the point of sale, or the rate at which services are produced. CURRENT PRACTICE Eliahu Goldratt developed the Theory of Constraints, a formal method used to analyze organizational constraints and to improve operations. For more information, go to www.goldratt.com/. Internal constraints include limits in capacity, materials, or labor. For example, in the insource–outsource illustration, Roadrunner Publishers needed cardboard to make book covers. The company could face a shortage of direct materials, or a direct materials constraint. A shortage of labor to run machines or to load books into packing crates would be a labor constraint. Similarly, a shortage of machines to bind the covers onto the books would be a capacity constraint. When faced with one or more constrained resources, managers have several options. They may: 1. Emphasize products to maximize the contribution margin within the constraint. 2. Relax the constraint by 1. Purchasing goods or services from an outside supplier. 2. Increasing the speed and constancy of bottlenecks by operating them during breaks and meals. 3. Increasing internal capacity by using overtime, outsourced labor or processes, and buying new equipment. 4. Redesigning products and processes to use existing capacity more efficiently. 5. Offloading some products that use high-technology bottleneck resources to older, less-efficient equipment that performs the same task. Managers can also maximize the contribution margin while simultaneously adopting one or more ways to relax the constraint. QUANTITATIVE RULE FOR CHOOSING THE PRODUCT MIX WHEN RESOURCES ARE CONSTRAINED When resources are constrained, we need to emphasize products and services that maximize the contribution margin per unit of constrained resource. For example, Fabulous Furniture produces teak tables and chairs for outdoor use. Normally the company sells about 100 tables and 800 chairs per month. Because of a strike at the local seaport, it is unable to purchase enough lumber locally to meet current demand. The sales manager wants to know which product to emphasize—the tables or the chairs—to maximize profits. The accountant calculates the contribution margin per board foot for tables and chairs to make this decision. The contribution margin per table is $400, and the contribution margin per chair is $150. Tables require 4 board feet of teak and chairs require 2 board feet. The contribution margin per board foot for tables is $100 ($400 ÷ 4 board feet) and for chairs is $75 ($150 ÷ 2 board feet). To maximize the contribution margin, the sales manager should emphasize tables and sell as many as possible. If the demand for tables is filled, then the sales manager should emphasize chairs. QUANTITATIVE RULE FOR RELAXING CONSTRAINTS FOR ONE OR TWO PRODUCTS The quantitative rule for relaxing a short-term constraint for direct materials, direct labor, or capacity is that managers would be willing to pay not only what they are already paying, but also some or the entire contribution margin per unit of constrained resource. Their goal would be to acquire added capacity, thereby eliminating the constraint. In the furniture example, Fabulous Furniture is currently paying $50 per board foot for teak. Suppose the company has manufactured as many tables and chairs as possible with the limited supply of teak and still has demand for chairs. Customers will buy elsewhere if they cannot purchase chairs from Fabulous. Fabulous forgoes $75 in contribution margin per board foot on each chair customers would have purchased had teak been available. Consequently, Fabulous can afford to pay what it currently pays ($50), plus up to the entire contribution margin per board foot ($75) to buy more teak. If Fabulous can find a source of teak for $125 ($50 + $75) or less per board foot, it can meet customer demand for chairs without incurring incremental losses. CHAPTER REFERENCE Chapter 3 introduced calculations for the indifference point between alternatives. As the incremental cost per unit (including the new cost of materials or labor) approaches the selling price of the product or service, managers become indifferent to purchasing more of the constrained resource for continued production. This general rule is valid under the following assumptions: • • • • The organization will forgo sales if the resource constraint is not relaxed. Fixed costs are unaffected by short-term decisions made to relax constraints. The managers want to maximize profits in the short term. Sales of one product do not affect sales of other products. Capacity constraints are time constraints; that is, limited time is available for processing products because one or more bottlenecks slow production. To maximize use of bottleneck resources, we emphasize products that have the highest contribution margin per bottleneck hour. We calculate the relevant contribution margin in terms of time needed at the bottleneck resource. For example, suppose Fabulous has only one three-axis milling machine (a computerized piece of equipment that cuts and routs unusual shapes). The milling machine can process only 4 tables per hour or 12 chairs per hour. The contribution margin per machine hour for tables is $1,600 (4 × $400), and for chairs it is $1,800 ($150 × 12). Chairs should be emphasized because they have the highest contribution per hour at the bottleneck resource. The following Roadrunner Publishers (Part 2) illustration provides an opportunity to practice making a constrained resource decision. ROADRUNNER PUBLISHERS (PART 2) CONSTRAINED RESOURCE Suppose the managers of Roadrunner Publishers decide that the company should continue to make its own book covers. In performing his analysis, Mark assumes ample capacity and materials are available. However, one of Roadrunner's children's books, Barry Plotter, Mathematical Wizard, sells many more copies than expected. This increase in demand leads to a shortage of the special cardboard needed for the book covers. In turn, Roadrunner is unable to publish enough books to meet current demand. Customers–both children and their parents–are becoming quite frustrated. QUALITATIVE ANALYSIS Mark discusses the cardboard shortage with the sales manager, Dina Wilkinson, who thinks the company will in all likelihood forgo sales if demand cannot be met in a timely manner. In addition, the sales manager believes Roadrunner must continue to build positive brand-name recognition for the Barry Plotter series, so that further books in the series will be well received. Given this information, Mark would like to find some way to produce enough books to meet customer demand. QUANTITATIVE ANALYSIS The books that have already been produced and sold covered all of the company's fixed costs related to developing, editing, and designing the books and their covers. The wholesale price of the books is $10.00 each. The direct materials ($0.75) and direct labor ($0.50) costs for the covers total $1.25. The remaining variable costs for each book are $1.50 for paper and $1.50 royalty to the author. Therefore, total variable costs per book are $4.25, and the contribution margin per book is $5.75. At Mark's request, the purchasing agent, Bruce Maxwell, researches alternative cardboard suppliers. Although Bruce locates a supplier, he is concerned because the lowest-cost supplier is demanding a price of $4.00 per cover for timely delivery. STRATEGIC PRIORITIZATION Mark decides that, in the short run, he is willing to give up some of the contribution margin for this title to build long-term customer satisfaction. Therefore, he is willing to pay as much as the original cost of the cardboard ($0.75 per book) and the original contribution margin ($5.75 per book), or $6.50 per book. He recommends that Bruce purchase additional cardboard at the asking price of $4.00 per book. The variable costs for this additional printing now include $4.00 (book cover materials), $0.50 (book cover labor), $1.50 (paper), and $1.50 (royalty), for a total of $7.50 per book. Thus, the contribution margin from each additional book that Roadrunner produces and sells will be $2.50 ($10.00 − $7.50). Even though this amount is lower than the original contribution margin of $5.75, Roadrunner continues to earn at least some contribution margin through its effort to relax the constrained resource of the book cover cardboard. STRATEGIC RISK MANAGEMENT Roadrunner Publishers (Part 2) REDUCING THE RISK OF LOST SALES Why did the manager in Roadrunner Publishers (Part 2) decide to relax the book cover constraint? He believed the company faced a risk of lost current and future sales. He decided to reduce this risk by accepting a lower contribution margin in the short term. What other options were available for relaxing the constraint? The company probably could not satisfy demand by increasing the efficiency with which it uses cardboard to make book covers. However, Roadrunner might have been able to outsource the book covers if other companies had cardboard stock on hand. Or Roadrunner could have purchased a less expensive cardboard stock to meet immediate demand. PRODUCT EMPHASIS: MULTIPLE RESOURCE CONSTRAINTS AND MULTIPLE PRODUCTS The preceding illustration is simplistic compared to many business environments. Most organizations have capacity constraints that affect more than one resource and more than one product. QUANTITATIVE RULE FOR MAXIMIZING CONTRIBUTION MARGIN WITH MULTIPLE CONSTRAINTS AND MULTIPLE PRODUCTS Q5 How is relevant quantitative and qualitative information used in product emphasis and constrained resource decisions? The quantitative decision rule is that managers want to maximize profits in the short term by selecting the product mix that achieves the highest contribution margin per set of constrained resources. When multiple resource constraints and multiple products are involved, managers must find the product mix that maximizes the contribution margin. To find this mix, simultaneous equations are solved using linear programming, a mathematical technique that maximizes a linear objective function (such as the sum of contribution margins from multiple products) subject to linear constraints (such as the number of hours available for different manufacturing or services processes). Optimal solutions can be computed using linear programming software packages such as Excel® Solver and Vanguard System™. When multiple products use different amounts of multiple resources, we set up the equations needed to solve the linear programming problem as follows: 1. Calculate the contribution margin for each product and determine the objective (target) function to be maximized. 2. List the amount of constrained resources required per product and the total amount of constrained resource available (often measured in hours). 3. Solve for the optimal product mix using Excel Solver or other software. 4. Interpret the output. The output from Excel Solver and other programs provides information about binding constraints and slack resources. A binding constraint is a resource that limits production, such as the number of hours available for inspection. Slack resources do not limit production and could be used if no other constraints limit production. Slack resources reflect idle capacity. Excel Solver output also provides a shadow price that tells us the contribution margin per constrained resource, given the other constraints in the problem. In addition, Excel Solver gives information about points at which the optimal product mix would change if changes occurred in contribution margins or constrained resources. The following Bertram Golf Carts illustration demonstrates these details. BERTRAM GOLF CARTS MULTIPLE CAPACITY CONSTRAINTS AND MULTIPLE PRODUCTS Bertram Golf Carts manufactures regular and premium golf carts. The company's managers want to determine the mix of products that will maximize their contribution margin, so they will know which products should be emphasized. Regular carts sell for $8,000, have a variable cost per unit of $5,600, and require 20 hours for assembly. Premium carts sell for $10,000, have a variable cost of $6,500, and require 50 hours for assembly. Because of the quality controls built into the assembly process, premium carts take only 2.5 hours to inspect and test, whereas regular carts take 5 hours to test and inspect. Bertram has 10,000 hours available for assembly and 1,200 hours for testing and inspection. In addition, a shortage of leather for seat covers limits production to only 150 premium carts. The product mix having the highest contribution margin can be determined using a graph and calculations as shown in Exhibit 4.4. First graph each of the three constraints. Then determine the feasible solution area, in which all constraints are satisfied (shaded area in Exhibit 4.4). Then calculate the total contribution margin for each corner of the feasible solution area (point, A, B, C, D, and E in Exhibit 4.4). Point C (130 premium golf carts and 175 regular golf carts) is the optimal solution because it would result in the highest total contribution margin. The Excel Solver Answer Report gives the optimal solution (see Exhibit 4.5). For Bertram, the optimal product mix is 175 regular carts and 130 premium carts (under Final Value in the Adjustable Cells section). The total contribution margin for this product mix is $875,000 (under Final Value in the Target Cell section). The optimal product mix uses all of the available hours in both assembly and testing; these resources are binding because they limit further production. However, the amount of leather material available is not binding; only 130 premium carts are made. Enough leather is available for an additional 20 premium carts. The unused leather is considered a slack resource. Notice that the results in Exhibit 4.5 are the same as inExhibit 4.4. EXHIBIT 4.4 Graphical Solution to Bertram Golf Cart Product Emphasis Problem The graphical solution approach works when the number of products and constraints is small, but this method is cumbersome for only two products and three constraints. An easier approach is to use an optimization software program such as Excel Solver for this type of problem. Instructions for using Excel Solver are presented in Appendix 4A. EXHIBIT 4.5 Solver Output for Bertram Golf Carts: Answer Report The Sensitivity Report provides sensitivity analysis around the product mix, contribution margins, and constrained resources (Exhibit 4.6). In the first section for adjustable cells, the objective coefficient represents the contribution margin per product: $2,400 for regular carts and $3,500 for premium carts. The “allowable increase” and “allowable decrease” values are the amount the contribution margin per unit could change before the product mix would change (holding everything else constant). For Bertram, the optimal product mix would change if the regular cart contribution margin increased to more than $7,000 ($2,400 + $4,600) or decreased to less than $1,400 ($2,400 − $1,000). Similarly, the contribution margin for premium carts could increase by $2,500 or decrease by $2,300 before affecting the optimal product mix. The lower section of the Sensitivity Report provides information about the constraints. The optimal product mix changes until total assembly time is increased by 800 hours to 10,800. Then one of the other constraints binds production and the mix no longer changes. Managers usually want to relax constraints, so the allowable decrease is not very meaningful. The shadow price provides the contribution margin per constrained resource. Following the general rule for constrained resources, Bertram's managers would be willing to pay up to $57.50 per hour in addition to what they are already paying to relax the constraint in assembly. Similarly, they would be willing to pay up to $250.00 per hour in addition to what they are already paying to relax the constraint in testing and inspection. The shadow price for leather is zero because the leather resource constraint is not binding. EXHIBIT 4.6 Solver Output for Bertram Golf Carts: Sensitivity Report STRATEGIC RISK MANAGEMENT Bertram Golf Carts RISKY ASSUMPTIONS In Bertram Golf Carts, the optimal product mix relied on several key assumptions. For example, the analysis assumed that the company could sell all of the golf carts produced. In a stable economy with a regular customer base, the company might be able to accurately forecast product demand. However, business shifts such as the current financial crisis and ongoing globalization might reduce overall demand or increase competition. Managers need to continuously monitor the economic environment for these types of shifts. The analysis also assumed that no changes would occur in selling prices or in the cost function. Managers could evaluate the effects of this risk using the Sensitivity Report produced by Solver. As discussed in the next section, the company may be able to use constrained resources more efficiently even if the product mix assumptions are reasonable. METHODS FOR RELAXING CONSTRAINTS Q5 How is relevant quantitative and qualitative information used in product emphasis and constrained resource decisions? Managers analyze operations and make decisions about the use of resources. Scarce resources, such as capacity constraints, must be carefully managed. We can use quantitative techniques to choose the product mix that maximizes the contribution margin for bottleneck resources. Alternatively, we can relax or elevate the constraint. Because each setting is unique, managers choose among a number of different techniques. USE CONSTRAINED RESOURCES MORE EFFICIENTLY In the Bertram Golf Carts illustration, managers could analyze the assembly and testing-inspection processes to find ways to use constrained resources most efficiently. One possibility would be to change when inspection takes place. If golf carts are inspected earlier and more often during assembly, spoiled units are removed from the line earlier in the assembly process. Fewer resources will then be needed in assembly and testing, helping to alleviate both assembly and testing constraints. Also, improvements in quality (lower defect rates) would ensure that only good units go through all processes. In addition, workers from nonbottleneck resources can be reassigned to the bottleneck resources to increase the speed and constancy of the process. This reassignment is especially important during breaks and meals. To maximize output, bottleneck resources should be running as many hours as possible, regardless of the production team's schedule. Chapter 14 discusses increasing throughput, the rate at which product moves through the manufacturing process to the point of sale, or the rate at which services are produced. Alternatively, efforts such as process reengineering (redesigning the manufacturing or service delivery process) can be undertaken to reduce use of the constrained resources. For example, Bertram could redesign its assembly process and outsource the assembly of the seats and seat covers to reduce the amount of time each cart spends in the assembly department. INCREASE AVAILABLE RESOURCES Another possibility is to increase available resources. For example, managers can ask employees to work overtime. They can also increase capacity by buying new equipment or hiring new employees. Increasingly, companies use temporary labor or other outsourcing arrangements to increase available resources on an as-needed basis. Thus, resources might be increased either internally or externally. QUALITATIVE AND RISK FACTORS FOR PRODUCT EMPHASIS AND CONSTRAINED RESOURCE PROBLEMS Relevant qualitative factors include any nonquantitative issues that managers should consider before making a decision. Below are examples of questions managers could ask to help them identify relevant qualitative factors, including business risks, for a product emphasis or constrained resource decision: • • • • • • • • • • Does the product emphasis agree with strategic plans? Are product choices affected by other factors, such as environmental impact or product safety? Are sales of one product likely to affect sales of other products? What kinds of product combinations are competitors offering? Do some products command high customer loyalty, even in out-of-stock situations? Are there other ways to relax a constraint? How would brand recognition be affected by delivery delays? Are costs likely to increase as operations get closer to capacity constraints? Will the price we pay now to relax a resource constraint affect the future cost of the resource? How would different product emphasis choices affect overall organizational risk? For example, should the organization avoid depending heavily on a single product or on a portfolio of high-risk products? Should the organization reduce dependence on raw materials having uncertain supply or volatile prices? QUALITY OF OPERATING DECISIONS Q6 What factors affect the quality of operating decisions? We learned in Chapter 1 that managers make higher-quality decisions when they use higher-quality information and higher-quality decision processes. It is not sufficient for managers to identify relevant information when making decisions. They must also consider the quality of information, ensure that operating decisions support organizational strategies, consider risk appetite, avoid decision biases, conduct sensitivity analyses, and reduce undesirable behaviors. QUALITY OF INFORMATION Three major factors affect the quality of information for nonroutine operating decisions: business risk, information timeliness, and analysis technique assumptions. CHAPTER REFERENCE See Exhibit 1.7 for the path to higher quality decisions. Business Risk Business risk (for examples, see Exhibit 1.5, p. 15) prevents managers from accurately anticipating all of the quantitative and qualitative effects of a decision. Future revenues, costs, and qualitative factors can vary depending on changes in the economic environment, customer demand, competition, government regulation, vendor quality, technology, and so on. The degree of risk varies from decision to decision. For example, less risk comes with a special order from a long-time customer than from a new customer. Similarly, less risk accompanies outsourcing with a nearby company than with a company on another continent. In addition, decisions having a shorter time horizon, such as a special order that can be completed within one week, are less risky than decisions having a longer impact, such as dropping a product. Information Timeliness Many operating decisions must be made quickly and rely on up-to-date information. For example, a customer might require a prompt reply to a special order request, or managers may need to change production plans to emphasize different products as circumstances change. Access to timely information is particularly important in industries such as computer manufacturing, where technology, demand, and prices change rapidly. Cost information that is only one month old may be irrelevant. Thus, the accessibility and currency of the information system affect the quality of decisions. Analysis Technique Assumptions The reasonableness of assumptions affects the quality of information generated from an analysis technique. For example, the modeling techniques introduced in this textbook (regression, CVP analysis, and linear programming) assume that the revenue and cost functions are linear and that operations remain in a relevant range of activity. Although the validity of assumptions cannot be known with certainty, the validity of assumptions in a rapidly changing business environment is more uncertain than in a stable environment. The quantitative decision rules we learned in this chapter assume that the organization's goal is to maximize short-term profits. This assumption ignores business risks or other qualitative factors that might be more important than short-term profits for some decisions. CHAPTER REFERENCE Exhibit 1.1 in Chapter 1 provides more details about the relationships among vision, core competencies, and strategies. STRATEGIC ALIGNMENT Operating plans are designed to help achieve an organization's long-term strategies. In turn, the strategies depend on an organization's vision, core competencies, and risk appetite. When addressing any operating decision, managers should consider whether each option is consistent with the organization's strategies, vision, core competencies, and risk appetite. For example, organizations such as Honda have established a market position based on high product reliability, making that characteristic an important strategic issue. Some organizations, such as WalMart, place strategic importance on low costs and prices. Ben & Jerry's strategy includes protecting the environment.4Many organizations reduce the effects of raw material price fluctuations by entering into long-term purchase contracts or through hedging. By considering these types of qualitative issues, managers avoid taking actions that conflict with the organization's long-term interests. DECISION-MAKER BIAS Sometimes decision makers are influenced by predispositions for a course of action, which reduces their ability to objectively and thoroughly analyze relevant information. The Motorola case in Chapter 1illustrated how bias in favor of one option can lead to poor business decisions. Biases can also cause managers to develop distorted forecasts (e.g., confirmation bias, p. 138) or include irrelevant information such as sunk costs or unavoidable fixed costs in their analyses. Another type of bias involves a preference for either quantitative or qualitative information. Some people tend to rely primarily on quantitative analyses because they are more comfortable with what they view as precise answers. Others, recognizing the uncertainties in quantitative analyses, prefer to rely on qualitative factors to make decisions. The best approach is to weigh carefully both quantitative and qualitative factors, taking into account the strengths and weaknesses of information for a particular decision. OPPORTUNITY COSTS Opportunity costs arise whenever decisions are made because another alternative is always a possibility. For example, when you picked your current college or university, you decided to forgo attending alternative institutions. Furthermore, the time you spend in class or studying could be spent on other activities, such as working or leisure activities. These alternatives are relatively easy to identify and to value, either quantitatively or qualitatively. However, managers and accountants may overlook opportunity costs because they do not have time to adequately explore alternatives within a decision-making scenario. Moreover, the accounting system may not provide information about alternatives, or the available cost information may be inaccurate because of allocated costs that are not relevant to a decision. In Roadrunner Publishers (Part 1), we assumed for simplicity that the managers had no alternative use for the space used by book covers and, therefore, no opportunity costs to consider. In Roadrunner Publishers (Part 3), we relax this assumption and explore how opportunity costs affect the outsourcing decision. ROADRUNNER PUBLISHERS (PART 3) INSOURCE OR OUTSOURCE WITH OPPORTUNITY COSTS Mark Bonaray, the cost accountant for Roadrunner Publishers, learns that the CEO would like to launch a new line of comic books. The comic books could potentially be produced in the physical space currently used for book covers. Therefore, Mark decides to modify his book cover outsourcing analysis to incorporate possible opportunity costs. Mark begins by estimating the contribution margin that could be obtained from comic books. Because this is a new product line, the accounting system does not contain information about revenues or costs for this alternative. The sales manager tells Mark that breaking into this market would require an author and artist who could develop intriguing story plots and charismatic characters. Assuming an appropriate author and artist can be obtained, she estimates sales of 10,000 comic books for the first few issues produced. If successful, demand could be as high as several hundred thousand books. Because this is a new product and the firm will most likely hire a relatively new author and artist, Mark estimates sales of only 10,000 comic books. He next calls several bookstores and learns that comic books retail for about $2.99 each. Bookstores pay about half of the retail price to publishers. Therefore, Mark assumes that Roadrunner could sell the comic books for $1.50 each. Mark next estimates the relevant comic book costs. One of the production managers estimates that variable costs would be $0.75 each. The fixed costs relating to the plant and equipment are sunk costs, but the author and artist would be paid a flat fee of $3,000 per book plus royalties of $0.10 per comic book sold. Thus, the contribution margin per book would be $0.65 ($1.50 − $0.75 − $0.10), and the total contribution would be (10,000 books × $0.65) − $3,000, or $3,500. Mark now adds the opportunity cost of $3,500 to his earlier cost analysis for outsourcing the book covers. The revised cost analysis is as follows: Mark had previously estimated that the company could save $5,000 if book covers were outsourced. He now estimates that the savings could be $8,500 ($5,000 + $3,500). If the comic books are successful, his estimate of the opportunity cost might be low. However, comic books would be a new product line subject to considerable business risk. Also, Mark continues to believe that problems may arise if the book cover outsourcer fails to make timely deliveries. Roadrunner could experience lost sales from book cover shortages, harming short-term profits as well as long-term relationships with authors. Successful authors could move to other publishers if book production shortages become a problem. Mark plans to discuss these issues with the CEO, who will make the final decision. In Roadrunner (Part 3), Mark could have subtracted the opportunity cost from the cost to buy instead of adding it to the cost to make. Either approach is correct, but opportunity costs from using capacity released by outsourcing a product or service should increase the cost to make or decrease the cost to buy. BUSINESS RISK AND SENSITIVITY ANALYSIS One way to improve decisions in light of low information quality and potential biases is to perform one or more sensitivity analyses. Sensitivity analysis helps managers evaluate how quantitative results would change with changes in various pieces of information. For example, estimates of incremental costs could be increased to evaluate the potential effects of risk. Sometimes the degree of risk in the quantitative estimates for one option might exceed the organization's appetite for risk, making that option less desirable than another option having less risk. CONTROL SYSTEM INCENTIVE AND BEHAVIORAL EFFECTS CHAPTER REFERENCE Chapters 15 and 16 explore the incentive effects of various performance measures. We learned in Chapter 1 that organizations adopt diagnostic control systems to encourage employees to achieve preset goals. These systems often include financial measures that can discourage optimal decision making. For example, managers may receive a bonus if operations achieve a targeted gross profit percentage. Managers with this reward might be unwilling to accept a special order that increases gross profit but decreases the gross profit percentage. Ideally, control systems should be designed to avoid such unintended consequences. APPENDIX 4A Using Excel Solver for Product Emphasis and Constrained Resource Decisions Q5 How is relevant quantitative and qualitative information used in product emphasis and constrained resource decisions? Linear programming problems can be solved using a spreadsheet application. This appendix provides detailed instructions for using Solver, a tool within Excel, to solve a product emphasis problem with resource constraints. We use data from the Bertram Golf Carts illustration to demonstrate the instructions. The instructions and exhibits in this appendix were prepared using Excel 2003 (no changes are needed for Excel 2007). Following is a summary of the steps we will learn in this appendix: 1. Determine the objective (target) function. 2. Create formulas for the resource constraints. 3. Set up an Excel spreadsheet. 4. Use Excel Solver to maximize the objective function. 5. Interpret the Solver output. 1. DETERMINE THE OBJECTIVE (TARGET) FUNCTION The general decision rule for a product emphasis problem when resources are constrained is to emphasize the product with the highest contribution margin per unit of constrained resource. The goal is to maximize the organization's total contribution margin. Therefore, the objective function for the linear programming problem is to maximize the sum of contribution margins. In Excel Solver, the objective function is called the target function. For Bertram Golf Carts, the objective (target) function is to maximize the total contribution margin from its two types of golf carts. Regular golf carts sell for $8,000 and have a variable cost per unit of $5,600. Premium carts sell for $10,000 and have a variable cost of $6,500 Objective (target) function = Total contribution margin = Regular carts × ($8,000 − $5,600) + Premium carts × ($10,000 − $6,500) = Regular carts × $2,400 + Premium carts × $3,500 2. CREATE CONSTRAINT FUNCTIONS The next step is to determine the function for each resource and product demand constraint. The function for a resource constraint is the sum of the quantity of the resource used by each product, which must be less than or equal to the maximum available amount of the resource. In the Bertram Golf Cart illustration, three constrained resources are assembly hours, testing and inspection hours, and leather for seat covers. Bertram has 10,000 hours available for assembly. Regular carts require 20 assembly hours, while premium carts require 50 hours. For assembly, the constraint function is Regular carts × 20 hours + Premium carts × 50 hours ≤ 10,000 hours Bertram has 1,200 hours for testing and inspection. Regular carts take 5 hours to test and inspect, while premium carts take only 2.5 hours. For testing and inspecting, the constraint function is Regular carts × 5 hours + Premium carts × 2.5 hours ≤ 1,200 hours Bertram has only enough leather for 150 seat covers. Regular carts do not have leather seat covers, so this constraint relates to only premium carts. Premium carts × 1 seat cover ≤ 150 covers The function for a demand constraint is the maximum quantity demanded for the product. Bertram has no product demand constraints; the managers assume that the company can sell all carts produced. 3. SET UP AN EXCEL SPREADSHEET Exhibit 4A.1(a) provides a general Excel spreadsheet format for a product emphasis problem with resource constraints. A spreadsheet using this format for Bertram Golf Carts is shown in Exhibit 4A.1(b). The following instructions describe how to create the spreadsheet. Begin by creating a spreadsheet with titles and headings similar to those shown in Exhibit 4A.1. Rename the cells to the right of the Changing Cells and under the product names. Solver uses these cells to enter the number of units for the optimal product mix. These cells (B5, C5, and so on) must be given names that are used later in the spreadsheet for the target function formula and the constraint formulas. To assign a name to a given cell, first place the cursor in that cell. Next, find the cell number in the Excel formula bar (if the formula bar is not visible, click on Formula Bar in the View menu). When you click on the cell number in the formula bar, the number will be highlighted. You can then replace the cell number with a name for the cell. This name will appear in Solver output reports, so you should choose a name that is recognizable. For Bertram Golf Carts, cell B5 is renamed “Regular” and cell C5 is renamed “Premium.” Now enter a 0 in each of the renamed cells. For Bertram, a 0 is entered in cells B5 (renamed Regular) and C5 (renamed Premium). After Solver is run, Excel will replace these entries with the optimal number of units. EXHIBIT 4A.1 Excel Spreadsheets for Product Emphasis with Constrained Resources In cell B8, enter an equal sign followed by the formula for the target function (i.e., the sum of the product contribution margins). When typing the formulas, use the names for cell references to the number of units for each product. If desired, format this cell as a dollar amount. For Bertram Golf Carts, the target function was determined in step 1. The formula is entered in cell B8 as: = Regular*2400 + Premium*3500 Because the initial units of regular and premium were entered as zeros in cells B5 and C5, Excel computes an initial value in cell B8 of $0. In column B, type a name for each constraint beginning in row 11. For Bertram Golf Carts, three constraints are named “Assembly hours” in cell B11, “Testing hours” in cell B12, and “Leather seats” in cell B13. The left- and right-hand sides of each resource constraint formula are entered in columns C and D, respectively. When typing the formulas, use the names for cell references to the renamed cells. For example, the formula for the Bertram assembly hours constraint was determined in step 2 as: Regular carts*20 hours + Premium carts*50 hours ≤ 10,000 hours Substituting the product cells names and omitting units of measurement, the formula becomes: Regular*20 + Premium*50 ≤ 10000 Then, the left-hand side of the formula is entered in cell C11 as = Regular*20 + Premium*50 and the right-hand side of the formula (the maximum amount of the resource available) is entered in cell D11 as 10,000. Because the initial number of regular and premium units was entered as zero in cells B5 and C5, Excel computes an initial value of 0 for the number of constrained resources used in cell C11. Make similar entries for all of the constraints. Check to be sure the spreadsheet is similar to the ones in Exhibits 4A.1(a) and (b). 4. USE EXCEL SOLVER TO MAXIMIZE THE OBJECTIVE FUNCTION Once all information is entered in the spreadsheet, select Solver on the Tools menu in Excel 2003 (Data tab in Excel 2007). If Solver is not on the Tools menu, add it using the Add-Ins feature on the Tools menu (in Excel 2007 click on the Microsoft Office Button, then Excel Options, then Add-ins, then Manage Excel Add-ins, and finally Solver Add-in). Once Solver is selected, a Solver Parameters dialog box like the first one shown in Exhibit 4A.2 will appear. The Solver Parameters dialog box is used to select calculation options and to define the target function, product mix (i.e., change) variables, and the constraints. First, define the target function in Solver by entering a reference in the Set Target Cell area of the dialog box to the target function in the spreadsheet (cell B8). You can either (1) type “B8” in the Set Target Cell area of the dialog box or (2) click in the Set Target Cell area of the dialog box and then click on the target function cell (B8) in the spreadsheet. (Excel will automatically convert “B8” to “$B$8.”) Second, ensure that Solver will maximize the target function by verifying that the button next to Max is selected. Third, define the variables that Solver will change to maximize the target function by entering a reference to the cells that contain the number of units for each product (cells B5 to C5 for Bertram). You can either (1) type the cell range “B5:C5” in the By Changing Cells area of the dialog box, or (2) click in the By Changing Cells area of the dialog box and then highlight the range of cells (B5 through C5) in the spreadsheet. Fourth, add constraints by clicking on the Add button, which will cause the Add Constraint dialog box shown in Exhibit 4A.2 to appear. The constraints are defined one at a time in the Add Constraint dialog box. The Cell Reference area is used for the constraint formula, while the Constraint area is used for the maximum quantity available of each resource. The following instructions refer to the first constraint for Bertram. To set the Cell Reference, you can either (1) type “C11” in the Cell Reference area of the dialog box, or (2) click in the Cell Reference area of the dialog box and then click on constraint formula cell (C11) in the spreadsheet. Ensure that the constraint mathematical operation in the middle area shows as “