Writing Assignment - Middlehurst House
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Learning Objectives
After studying Chapter 9, you will be able to:
Describe an eight-step process for decision making.
Understand the use of differential analysis in making basic decisions.
Identify and use relevant costs and revenues in make or buy decisions.
Evaluate special sales pricing decisions.
Make decisions when there are resource constraints.
Determine the relevant costs and revenues in sell or process further decisions.
Evaluate decisions involving adding or deleting segments.
9 Managerial Decisions: Analysis of RelevantInformation
Monkey Business Images/Monkey Business/Thinkstock
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Understand the basic elements of equipment replacement decisions.
Incorporate ethical considerations in decision making.
Explain the role of market and cost information in pricing decisions.
Decisions, Decisions, Decisions
Shirley Rich operates a series of take-out rib and sandwich shops, called Rich Ribs, in the city’s suburbs. Before leaving on vacation, Shirley asked her controller, Alan Belinky, to prepare cost analyses of several decisions she has been considering. She met with Alan to outline each decision.
Decision 1: A major employer in the area called Shirley and asked whether a deal could be arranged to serve Rich Ribs at a company picnic and later perhaps regularly in its cafeteria. Shirley’s company name may or may not be identi�ied. The company’s offering price is roughly 60% of Rich’s a la carte menu price.
Decision 2: The shop on Sherman Avenue has been showing a monthly net operating loss for the last six months. The shop’s lease expires at year-end. Also, a new mini shopping mall is opening in a growing part of the city not presently served by Shirley’s shops. Shirley could close the Sherman shop and shift the manager to the new mall shop.
Decision 3: A local bakery with an excellent reputation in the area has offered to sell breadsticks to Shirley. Rich Ribs includes a serving of breadsticks with every take-out dinner order. Right now, Shirley bakes her own breadsticks in her kitchen every day and is proud of their quality, but the bakery price offer seems very low.
Decision 4: Shirley is thinking of adding pizza to her menu, but the kitchen’s oven capacity would be stretched severely if she keeps all other menu items. She wants to use her kitchen capacity in the most pro�itable way.
Shirley has a “common sense feel” about the answers to these decisions, but she needs economic proof. She looks to Alan to assemble, analyze, and present the relevant information for each issue. She must then weigh all the quantitative and qualitative factors and decide.
Yes, “decisions, decisions, decisions” is a common lament. However, decision making creates action. It is the exciting part of management. Managers’ experiences and skills are applied to speci�ic problems. The decision may be signi�icant, such as when and where to build a new $1 billion manufacturing facility. Or it may be mundane, such as sending a customer contract by �irst-class mail or overnight by FedEx. In either case, consciously or subconsciously, managers follow a process: de�ine the problem, consider choices, collect and analyze relevant data, make a decision, and act.
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This chapter examines groups of decisions that require particular decision rules, relevant data, and formats. These decision types occur commonly in all business activities and even in our personal lives. These groups are:
1. Make or buy—where to get resource inputs. 2. Special sales pricing—is a special sales price justi�iable? 3. Use scarce resources—how to get the most out of limited resources. 4. Sell or process further—when to sell. 5. Add or delete a segment—which to do.
Other decision groups, such as replacing equipment and expanding capacity, are explored in Chapter 10.
Decisions discussed here are necessarily simpli�ied. The real world offers much more complexity. Decisions are about the future, where much uncertainty exists. The discussions in this chapter, though, imply a certainty about the future. In textbook problems, we consider only a few variables that impact decision results. In reality, literally hundreds of variables are moving in different directions at the same time. Therefore, an organized approach helps managers establish a process, select relevant variables, and add format to their analysis.
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9.1 The Decision-Making Process Every managerial decision is made with the mission and the strategic goals of the organization in mind. Organizing to make decisions implies structure and methodology, but not arbitrariness or rigidity. The following eight-step process is useful for decision making:
1. De�ine the decision issue. 2. Specify the decision objective and decision rule. 3. Identify the choices or alternatives. 4. Collect relevant data on the choices. 5. Format and analyze information about each choice. 6. Make the decision. 7. Implement the decision. 8. Evaluate the results of the decision.
This chapter focuses on those steps taken by managerial accountants. For Step 2, we outline a decision rule and guidelines. For Step 4, we de�ine relevant data. For Step 5, we present formats for analyses. In addition to quantitative analysis, major qualitative issues that in�luence decisions are raised. And for Step 6, we apply differential analysis to select the preferred choice, given the facts.
An important element underlying these processes is the empowerment of managers throughout the �irm to make decisions. Decisions are based on a clear understanding of organizational goals, training in decision analysis, sharing decision-making information, exercising the authority to act, and having an evaluation process.
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9.2 Differential Analysis Differential analysis uses relevant revenues and costs to make decisions. It is the result of de�ining a decision rule and quantifying and formatting relevant information.
The Basic Decision Rule
The basic differential analysis decision rule is:
Select the choice that yields the greatest incremental pro�it.
Incremental pro�it is the difference between the relevant revenues and the relevant costs of each choice. Relevant revenues and costs are de�ined as the current and future revenues and costs that differ among the choices considered. In most cases, the term “incremental” is used as a substitute for “relevant.” In choosing among choices, all past and committed costs (often referred to as sunk costs) and all costs that remain the same across all choices are irrelevant and are ignored. For instance, suppose product X has been produced at a cost of $100 and can be sold for $175. Alternatively, an additional $10 can be spent to convert product X into product Y, which would sell for $200. The incremental revenue would be $25 ($200 – $175), the incremental cost would be the additional cost of $10, and the incremental pro�it would be $15 ($25 – $10). The $100 cost to produce product X is a sunk cost because it has already been incurred.
A decision is frequently a choice of:
Do it, or don’t do it. or Do A, or do B, or do C, or etc.
In the �irst case, “don’t do it” is the status quo (i.e., the present condition); “do it” has incremental revenues and costs attached. In the second case, incremental revenues and costs for each choice are measured. In either case, the decision is based on which choice generates the highest incremental pro�it —incremental revenues minus incremental costs.
Relevant revenues are generally cash in�lows, and relevant costs are generally cash out�lows. Out-of- pocket costs refer to costs that are cash out�lows. If cash �low and accrual numbers differ, the managerial emphasis is often on cash.
In many cases, capacity impacts decisions. Capacity costs are frequently �ixed and are irrelevant to most short-term decisions. A relevant factor is the opportunity cost of using capacity. If excess capacity exists and no alternative uses are apparent, the opportunity cost is zero—the unused capacity has no next-best use. If capacity is fully used, earnings from its alternative uses and costs of acquiring additional capacity are considered.
Incremental Analysis Versus Total Analysis
Differential analysis contrasts choices by comparing incremental contribution margins. Two commonly used approaches are applicable to all decision types: the incremental analysis approach and the total analysis approach. The incremental analysis approach includes only incremental revenues and incremental costs of each choice. The total analysis approach shows the results for the total entity, including the alternative and then excluding the alternative. To evaluate adding a new product, the format is:
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Clearly, the two approaches yield the same incremental pro�it. The incremental analysis approach has the advantage of showing only relevant amounts. All sunk and non-incremental amounts are ignored. The total analysis approach reports the �irm’s gross results, with and without the decision’s impacts.
An Example of Differential Analysis
MaineLine (ML) Caps is located in Augusta, Maine, with a factory in South Carolina. Steve Berman, CEO, recently purchased this small manufacturer of baseball-type hats. It produces several styles in a variety of materials, but all caps are essentially the same. The caps are marketed under the name ML Caps. Steve has just �inished an initial budget for 2020, including this income statement:
Sales (100,000 units at $10 per unit) $1,000,000
Less production costs:
Variable production costs ($3 per unit) $300,000
Fixed factory costs 300,000 − 600,000
Gross pro�it $400,000
Less operating expenses:
Selling expenses (15% of sales) $150,000
Administrative expenses 150,000 − 300,000
Operating income $100,000
Steve’s factory operates at 80% of capacity. He is currently weighing several alternatives to increase capacity utilization and pro�its. His analysis shows the choices as:
1. Maintain the status quo. 2. Expand sales of ML Caps to 125,000 by lowering the selling price from $10 to $9 per unit. 3. Use the remaining capacity to make an insulated cap for cold weather runners, called CoolHat.
He estimates a sales price of $8 per unit, selling expenses of 15%, variable production costs of $4 per unit, and no change in total �ixed costs.
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The three choices are compared in Figure 9.1 using a total analysis approach. Choice 2 increases net income to $131,250, a differential increase of $31,250. With Choice 3, the CoolHat, operating income increases by $70,000.
Figure 9.1: Total analysis approach to differential analysis
The incremental analysis approach is shown in Figure 9.2. No mention is made of the original sales of 100,000 units or �ixed costs, which do not change. All choices are incremental to Choice 1, the status quo. Therefore, while Choice 1 is not shown in Figure 9.2, the other choices show the contribution margin differential to Choice 1’s $100,000 of operating income.
Figure 9.2: Incremental analysis approach to differential analysis
Based on quantitative facts, Berman will select Choice 3. But before the decision is made, short-term qualitative issues and long-term considerations should be evaluated. Is the CoolHat consistent with the
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�irm’s product plans? Will it take resources from Steve’s primary product—ML Caps? Because Steve is an avid runner, are his personal biases confusing his thinking? Are additional equipment or worker skills needed? Although supposedly a short-term decision, these issues concern Steve.
Policy Issues Affecting Relevant Costing Decisions
As with all real-world issues, the decision-making path is more complex than the basic rules imply. The differential analysis model is so simple and appealing that we can easily be lulled into a false sense of objectivity.
ABC and Relevant Costs. Companies with well-developed activity-based costing systems are in more knowledgeable positions to make relevant costing decisions. With carefully selected cost drivers and cost functions, changes in costs from a change in activity can be seen more clearly.
The Timeframe. Certain assumptions are made in differential analysis. A short-term horizon is assumed, variable costs are relevant, and most �ixed costs are irrelevant. However, managers must recognize that all important decisions have both short-term and long-term impacts. In many cases, investments must be made that last longer than the immediate timeframe. Decisions made today often are not easily reversed tomorrow. Also, decisions made on a one-time basis or made for an immediate gain may change the options available in the long run. By selecting Choice 3 in our example above, Steve has committed all unused capacity. If ML Caps sales grow, he must somehow expand capacity or lose sales.
Strategic Planning Issues. A �irm’s strategic plan looks at product offerings, pricing strategies, competitive positions, and �inancial performance goals. “Long haul” policies are implemented in the short run by tactics and decision guidelines. Incremental decisions are often just minor additions at the margin. The major pricing, production, and marketing decisions must follow long-term strategies that have been carefully thought through.
Often decisions are masked as an incremental decision, when they are really policymaking, long-term decisions. For example:
Will a one-time sale at a low price become repeat business? Will regular customers seek price breaks to compete with off-brand look-a-likes? Will purchasing cheaper lower-quality parts eventually hurt a �irm’s image as a high-quality producer? Will outsourcing (i.e., obtaining a product or service from a vendor rather than internally) undermine harmony that the company and its labor union have worked hard to develop? Will stopping and starting production of a temporarily unpro�itable product cause losses of market share for an entire product line and of skilled employees who make the product?
While relevant costing is a powerful analytical tool, no decision can be made in isolation.
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9.3 Make or Buy Decisions The decision questions for the make or buy decisions are:
Should we make an item or purchase it from a vendor? Should we perform a service or obtain the service from an outside source?
Nearly all products and services offered on the market today result from basic make or buy decisions. A sample of these decisions includes:
The “Make” Alternative The “Buy” Alternative
Make the component part in our factory in Indiana.
Buy it from a nearby supplier, a nonunion vendor in another state, a Taiwanese producer, or another division of our own company.
Operate our �leet of delivery trucks.
Hire various freight companies.
Run our printing shop. Contract with local printers.
Employ our own cleaning staff.
Hire a cleaning service.
Manage our facilities. Hire a facilities management company.
Cook for ourselves. Eat in the cafeteria.
Managers consider make or buy decisions for various reasons, including to:
Reduce costs Use or to free up capacity Improve quality or delivery performance Encourage greater productivity from internal operations by forcing competition with outsiders Get new technology Free scarce investment funds for other uses
Key Decision Rule and Guidelines
The key decision rule is:
Buy the product or service if the relevant costs of buying are less than the relevant costs of making; otherwise, make it.
The decision rule is still to earn the highest pro�it. But since make or buy decisions generally deal only with costs, the decision rule minimizes cost. If we buy from a vendor, we outsource. We are in-house sourcing if we make the item ourselves.
Relevant make costs are the direct costs of producing an item plus any opportunity costs. Direct costs include direct materials, direct labor, and variable factory overhead costs. Included also are any incremental �ixed costs caused by the make decision, plus any traceable costs, such as unique tooling costs. These are called avoidable costs if the decision is to buy.
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Relevant buy costs are the item’s purchase price, shipping and handling costs, and any costs incurred to get the purchased item into usable form. Inspection and testing costs are examples. Another relevant cost issue is alternative uses of space vacated, if the part is now purchased. The space could be rented at some market rate, used by another department, or used to make other parts.
Data Analysis Format
The make or buy analysis format lists the relevant costs to make and the relevant costs to buy in a two- column format, shown as follows:
Make Costs Buy Costs
Materials and direct labor $ Purchase cost plus handling costs $
Variable overhead costs $
Avoidable �ixed overhead costs $
Other avoidable or incremental costs $
Opportunity costs of additional resources needed
$ or Incremental revenue or earnings from use of released resources
($)
Total make cost $ Total buy cost $
Using an incremental analysis approach, any costs that do not change are ignored, since they are irrelevant. Direct product costs and purchase costs can be either an additional cost on one side or a negative cost on the other. For example, if by outsourcing, of�ice space is no longer needed and can be leased for $5,000, the revenue reduces the buy costs. Or, it can be viewed as an additional make cost, since by performing the service ourselves we incur a $5,000 opportunity cost. Either way works. The bottom line is the comparison of the incremental make cost and the incremental buy cost. Select the alternative with the lower cost.
An Example
Lester Corporation has bids from several suppliers for a control device, a unit used in several models of its Hibeam Line of lighting �ixtures. Lester has made these devices for the past several years and needs 30,000 units for 2020 production requirements. Arday Wiring provided the lowest-cost bid at $3 per unit delivered. Quality control inspections of purchased units would cost Lester $3,000. Lester’s costs for 25,000 units made in 2019 were:
Per Unit Total Costs
Materials $1.25 $31,250
Direct labor .60 15,000
Variable overhead .50 12,500
Fixed overhead applied 1.00 25,000
Total $3.35 $83,750
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All costs are direct costs, except �ixed factory overhead. The only direct and avoidable �ixed factory overhead is $6,000, the annual cost of leasing specialized equipment required to make the control device. If the device is purchased, Lester could return the specialized equipment, void the lease, and use the space for storage. Renting storage space would cost $4,000 next year.
The relevant make and buy costs are:
Make Costs Buy Costs
Materials ($1.25 × 30,000) $37,500 Purchase cost ($3 × 30,000) $90,000
Direct labor ($0.60 × 30,000) 18,000 Quality control costs 3,000
Variable overhead ($0.50 × 30,000) 15,000 Rent savings (4,000)
Equipment lease cost 6,000
Total make costs $76,500 Total buy costs $89,000
Net make advantage $12,500
We can make several observations:
The variable costs on both sides are relevant. The $6,000 cost of leasing the equipment is relevant because the equipment lease payment is avoided under the buy choice. The remaining �ixed factory overhead is unavoidable and irrelevant to the decision. The $4,000 rent savings is relevant because it occurs only in the buy choice. The relevant volume is 30,000 units (the 2020 expected volume). Comparing the 2019 make full cost of $3.35 per unit to the buy cost of $3 hides important cost behavior patterns.
The recommendation is to continue to make the unit and save $12,500.
Contemporary Practice 9.1: Outsourcing of Hospital Services
Financial data analysis from a sample of 315 California hospitals revealed “that the outsourcing of clinical and non-clinical services improves the current and future �inancial performance for hospitals. Similar results are found for for-pro�it and not-for-pro�it hospitals but weaker results are reported for governmental hospitals when current �inancial performance is used.”
Source: Chang, K.J. & Said, A.A. (2014). The impact of outsourcing on hospital performance. International Journal of Management Accounting Research, 7–26.
Strategic and Qualitative Factors
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The make or buy decision focuses on choosing the lowest cost. But many subtleties surround the decision. In the prior example, only quantitative monetary facts were considered. Quality, delivery, labor force, and investment implications are frequently key issues.
Often, product and service quality is the highest-ranking factor and could support either the make or buy side. By making the product, we can control quality in all aspects of production. On the other hand, a particular task may require specialized knowledge. We may not have this expertise. An outside specialist may be faster and produce higher-quality output. Quality can be so important that cost differentials are ignored.
Delivery capability in just-in-time systems is critical. Again, perhaps in-house sourcing has an advantage since our production planners can schedule production on an “as needed” basis. Or the outside supplier may use delivery capability as a key competitive issue and be better able to meet complex requirements. Vendor certi�ication programs have allowed buying �irms to set benchmarks for performance and to narrow possible suppliers to a group known for high achievement.
Labor stability is another major make or buy consideration. For the United Auto Workers Union (UAW) and American auto producers, outsourcing is a major area of contention in labor negotiations. The auto companies have historically been vertically integrated. These companies, to be competitive with foreign producers and to increase internal productivity, are searching for the most ef�icient suppliers. Many suppliers are very ef�icient, more so than the automakers’ own captive divisions. The UAW, concerned about member job losses, is demanding labor contract provisions that guarantee in-house production. Also, a sense of community responsibility affects how managers decide where work—and, therefore, jobs—are located.
Global business transactions expand the decision beyond whether to make or buy. Now, if we make, where do we make? If we buy, where do we buy? Brazil, Mexico, China, Korea, and Eastern or Western Europe are possible sources. Also, many multinational �irms have facilities in several countries and can shift production depending on costs, quality, materials proximity, and product demand.
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9.4 Special Sales Pricing Decisions The decision question for the special sales pricing decision is:
Will we bene�it from special sales, generally made at prices lower than those charged to our regular customers?
This decision evaluates added sales opportunities using contribution margin analysis. Often, one company’s make or buy problem is another company’s special sales pricing problem. Examples of special sales pricing decisions include:
Generating discount-priced sales to use excess production capacity Accepting sales that cover only out-of-pocket costs to keep a workforce employed during a recession Making a one-time sale to move stale merchandise Responding to a request for a special product feature from a regular customer Pricing to enter a new competitive marketplace
Clearly, knowledge of cost behavior, volumes, and capacities is a major in�luence on pricing and marketing.
Key Decision Rule and Guidelines
The key decision rule is:
Subject to the following speci�ic guidelines, make the special sale if we earn a positive incremental pro�it from the special sale.
The guidelines or assumptions necessary to allow the basic rule to work are:
Excess capacity exists, with no alternative use of the capacity. The opportunity cost of using the capacity is zero or at least very low. Special sales should not interfere with regular sales. The special sale is a one-time order and will not become repeat business.
If all of these guidelines are not met, the analysis will have additional relevant revenues and costs to consider.
The minimum price must cover out-of-pocket costs plus any opportunity cost of making the sale (lost pro�its from regular sales or lost production). If the assumptions are ful�illed, there is no opportunity cost incurred. The economic rule is to produce and sell until the incremental revenue equals incremental cost—until a zero incremental pro�it is reached.
Data Analysis Format
The format of relevant data for special sales decisions appears as follows:
Incremental revenue $
Less incremental costs:
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Additional variable costs ($)
Additional direct �ixed costs ($)
Incremental pro�its $
Only relevant revenues and costs are shown. Variable costs are often determined by using the variable costs of regular business adjusted for any changes due to the special pricing situation, such as different formulas for baby foods, heavy-duty shock absorbers for police cars, and overtime police wages for a special concert on campus. Any additional supervision, preparation time, shipping, and packaging are relevant.
An Example
Assume that Backman Corporation’s capacity is 90,000 units of a cellular phone receiver, including 15,000 units made on overtime. Backman Corporation is currently producing and selling 80,000 units per year at $8 per unit. Variable production costs are $3 per unit, and annual �ixed factory overhead costs are $200,000. Variable shipping costs are $0.50 per unit; total administrative expenses are all �ixed and amount to $120,000. The pro�it calculation is as follows:
Sales (80,000 units × $8) $640,000
Less factory and shipping costs:
Variable (80,000 units × $3.50) $280,000
Fixed overhead 200,000 −480,000
Gross pro�it $160,000
Less administrative expenses −120,000
Operating income $ 40,000
An Argentine communications company approaches Backman Corporation with an offer to buy 10,000 receivers at $6 each. Sales in Argentina should not affect Backman Corporation’s regular sales. The special units would require minor modi�ications and force more overtime, adding $0.80 per unit to variable costs. Additional supervision would cost $3,000. The entire lot would be packed and shipped to Argentina for $2,000. The analysis shows:
Incremental sales (10,000 units × $6) $60,000
Less incremental costs:
Incremental variable factory costs (10,000 × $3) −30,000
Additional variable factory costs (10,000 × $0.80) −8,000
Additional �ixed supervision costs −3,000
Additional shipping costs −2,000
Incremental pro�it $17,000
Incremental pro�its of $17,000 are added to the pro�it from regular sales to create a forecast of $57,000 for operating income. The special sale adds to Backman Corporation’s total pro�it even though the $6
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price is $1.50 below the average cost of $7.50 (total product and administrative expenses of $600,000 divided by 80,000 units). The decision rule and the criteria are met. Make the special sale.
Nonsegmented Markets. Accepting special prices is a sound policy only if the special market can be kept separate from the regular market. For example, in the preceding illustration, assume that the international market begins to affect the domestic market to the extent that the domestic price drops from $8 per unit to $7.60 per unit (a 5% drop). In this case, the �irm’s pro�it calculation for the next period would appear as follows:
Incremental pro�it from the Argentine sale $ 17,000
Less lost revenue from price reduction (80,000 units × $0.40) –32,000
Incremental pro�it (loss) $(15,000)
If the special market price in�luences the domestic market, pro�its decrease from $40,000 to $25,000 – an incremental loss of $15,000. Don’t make the special sale.
No Excess Capacity. Assume that Backman Corporation’s capacity was only 85,000 units instead of 90,000 units and that the Argentine sale is all or nothing. By accepting the order, 5,000 units of regular business must be given up. The calculations are as follows:
Incremental pro�it from the Argentine sale $ 17,000
Less contribution margin on lost regular sales [5,000 × (8 – $3.50)] –22,500
Incremental pro�it $(5,500)
Losing 5,000 units of regular sales to accommodate the 10,000 unit Argentine sale will result in the company giving up pro�its. Don’t make the special sale.
Not a One-Time Sale. A special sale may be a sample order, with an unknown probability of larger future contracts. If repeat sales are expected, Backman Corporation must be very careful not to commit itself to a low-margin business.
Strategic and Qualitative Factors
Product pricing is a key market positioning tool. Low-priced special sales can preempt strategic plans. Management should consider how a special sale �its into long-term marketing goals. Another consideration should be whether using capacity for this sale is consistent with the strategic use of production capabilities. The decision guidelines previously presented (excess capacity, segmented markets, and one-time sale) are tactical rules to help prevent subtle economic errors. If we want a premium product and price image, discount deals may tarnish it. Our dealers probably depend on our pricing and product image stability.
Accepting another one-time sale is easy to do. More of our capacity becomes allocated to low-pro�it business on a routine basis. If the market segmentation guideline does not apply, regular business begins to shrink and special sales expand. Fewer and fewer customers are paying prices that cover all costs, while more sales at special prices pay only a portion of the �irm’s operating costs.
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9.5 Use of Scarce Resources Decisions The decision question for the scarce resource decision is:
When a productive resource is limited, how do we allocate the use of the scarce resource?
The scarce or limited resource decision is an extension of the special sales pricing decision except that no excess capacity exists, but there is some constraint. Several examples of scarce resource decisions are shown in Figure 9.3.
Figure 9.3: Scarce resource examples
All of these examples entail the concept of contribution margin per unit of scarce resource, which is contribution margin per unit divided by the amount of scarce resource used by each unit. For example, assume that Product 28 has a $10 per unit contribution margin and needs 30 minutes on a polishing machine that is a major factory bottleneck. Then, $20 per hour ($10 ÷ 0.5 hours) is the contribution margin per hour of polishing machine time when producing Product 28.
Key Decision Rule and Guidelines
The scarce resource decision rule is:
Optimize pro�its from a scarce resource by selecting the products or services with the highest contribution margin per unit of the scarce resource.
This rule yields the product mix that maximizes total pro�its. Products are ranked by their ability to generate the highest contribution margin per unit of scarce resource used. The scarce resource constraint is often a temporary situation. Over time, we can train more skilled workers, buy more equipment, or rent more space to eliminate the constraint.
Guidelines for selecting the most pro�itable set of products or services are:
We must know the amount of scarce resource needed (input) to produce a unit of output. The product with the highest contribution margin per unit of scarce resource is selected, then the second highest, and so on until the scarce resource is used. Normally, the analysis uses contribution margin.
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Allocated, common, or indirect �ixed costs are irrelevant to the decision.
When incremental direct �ixed costs exist, we should also incorporate these costs into the analysis.
Data Analysis Format and an Example
The data analysis format uses the contribution margin per unit of output and the scarce resource needed to produce that unit. The result is a pro�it ranking of all products based on a contribution margin per unit of scarce resource.
As an example, the Museum Repro Company (MRC) markets reproductions of well-known sculptures. Finish work is done by four highly skilled artists. MRC cannot �ind additional artists to meet the sales demand. Data on four MRC’s pieces are:
Roman Greek Aztec Egyptian
Sales demand (units) 1,000 units 200 units 500 units 500 units
Hours of work per unit 2 5 6 10
Indirect �ixed costs per unit $50 $110 $120 $200
Sales price per unit $250 $350 $600 $1,000
Variable costs per unit 150 150 240 550
Contribution margin per unit $100 $200 $360 $450
Divided by hours of work per unit ÷ 2 ÷ 5 ÷ 6 ÷ 10
Contribution margin per hour of work $50 $40 $60 $45
Priority ranking 2nd 4th 1st 3rd
Assume that the four artists each work about 2,000 hours per year. MRC will use the 8,000 hours available as follows:
Priority Piece
Hours per Unit Units
Hours Required
Remaining Available Hours
Contribution Margin per
Hour Contribution
Margin
8,000
1st Aztec 6 × 500 = 3,000 5,000 $ 60 $180,000
2nd Roman 2 × 1,000 = 2,000 3,000 $ 50 100,000
3rd Egyptian 10 × 300 = 3,000 0 $ 45 135,000
$415,000
Sales Demand Not Met:
Egyptian 200 units
Greek 200 units
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If MRC produces all of the needed Aztec and Roman units and only 300 Egyptian units, the detail artists’ 8,000 hours are entirely used. This product mix generates the highest contribution margin given the artists’ available time. Note that indirect �ixed costs are ignored in the analysis, since these costs will not change regardless of the production mix.
Strategic and Qualitative Factors
The qualitative issues in the scarce resource analysis are questions of product offerings. Why is MRC’s capacity limited? Is the marketplace demand driven? Scarce resource analysis can highlight possible poor pricing. In the MRC example, Egyptian and Greek prices might be raised to improve the contribution margin per hour of artist time to match or exceed Aztec’s contribution margin. Also, the basic analysis ignores the complementary aspect of various items in a product line. To compete in a market may require a complete product offering or a full menu.
Also of concern is the use of the scarce resource itself. Can steps be taken to conserve capacity, to substitute less critical resources, or to buy additional capacity? MRC can get an estimate of the value of additional capacity. In the MRC example, another employee working 2,000 hours per year would produce the following additional contribution margin:
Hours per Unit Units
Hours Required
Contribution Margin per Hour
Additional Contribution
Margin
Egyptian 10 × 200 = 2,000 × $45 = $ 90,000
The added contribution margin is $90,000, which is after the variable labor costs have been deducted. At that price, should MRC train another detail artist? Yes.
Contemporary Practice 9.2: Differential Analysis at Starbucks
“In 2002, Starbucks was trying to decide whether to spend $40 million system-wide to add 20 hours of labor per week to each store in order to speed up service. Looking at it purely from the cost perspective, that $40 million would shave seven cents a share off earnings.” However, in a study of customer satisfaction, Starbucks found that speed of service is very important and that highly satis�ied customers spend 9% more money than customers who are just simply satis�ied. Starbucks, therefore, decided to spend the $40 million, apparently concluding that the incremental revenues from highly satis�ied customers would more than offset the incremental labor cost of $40 million
Source: Chittum, R. (2006, October 30). Price points. The Wall Street Journal, R-7.
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9.6 Sell or Process Further Decisions The decision question for the sell or process further decision is:
Should the product be sold as is, or should it be processed further and then sold?
A common sell or process further decision deals with a product that can be sold now or processed further and sold later as a different product. In other cases, processing further can spawn multiple products from a common input. These are called joint products, and the further processing becomes a decision at the split-off point. Until this point, the common input is a single product. An example of a split- off point in a re�ining process is where the decision to process crude oil into joint products of gasoline, heating oil, and motor oil is made. The decision is to sell the crude oil or to re�ine and sell the joint products.
Key Decision Rule and Guidelines
The key decision rule is:
Process further if the incremental revenue from processing further is greater than the incremental costs of processing further.
The basic guidelines are:
All relevant additional processing costs are assumed to be incremental. Costs incurred prior to the split-off point are common to both sell and process further choices and are irrelevant to the process further decision. The decision is independent of product costing. Product costing attaches all product costs to units, including common and past costs. In process further decisions, only future revenues and costs are relevant. The decision assumes that products are either sold as is or processed further. If capacity allows, we could do both if both generate positive contribution margins.
The decision task is to always look at future costs and revenues and not past ones. We are in the present moment with something of value and looking into the future. We can sell it now. Or, we can do additional work, spend more money, and sell in the future. Past costs cannot be changed and are common to both choices.
While common or joint costs may be irrelevant in process further decisions, they are real costs, must be incurred, and should be attached to products as they �low through production processes. Chapter 5 discusses product cost procedures when products are produced from common processes.
Data Analysis Format and Examples
Assume, for example, that Tipton Company’s un�inished hardwood desks for home of�ices sell for $180, with a manufacturing cost of $100. The company can stain the desks at an additional cost of $30 each, yielding a desk that sells for $225. Due to market demand, the company could only sell 500 stained desks. The data format shows:
Revenue from sale of stained desks (500 units × $225) $112,500
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Less revenue from sale of unstained desks (500 units × $180) − 90,000
Incremental revenue $ 22,500
Less cost of staining (500 units × $30) − 15,000
Incremental contribution margin from processing further $7,500
The decision is obvious: stain and sell 500 desks because the incremental contribution margin from processing further is positive.
Four important assumptions were made. First, the desk’s manufacturing cost is assumed to be irrelevant, because the cost of desks is the same for unstained or stained desks. Second, the company is assumed to have capacity to process desks further without losing sales of other products. Third, the process further costs are assumed to be avoidable costs. And fourth, if the desks are not processed further, they can be sold unstained.
Joint Products—Process All or None. Assume that Kilgore Corporation produces an industrial wax with a sales value of $4 per gallon. The manufactured cost is $3.25 per gallon. Kilgore can convert 60,000 gallons of industrial wax through a process that yields equal amounts of three high-quality auto waxes: Super Gloss, Shiner, and Deep Glow. Costs of converting industrial wax into the three products are $40,000. The market values of the three waxes are $6, $5, and $4.80 per gallon, respectively. Should Kilgore process further?
Quantity Price Revenue
Super Gloss 20,000 gallons × $6.00 = $120,000
Shiner 20,000 × 5.00 = 100,000
Deep Glow 20,000 × 4.80 = 96,000
Total revenue after processing $316,000
Less revenue lost from industrial wax ($4 × 60,000 gallons) −240,000
Incremental revenue from processing further $ 76,000
Less cost of processing further − 40,000
Incremental contribution margin $ 36,000
The decision is to process further. Notice that the industrial wax production cost is not included since it is a sunk cost.
Joint Products—Which Products Should Be Processed Further? If processing costs are variable and if each auto wax can be produced independently, what should be done? Assume that additional variable processing costs per gallon were $1, $1.25 and $0.40, respectively. The analysis on a per-gallon basis is:
Process Further Price
Industrial Wax Price
Additional Revenue
Additional Processing Costs
Additional Contribution
Margin
Process Further Decision
Super Gloss
$6.00 − $4.00 = $2.00 − $1.00 = $1.00 Yes
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Process Further Price
Industrial Wax Price
Additional Revenue
Additional Processing Costs
Additional Contribution
Margin
Process Further Decision
Shiner 5.00 − 4.00 = 1.00 − 1.25 = (0.25) No
Deep Glow
4.80 − 4.00 = 0.80 − 0.40 = 0.40 Yes
Super Gloss and Deep Glow should be produced, but Shiner has a negative incremental contribution margin and should not be made. If Kilgore has a limited supply of industrial wax, it should make Super Gloss �irst and then Deep Glow.
Strategic and Qualitative Factors
The short-term version of this decision assumes further processing stages can be shut down or started up with few impacts. Rarely is this the case. Fixed costs will continue, skilled labor may be dif�icult to keep available, and product market shares may be dif�icult to maintain. Thus, the best short-run quantitative choice may not achieve the planned results, or the long-run damages may overwhelm the short-run bene�its.
In many processing operations, signi�icant capacity costs exist. In real life, metals commodity prices often determine whether copper, zinc, and gold mines operate or temporarily suspend production. In beef cattle, pork, and poultry operations, prices of retail and wholesale products and processing costs are constantly monitored and forecast at each stage to make optimal sell versus process further decisions.
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9.7 Add or Delete a Segment Decisions The decision question for adding or deleting a segment is:
Is the �irm more pro�itable with or without the segment?
Examples of this decision include:
Opening or closing a retail branch store Adding or eliminating a product or an entire product line Adding or eliminating a specialized service in a hospital Combining purchasing departments in two plants into one unit
In each of these examples, the answer depends on whether the �irm is better off with or without the particular segment and hinges on the direct or segment contribution margin, which excludes allocated common costs. The analysis must resist the temptation to focus on net income of the segment. Also, the decision must consider the strategic value of the segment to the �irm’s long-term success.
Key Decision Rules and Guidelines
The key decision rules are:
Add the segment if the �irm’s pro�its are higher after adding it. Drop the segment if the �irm’s pro�its are higher after eliminating it.
These rules assume that the following guidelines are in place:
Segment evaluations use direct contribution margin. Segment eliminations focus on lost revenue and avoidable costs. Segment additions focus on incremental revenues and costs.
Figure 9.4 shows two income statements for Hodes Clothiers and its three departments. One format shows operating income for each department, after allocating common indirect expenses equally to the three departments. The other shows direct contribution margin for the three departments. Amounts are in thousands.
Figure 9.4: Department performance for Hodes Clothiers—a merchandiser
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Department C appears to be losing $30,000 under the operating income format. Using this format, the �irm is attempting to evaluate its segment’s performance based on its operating income. But is Department C a loser? By reorganizing the data into a contribution margin format, Department C shows a $20,000 contribution to common expenses and pro�its. This difference results from the fact that no indirect costs are eliminated if Department C is deleted.
The operating income format often hides the expense behavior (variable and �ixed) and traceability (direct and indirect). The contribution margin format generally presents a clearer story.
Data Analysis Format and an Example
Hodes’ president sees the net loss for Department C and considers eliminating the department. Assume that deleting Department C has no impact on Departments A and B or on indirect expenses. An incremental analysis in thousands shows:
Department C revenue lost $(100)
Department C cost of sales avoided 60
Department C variable selling expenses avoided 10
Department C direct �ixed expenses avoided 10
Lost direct contribution margin from Department C $(20)
Hodes would lose $20,000 in pro�its if Department C is dropped. Department C should be kept unless a higher earning alternative exists.
Strategic and Qualitative Factors
This decision is tied to the scarce resource decision. To drop or add a segment is rarely an isolated decision. What will replace the dropped segment? What does the new segment replace? The opportunity
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cost is generally not zero. It must be quanti�ied and then compared to the incremental change in contribution margin. In the previous example, a Department D and its incremental revenues and expenses could replace Department C, or Departments A and B could expand.
While complementary and substitution effects have been presented already, the subtle impacts on other products and departments are often dif�icult to measure. While direct contribution margin is used, certain direct costs may be neither entirely avoidable nor controllable by the decision maker.
Many companies are “downsizing,” which includes a variety of strategies. Simple cost reduction should mean eliminating expenses that are contributing least to organizational goals. Seeking out waste and nonvalue-adding activities should be part of normal budgeting and cost control systems. Major organizational restructuring may include the elimination of product lines, entire factories, or a layer of management. Each of these is a version of the delete a segment decision. The same analytical process applies.
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9.8 Equipment Replacement Decisions The basic question for an equipment replacement decision asks:
Is greater bene�it received from acquiring new equipment or continuing to use the old equipment?
To answer this question, expenses incurred or revenues earned from using the old and the new equipment must be known. New equipment has two relevant measures: the incremental investment in new equipment and the increased contribution margin earned from the new equipment. Decision rules that include multiyear investment analyses are discussed in Chapter 10. For illustration purposes here, we assume new equipment is rented and not purchased.
For example, a printing department has reached an activity level that requires two Model 310 printers. These machines have a total annual rental cost of $500,000. Operating costs add another $100,000 per machine. A larger and faster Model 420 would have more capacity than two Model 310s. A Model 420 rents for $480,000 per year and has an operating cost of $150,000 per year. With this simpli�ied data, the analysis is:
Rent of two Model 310s avoided $500,000
Operating costs of two Model 310s avoided 200,000
Rent of Model 420 incurred −480,000
Operating costs of Model 420 incurred −150,000
Savings from renting Model 420 $ 70,000
The quantitative analysis says rent Model 420. We also get more capacity, which actually is another quanti�iable bene�it.
While renting or leasing equipment is a common �inancing alternative, purchasing is the basic method of acquiring new assets. An investment is made today, and bene�its are earned over the asset’s life. Evaluating all aspects of these decisions is a Chapter 10 task.
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9.9 Ethical Considerations The fundamental ethical issue in incremental decision making is validity of estimates of future revenues and costs. “Show me a proposal, and I can make it look good or bad” epitomizes the ethical problem facing many managerial accountants. However, the objective approach of “just give me the facts,” is often easier said than done. Facts are often estimates of the future. Biases, known or unrealized, can easily in�luence these estimates. What does the boss want the analysis to show? How can I make this project look good enough to get approved? These are pressures and in�luences that can destroy the basic “level playing �ield” decision-making process. Steps can be taken to reduce the likelihood that decision analyses are not subverted by biases, intentional or unintentional, and include:
In-depth management reviews of assumptions and supporting data before a decision is made to ensure management’s conspicuous attention to objectivity Development of managerial attitudes that support critical evaluations and avoid “kill the messenger bearing bad news” attitudes Creation of known criteria that emphasize the importance of validating relevant revenue and cost data estimates Post-decision audits to validate past estimates of future results
In many cases, managerial attitudes toward objective assessments begin at the top of the organization and “trickle down” to the lowest management levels.
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9.10 Costs and Pricing Decisions One of the most dif�icult and critical decisions facing a manager is pricing. A �irm’s pricing policy is a major part of its overall strategic positioning. A great pricing debate centers on whether prices are based on market conditions (supply and demand) or on production costs (recovery of costs). Certain environments tend to emphasize one or the other as shown in Figure 9.5.
Figure 9.5: Characteristics that encourage certain pricing behaviors
In spite of the characteristics shown in Figure 9.5, market prices are still strongly in�luenced by cost functions. For example, competitive copy center pricing near college campuses pushes the per-copy price close to actual cost, given volume and cost behavior. In addition, conditions do change. The natural gas industry has moved from a regulated industry to a highly price-competitive situation, while becoming even more capital intensive.
Global competitiveness has introduced market price as a starting point in product design and costing—a target market price minus a desired markup equals an allowable product cost.
In cost-based pricing, markup pricing methods are widely used. To arrive at the price, a cost is computed, and a markup, stated as a percentage of cost, is added. The purpose of the markup is to cover nonproduct costs and generate a pro�it. The term “cost” as used in this method is ambiguous until carefully de�ined.
Full Cost Pricing
The most widely used markup pricing approach is full cost. Full cost pricing is a price commonly based on total manufacturing costs, including �ixed and variable product costs. Proper treatment of �ixed cost presents a problem in full cost pricing. As volume increases, the �ixed cost and full cost per unit decrease. If price follows cost, price goes down, which further spurs demand. Unfortunately, volume decreases create serious distress. Per-unit full costs increase, forcing up prices. Demand falls more, costs go up again, and so on. Full cost pricing has the following potential problems:
A full cost per unit is accurate at only one level of volume. Seldom does a full cost re�lect incremental costs when volume changes. To calculate a full cost, often arbitrary cost allocations are made.
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Given a market framework in which price is set where incremental cost equals incremental revenue, full cost-based pricing almost guarantees a “wrong” price.
However, full costing does offer some countering bene�its:
Using full costs causes all products to bear a “fair share” of all common costs that must be covered. Full cost includes long-term cost patterns in pricing strategies. For certain ranges of activity (perhaps the relevant range), the per-unit full cost may change very little as volume increases or decreases. Being the long-term, low-cost provider is a very effective competitive strategy, particularly when cost includes both product and nonproduct costs.
Variable Cost Pricing
Another pricing approach uses variable cost as the cost base. One advantage is that dif�iculties with allocating indirect and �ixed costs are avoided. Also, if reasonably accurate estimates of demand given various prices exist, it may be possible to �ind a price that maximizes pro�its in a classic supply–demand economic sense.
If variable cost is used, any added markup must be large enough to cover all �ixed costs and to provide a pro�it. A danger always exists that variable cost may be thought of as full cost. Prices that cover only a portion of total costs will, in the long run, lead to serious �inancial problems.
Market-Based Pricing
If prices are market driven, the debate over full or variable costs does not disappear. Market price minus cost yields a pro�it measure: (1) using full cost, a gross margin, or a net pro�it and (2) using variable cost, a version of contribution margin. These margins can be linked to return on investment in evaluating the performance of existing investments (more in Chapter 11) and in making new investments (more in Chapter 10). Prices are nearly always part of return-on-investment analyses. Thus, even when prices are not cost based, costs in�luence how managers view product pro�itability, attack market segments, and decide whether to enter or exit markets.
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Summary & Resources
Chapter Summary Managers in any organization make decisions; some are short run, while others have long-run implications. This chapter creates a structured approach to make and implement decisions involving costs and revenues.
Differential analysis can be applied to a wide variety of decisions. The basic rule is to select the choice that gives the greatest incremental pro�it. Incremental pro�it is the difference between the relevant revenues and the relevant costs of each choice. Relevant revenues and costs are de�ined as the current and future values that differ among the choices considered.
The decision groups examined are make or buy, special sales pricing, scarce resources, sell or process further, and delete or add a segment. For each decision group, a key decision rule and guidelines are stated, and a format for analyzing relevant data is developed. While the basic decision assumes a short- term timeframe, the real-world applications often include long-term elements. Qualitative issues affect every decision, with strategic and policy concerns looming in the background.
Cost information is relevant to pricing analyses regardless of whether prices are market driven or cost based. Finally, full cost and variable cost pricing approaches give a different base for determining a markup for cost-based prices.
Key Terms
contribution margin per unit of scarce resource The contribution margin per unit of output divided by the quantity of scarce or limiting resource inputs used by a unit.
differential analysis The revenue and cost differences among alternatives.
full cost pricing The pricing method that adds a markup to the full cost of a product (generally the total manufactured cost).
incremental analysis approach An approach to decision making that uses only the changed revenues and costs and eliminates all irrelevant data from the analysis.
incremental pro�it The difference between the relevant revenues and the relevant costs of each choice.
in-house sourcing The decision to make a product or service instead of buying it from a vendor.
markup The amount or percentage of cost or sales price that is added to the cost to create a selling price.
markup pricing method
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A method of pricing that takes a percentage of cost or sales price and adds it to the cost to determine a sales price.
opportunity cost The sacri�iced returns or bene�its forgone because an alternative was rejected.
outsource The decision to purchase a product or service from a vendor instead of making or providing it in- house.
out-of-pocket costs Any cost that is incremental and that is to be paid in cash.
relevant buy costs An item’s purchase price plus any costs to get the purchased item delivered and into usable form.
relevant make costs The direct costs of producing an item plus any opportunity costs.
relevant revenues and costs The revenues and costs that differ among the choices considered.
sunk costs Costs that have already been incurred.
total analysis approach An analysis that shows the total pro�it associated with each alternative rather than just the change in pro�it.
Problem for Review Calderone Company, of Milano, Italy, sells a consumer electronics product called Teris at a price of €35 (euros) per unit. Teris costs per unit are:
Prime costs €15
Overhead 15 (60% of which is �ixed)
Total costs €30
A special order for 20,000 units was received from Chou Distributors, an import/export �irm in Beijing, China, a new market area for the company. Additional shipping costs on this sale are €4 per unit.
Questions:
1. If Calderone is operating at full capacity, what is the minimum price per unit that should be set for the Beijing order? Comment.
2. If Calderone has excess capacity, what is the minimum price? Comment.
Solution:
This is a special pricing problem. Calderone must determine whether:
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Excess capacity exists—”no” for Part 1 and “yes” for Part 2. The order will not interfere with regular business—probably will not since the order is from an importer in Beijing and the �irm has no other business in China. A positive contribution margin exists—will depend on the price selected.
For Part 1, Calderone must take sales from regular customers and, thus, must earn at least the same contribution margin from Beijing sales as from regular sales. Since the Beijing sale will cost €4 per unit more in shipping costs, the selling price should be at least €39 per unit (€35 + €4).
For Part 2, the price should cover only incremental costs of the additional units: €15 for prime costs (i.e., direct materials and direct labor costs), €6 for variable overhead (0.40 × €15), and €4 for shipping costs. The minimum price must, therefore, be greater than €25 to earn a positive contribution margin.
Questions for Review and Discussion 1. Why is identifying decision alternatives one of the most important steps in the decision-making
process? 2. Hedy Silber, owner of several small local businesses, said recently, “The general rule I follow in
making short-run decisions is that variable costs are almost always relevant and �ixed costs are almost always irrelevant.” Do you agree? Why, or why not?
3. Why is the timeframe—short-term or long-term—important in decision making? 4. The president of Lor Company said, “Accounting data are useful for predicting the results of
various choices, but, in my company, the �inal decision often depends on other factors.” Explain this statement.
5. Identify the guidelines that should be met for a special sales pricing decision. Explain why they are important. What happens when each is violated?
6. If capacity is scarce, how can opportunity costs be used to decide whether a product should be sold now (an intermediate product) or �inished and sold as a completed product?
7. Explain how a special sales decision in one �irm might be a make or buy decision in another �irm. 8. If a restaurant owner considers adding a new main course and deleting another for pro�itability
purposes, what decision rule should be applied? What type of decision is this? 9. Pat Brittain of Quick Supplies says she prefers the incremental analysis method because it
eliminates all unnecessary data. Candace Soler of Of�ice Managers, Inc. prefers the total analysis approach because she can see the “big picture.” Comment.
10. The marketing vice president of Hartman Fabrics says that product prices should always be set by supply and demand in the marketplace to ensure high sales levels. The controller says that product prices should always be based on cost to ensure pro�itability. Who’s right? Explain.
Exercises 9-1. Incremental Versus Total Analysis Approaches. Levetan Company currently handles 8,000 information requests per month. Financial data for last month are:
Sales $240,000
Variable costs 144,000
Fixed costs 60,000
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The company needs to expand its operations to serve 9,000 requests per month. Fixed costs would increase $15,000 because of the expansion.
Question:
Prepare both a total analysis approach and an incremental analysis approach to evaluate the decision. Compare the results.
9-2. Make or Buy Analysis. Miller Company needs 20,000 units of a certain part to use in its production cycle. If Miller buys the part from Thomas Company instead of making it, Miller could rent the released facilities as storage to another manufacturing �irm for $10,000. Sixty percent of the �ixed overhead applied will continue to be incurred regardless of what decision is made. The following information is available:
Cost to Miller to make the part:
Direct materials $ 4
Direct labor 16
Variable overhead 8
Fixed overhead applied 10
$38
Cost to buy the part from the Thomas Company: $36
Questions:
1. Which alternative is more desirable for Miller and by what amount? 2. What assumptions about cost behavior might be troublesome by either buying or making?
9-3. Sell or Process Further. Mr. Ed, Inc. produces three products (X, Y, and Z) in a single process that costs $30,000. They can each be sold as is or processed further into another product. Quantities, market values, and additional costs are:
Products Gallons Market Value Now Additional Costs Market Value After
X 10,000 $1.00 per gallon $10,000 $3.20 per gallon
Y 10,000 2.00 per gallon 20,000 3.75 per gallon
Z 10,000 3.00 per gallon 15,000 5.00 per gallon
Question:
What should the company do? Identify several assumptions you have made in order to decide.
9-4. Pricing for Special Sales. Wittenstein Company sells Product A for $30 per unit. The per-unit cost on the full capacity of 200,000 units is:
Direct materials $10
Direct labor 5
Overhead 12
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Manufacturing costs $27
The overhead is one-third variable and two-thirds �ixed.
A Japanese �irm has offered to buy 20,000 units. Additional shipping costs of this order would be $3 per unit. Wittenstein has suf�icient existing capacity to manufacture the additional units. Wittenstein’s sales manager wants to earn an incremental pro�it of $50,000 from this sale.
Question:
What is the minimum price per unit Wittenstein should charge?
9-5. Department Pro�its. Mandel Sales runs several small department stores. The Toledo store showed the following “poor” results in thousands:
Dept 1 Dept 2 Dept 3 Dept 4 Totals
Sales $700 $1,000 $800 $1,500 $4,000
Cost of goods sold (350) (500) (450) (800) (2,100)
Gross margin $350 $500 $350 $700 $1,900
Direct expenses (100) (400) (400) (300) (1,200)
Common expenses (100) (300) (100) (300) (800)
Net income $150 $(200) $(150) $100 $(100)
Question:
Comment on the impact of each of the following actions.
a. Delete Department 2. b. Delete Department 3. c. Delete Departments 2 and 3. d. Replace Departments 2 and 3 with a new Department 5 that would earn a positive direct
contribution margin of $25. e. Reallocate the common expenses.
9-6. Special Hat Sales. Rothouse Corp. can make 10,000 caps per year. Rothouse can sell 9,000 caps per year to NASCAR racing fans for $10 per hat. The cost per hat based on making 10,000 caps is:
Prime costs $5.00
Overhead costs 3.00 (Overhead is two-thirds �ixed at that volume.)
Paul Forman offers to buy 1,000 hats with special boxing insignias for $7 per hat. Attaching special insignias will cost Rothouse $200.
Question:
What should Rothouse do? Explain.
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9-7. Sales Priorities With Scarce Resources. The Chief Wahoo Cooperative employs highly skilled Native American artists to produce sand paintings for sale in craft stores. The artists make large, medium, and small paintings. The sales and production data are:
Large Medium Small
Sales price $80 $50 $25
Materials and artists’ time costs 38 25 16
Hours per piece 1 0.5 0.2
Question:
If artists’ time is scarce, what size priorities should be set by the cooperative?
9-8. Eliminating a Department. Mason Mill Department Store has �ive departments – A, B, C, D, and E. Department E’s future is being evaluated using the data below:
All Others Department E Total
Sales $ 4,500,000 $ 500,000 $5,000,000
Cost of sales 2,200,000 300,000 2,500,000
Gross margin $ 2,300,000 $ 200,000 $2,500,000
Rent and services $ 800,000 $ 200,000 $1,000,000
Direct salaries 450,000 50,000 500,000
Advertising expenses 450,000 50,000 500,000
Total expenses $1,700,000 $300,000 $2,000,000
Net pro�it (loss) $600,000 $(100,000) $500,000
Rent and services are corporate committed �ixed expenses and are allocated evenly to the �ive departments. Sixty percent of the advertising expenses varies with sales; the other 40% will not change regardless of the decision and is allocated using sales dollars.
Question:
Comment on the following statements:
a. Department E is earning $150,000 in variable contribution margin for ABCDE. b. Department E is earning $100,000 in direct contribution margin for ABCDE. c. The company’s overall pro�itability without Department E would be $600,000.
9-9. Sell at Split-Off Versus Process Further. Ri�ki Re�ining produces naphtha, kerosene, and other distillates from a joint process costing $120,000 for a certain volume of crude oil. From this process, 1,000 barrels of naphtha can be produced and are allocated $35,000 of joint costs. This can be sold at the split-off point for $60 per barrel or further processed into other products and sold for $85 per barrel. The processing cost for further re�ining 1,000 barrels of naphtha is $20,000.
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The other distillates can be sold now for $80,000 or processed further for $40,000 and sold for $110,000. Kerosene can be sold for $60,000 at the split-off point. Kerosene is also allocated $35,000 of the joint costs. Other distillates are allocated the remaining joint costs.
Questions:
1. Which products should be sold at the split-off point or processed further? 2. What is the most the company can pay for crude oil and not lose money on the re�ining process?
9-10. Make or Buy Indifference Point. Charlie Rodgers contacted a Malaysian manufacturer that will charge $40 per unit plus $200,000 for special equipment and dies for a lens assembly for an overhead projector. But he thinks he can make it himself for the following costs:
Prime costs $21
Other variable costs 3
Total variable costs $24
Charlie knows that incremental salaries, equipment rentals, and other �ixed costs to make the assembly will run $360,000 per year. Common costs of manufacturing are applied to products at 60% of prime costs. Charlie plans to sell these projectors for $150 per unit.
Question:
Find the sales volume in units where Rodgers will be indifferent between making the lens assembly or buying it.
9-11. Process or Sell Decision. Weinmann Meat Company produces a meat product that can be sold after the slaughtering process, or it can be smoked and then sold. For next month the company has scheduled production of 40,000 pounds which, if sold unsmoked, would bring a selling price of $2.30 per pound. Costs associated with producing the unsmoked product are $1.20 per pound plus �ixed facilities costs of $30,000 for the month. If 40,000 pounds are produced, the entire slaughtering capacity will be used.
If the 40,000 pounds are smoked, smoking capacity, which would otherwise be idle, will be used entirely also. The additional variable costs, mainly for heat and smoking ingredients, are estimated to be $0.40 per pound, and the selling price of the smoked product is $3.30 per pound. The monthly committed �ixed costs on the portion of the facility used for smoking the meat amount to $8,000, and avoidable �ixed costs are $5,000.
Question:
Prepare an analysis to help the manager decide whether the 40,000 pounds should be smoked or not be smoked.
9-12. Equipment Replacement. Last week Deutsch Enterprises purchased a new irrigation system called Spray costing $60,000. Its annual cash operating costs are estimated to be $35,000. It has a four- year useful life and no residual value. Today, a salesman has offered Deutsch a new system called Sprinkle that will cost $60,000 and will also have a four-year useful life with no residual value. The Spray equipment can be used as a trade-in for a $10,000 allowance. The annual cash operating costs of
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Sprinkle are estimated to be $20,000. Sales of $400,000 and other operating expenses of $180,000 per year will be the same under either alternative.
Question:
Ignoring the time value of money to be discussed in Chapter 10, should Deutsch purchase the Sprinkle system? Explain.
9-13. Managerial Accounting Decisions. In the following vignettes, make a recommendation to your boss—the person described in each situation. And, suggest any other issues your boss should consider beyond the data provided.
a. Cleaver Corp. incurs the following annual costs in making one part for its products: Total Costs for 20,000 Units
Prime costs $200,000
Variable factory overhead 200,000
Fixed factory overhead 300,000
Haskell Co. offers the same part for $25 per unit. If the parts are purchased from Haskell, plant space currently used by Cleaver for making the parts can be rented for $30,000 a year. Also, $100,000 of �ixed factory overhead could be avoided if the part is purchased.
Question:
Make or buy?
b. Barney Fyfe is thinking of making a key part for his main product. He forecasts 40,000 units as being required. His make costs are shown below. Mayberry Corp. offers to make this part for $5 per unit.
Question:
Make or buy?
Purchased materials costs $60,000
Variable labor and overhead 40,000
Common �ixed overhead 70,000
Avoidable direct �ixed overhead 50,000
Unavoidable direct �ixed overhead 30,000
c. Arthur Fonzarelli is considering an outside cleaning service for his of�ice building. He knows that Cunningham’s Maidens will clean for a contract price of $25 per hour with hours estimated to be 2,000 per year plus supplies of $5,000. Fonzarelli knows his current annual costs are $40,000 for a full-time cleaner, $12,000 for equipment rental and supplies used, and $10,000 for allocated corporate common expenses based on square feet used by the cleaning department.
Question:
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Make or buy?
9-14. Special Sales Pricing. Yuen Company, in Washington, D.C., is selling 80,000 pairs of jade earrings at $10 per pair. The variable cost is $6 per pair, and the annual �ixed cost is $120,000. A Virginia discount house has offered to buy 10,000 additional pairs of the product which would be slightly modi�ied for the Virginia market, but the modi�ications would not affect production costs. The discount house will pay $7 per pair.
Questions:
1. If the two markets can be distinguished, should the order be accepted (assuming capacity exists and has no other use)? Explain.
2. The manager feels that the two markets might not be distinguished and that the lower price would cause regular sales to fall by 5,000 pairs. Should Yuen accept the discount house offer? Explain.
3. If the discount house offer is raised to $9 per pair and competition resulting from the special sale causes the regular price to drop to $9.50 to maintain the same regular sales volume, should Yuen accept the discount house offer? Explain.
9-15. Ethics of Product Pricing. Pepper Pike Resources (PPR) provides of�ice equipment systems development and maintenance services. Its customers are a wide array of businesses. Maintenance services are provided through an annual contract with a �ixed annual fee plus additional charges for “emergency calls” on an as-needed basis. PPR won a competitive bid with the City of Beachwood to maintain a large number of of�ice workstations. The contract is for three years and calls for routine maintenance checks to be done quarterly as part of the annual fee, emergency calls billed at the “full” cost per hour of service representatives, and parts replaced for free except for major hardware components. The per-hour rate will be updated annually.
It is now a year and a half into the contract. The city controller is concerned with the growing cost of machine maintenance. After examining the situation, the controller has found:
1. Emergency calls have doubled in the past six months and are growing. 2. The “full” cost service rate has gone from $25 per hour last year to $32 per hour this year. 3. Of�ice workers are complaining about too much downtime.
A meeting with the PPR representative found that all routine maintenance has been performed on schedule. Also, while some personnel costs have increased, the main reason for the jump in service rate was a change made in how certain fringe bene�it costs were assigned to service personnel. The PPR rep also mentioned the aging nature of the equipment and the need to upgrade the entire system.
Question:
Comment on possible implications of each of the controller’s �indings.
9-16. Product Combination Decision. Data concerning the four product lines of Tritt Corporation are as follows:
Product Line
A B C D
Selling price per unit $300 $250 $130 $70
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Product Line
A B C D
Variable cost per unit 250 80 50 40
Hours required for each unit 5 10 4 2
Maximum market potential (units) No limit 6,000 8,000 4,000
Total �ixed costs $100,000
Total hours available 96,000 hours
Questions:
1. Based on this data, choose the best product combination. 2. How would the answer change if the company were required to deliver 2,000 units of each
product line to a major distributor? The maximum market potential includes the distributor’s units.
9-17. Markup Pricing. Assume that the following cost analysis has been performed for a speci�ic customer order for Sandy Springs Products, Inc. The president, Phil Cuba, is experimenting with different pricing strategies. He thinks 100,000 units can be sold. Fixed costs have been allocated using various activity bases.
Per Unit Total
Variable manufacturing costs $4.25 $425,000
Direct �ixed manufacturing costs 1.50 150,000
Indirect �ixed manufacturing costs 3.75 375,000
Total manufacturing costs $9.50 $950,000
Variable selling expenses $1.80 $180,000
Indirect �ixed selling expenses 1.45 145,000
Total selling expenses $3.25 $325,000
Questions:
What markup percentage is required to earn $120,000 if the price is set:
1. Assuming that the order is a one-time sale? 2. Assuming that the order will become part of the regular product line?
Problems 9-18. Changing Product Lines. Shelley Greenberg, president of Buckeye Department Store, thinks that the Paint Department should be dropped. She wants to add a Peanut Butter Boutique in the same space. Data for next year in thousands are:
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Paint All Other Departments Proposed Peanut Butter Boutique
Sales $10,000 $90,000 $20,000
Cost of sales –(6,000) (54,000) (15,000)
Gross margin $4,000 $36,000 $5,000
Direct expenses (1,000) (14,000) (3,000)
Allocated expenses (4,000) (16,000) (1,000)
Operating income ($1,000) $ 6,000 $1,000
Allocated expenses are common costs and are assigned by a mathematical formula.
Question:
Ignoring your attitude toward peanut butter, what should Greenberg do to maximize pro�its? Explain.
9-19. Sell or Process Further. Comet Company produces Green Awfully Sticky Stuff (GASS) at a cost of $30,000 per batch. A batch of GASS can be sold as is for $50,000 or processed through Department A where Products A and AA are made. Or the GASS batch can be processed through Department B where Products B and BB are made. Costs and revenues of processing further in Departments A and B are:
Incremental Costs Products Market Value
Department A $20,000 A $13,000
Department B $150,000 B $100,000
BB $95,000
Questions:
1. What should be done with a batch of GASS that Comet has on hand? Show calculations to support your decision.
2. If the cost to produce a batch of GASS increased to $60,000, would you decide to continue to produce GASS?
9-20. Dropping a Product. Dick Price, an old prospector, runs a side business. He buys rattlesnakes from “snake hunters” in west Texas, paying an average of $10 per snake. Each snake comes complete. He produces canned snake meat, cures hides, and makes souvenir rattles. At the end of a recent season, Dick is evaluating his �inancial results:
Meat Hides Rattles Total
Sales $30,000 $8,000 $2,000 $40,000
Cost of snakes 18,000 4,800 1,200 24,000
Gross pro�it $12,000 $3,200 $800 $16,000
Processing expenses $6,000 $900 $600 $7,500
Common expenses 4,000 600 400 5,000
Operating expenses $10,000 $1,500 $1,000 $12,500
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Meat Hides Rattles Total
Operating income (loss) $2,000 $1,700 $ (200) $3,500
Cost of snakes assigned to each product is based on a ratio of cost to revenue. Processing expenses are direct costs and avoidable. Common expenses are allocated on the basis of direct processing expenses and are Dick’s basic living expenses. Dick has a philosophy of “every tub on its own bottom” and is determined to cut his losses on rattles.
Questions:
1. Is he really “losing” money on rattles? Explain. 2. An old miner has offered to buy every rattle “as is,” without processing, for $0.50 per rattle. Will
this eliminate the “loss” problem and improve Dick’s pro�itability?
9-21. Make or Buy Decision. Neiditch Automotive Systems developed a new windshield cleaning system for the original-equipment auto market. The system requires an electronic motor that the �irm does not currently produce but is available from suppliers. The best bid is from CGY Electronics at $23 per unit for any volume within the �irm’s relevant range.
Neiditch’s production manager believes that the motor can be made in-house, although additional space and machinery would be required. The �irm now leases, for $80,000 per year, space that could be used to make the new motors. However, another subsystem is now assembled in this space. Neiditch would have to lease additional space ,which rents for $175,000 per year in an adjacent building, for the assembly process. It is suitable for assembly work but not for motor production. Additional equipment needed would rent for $200,000 per year.
The controller has developed the following unit costs based on the expected demand of 100,000 units per year:
Prime costs $14.00
Rent for space .80
Machinery rental 2.00
Variable overhead 4.00
Allocated �ixed overhead 6.00
Total costs $26.80
Question:
Should Neiditch make or buy the motors?
9-22. Process Further Situations. Read the following cases.
Situation # 1: Ruth Baker purchased the champion cow at the county 4-H fair. The city government has demanded that she get rid of it and stop violating the city’s noise and odor ordinance because of the mooing. It cost $2,000 and weighed a ton! Her best options are shown below. What is her best alternative use for the cow? (Ignore vegetarian preferences!)
Option A: Sell the whole cow to the Jordan’s Meat Market for $2,500.
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Option B: Make hamburger. Processing costs of $200, revenue of $2,600.
Option C: Fatten cow, make Kobe beef (a Japanese delicacy). Processing costs of $3,900, revenue of $5,800.
Option D: Feed cow (cost $1,000, including �ines), take cow to football games—no revenue, but a lot of fun.
Situation # 2: Tinman Juice Company presses Michigan cherries, producing raw cherry juice. The cost of producing a “batch” of cherry juice is $10,000, including the cost of the cherries. From one batch comes 10,000 gallons of juice. This can be sold on the cherry juice market for $15,000. The owner is considering various “all natural” products that would give alternative uses for the juice. Estimated revenues, costs, and volumes for each option are:
Option Additional Costs Product Outputs Quantities Market Value
A $4,000 Cough medicine 2,000 gallons $6 per gallon
Coffee substitute 1,000 gallons $4 per gallon
Cherry drink power 500 pounds $10 per round
B $15,000 Frozen concentrate 14,000 cans $2 per can
C $20,000 Muscle ointment 2,000 cases $15 per case
Hair growth grease 1 pound $500 per ounce
Questions:
1. What decisions would maximize pro�its for each �irm? 2. As the �inancial advisor, how would you rank the four alternatives (juice only, option A, option B,
and option C)? Show your computations.
9-23. Special Sales Pricing. Koizumi Company manufactures study lamps in Osaka, Japan. Next year’s budget estimates sales to be 500,000 lamps at ¥1,700 each. Variable costs are ¥900 per lamp, and �ixed costs are budgeted at ¥300 million or ¥600 per lamp. Recently, a purchasing agent from Decatur Superstores in the U.S.A. offered to buy 100,000 lamps at a price of ¥1,350 each. By working overtime and adding extra shifts, Koizumi would have suf�icient capacity. Additional overtime premiums would be ¥7.5 million. Additional supervision costs are ¥2 million. Total selling and administrative expenses will not change if the order is accepted.
Koizumi’s �inance manager argues, “With the extra volume, the full cost of regular sales would be reduced from ¥1,500 per unit to ¥1,400. At this level Koizumi would make an extra ¥100 per unit on all regular sales but still lose money on the special sales because of overtime costs and the lower price.” He thinks that the “economics of the deal” are too risky and that it violates the �irm’s strategic pricing policies that have helped Koizumi create a reputation for quality.
Questions:
1. Is the �inance manager’s quantitative analysis sound? Explain your decision. 2. What does the �inance manager mean by “too risky?” 3. Why might this be a violation of the �irm’s pricing policies?
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9-24. Evaluating a Segment. The Klein family has developed an extensive bakery business in Atlanta and now has 90 shops. Annually, several new outlets are opened, and old ones are closed. Nathaniel, the controller, reviews the performance of each location and of all store managers. He is currently evaluating Store 54, operated by a relatively experienced manager. Business statistics for the company and Store 54 data are:
Average Store
Percentages Store 54
Sales 100% $400,000
Expenses:
Cost of baked goodies 35% $150,000
Store salaries and wages 20 110,000
Store occupancy costs 30 120,000
Home of�ice expenses 10 50,000
Total expenses 95% $430,000
Net income 5% $(30,000)
The store’s lease is a three-year commitment for $30,000 per year. If Store 54 is closed, a nearby Klein store would attract $50,000 of Store 54’s lost gross margin. Store 54’s manager has a �ive-year personal services contract for $30,000 per year and could be transferred to a new store. All other salaries and occupancy costs can be eliminated. Home of�ice expenses are allocated evenly among the 90 stores.
Questions:
1. Should Store 54 be closed now? Why, or why not? 2. If Store 54 gets a 6-month reprieve, in which areas should the manager attempt to improve?
9-25. Evaluating a Special Order. Huang Automotive in Taiwan is presently operating at 75% of practical capacity and producing annually about 200,000 units of a power steering system component. Huang recently received an offer from a Korean truck manufacturer to purchase 40,000 components at NT$225 (new Taiwanese dollars) per unit. Flexible budgets for production of 200,000 and 250,0000 units are:
200,000 Units 250,000 Units
Direct materials NT $18,000,000 NT $22,500,000
Direct labor 6,000,000 7,500,000
Factory overhead 24,000,000 27,000,000
Total costs NT $48,000,000 NT $ 57,000,000
Cost per unit NT $240 NT $228
Peter Wu, vice president of sales, thinks accepting the order will get the company’s “foot in the door” of an expanding international market, even if the company loses a little on this order.
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T. J. Chan, Vice President of Engineering, feels that any new market should �irst show its pro�itability and that this offer is below last year’s cost per unit of NT$240. “This guarantees a loss on the order,” he says.
Lili Zhang, treasurer, has made a quick computation which indicates that accepting the order will actually increase dollars of gross margin.
Questions:
1. Estimate Huang’s variable cost per unit. 2. Show how Mr. Chan and Ms. Zhang are analyzing the situation. Using the given facts, what does
the incremental analysis of the Korean sale show? 3. What major nonquantitative factors might affect the decision to accept or reject the special
order?
9-26. Scarce Resources and Minimum Requirements. Data for four products produced by Eden Enterprises are given below:
Product A Product B Product C Product D
Selling price per unit $13 $20 $5 $25
Variable cost per unit 6 5 2 16
Allocated costs per unit 4 8 1 3
Units produced per hour 4 units 2 units 8 units 3 units
Maximum sales limit 5,000 units 5,000 units 10,000 units No limit
Minimum requirements 1,000 units None 2,000 units 1,200 units
Total capacity is 6,000 hours. Minimum requirements meet existing sales commitments. Marketing has provided a “best estimate” of maximum sales expected for each product.
Question:
Based on the above data, choose the best product combination.
9-27. Alternative Uses of Capacity. Rhoton Equipment built a new facility �ive years ago but is using only 60% of its capacity to produce several machining equipment product lines. Management would like to use the excess capacity and has three possibilities. Only one of the three can be selected.
a. Rhoton could produce an additional 600 units per year of its most popular machine and focus marketing efforts on European metal parts producers. Management estimates that additional freight costs would amount to $550 per machine and �ixed factory overhead would increase by $150,000. To cover the additional cost, the selling price per machine on European sales would be increased by $800 per machine. Incremental international selling costs would be about $200,000 per year. Rhoton has earned a contribution margin of $1,800 on each unit in the past.
b. Rhoton could produce and market a smaller model of an existing laser lathe. The capacity could be used to produce 200 units per year that would sell for $15,500 each. Management has estimated the following unit variable costs.
Prime costs $4,500
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Variable overhead 2,000
Variable selling 500
Total costs $7,000
The new lathe would add �ixed costs of $700,000 to �ixed overhead expenses and $250,000 to �ixed selling expenses.
c. Benedek Testing Company has offered to lease the facilities at $30,000 per month plus 2% of the net revenues generated from the facilities by Benedek. Net revenues are estimated at $15,000,000 per year.
Questions:
1. Which of the three alternatives should management select? Show calculations to substantiate your decision. Comment on the relative riskiness.
2. What is the opportunity cost of this decision?
9-28. Contribution Margins. Zehnder Company, a Swiss �irm, sells three products. Financial data for a typical month are (in thousands of Swiss francs):
Products
J K L Total
Sales SFr 300 SFr 500 SFr 800 SFr 1,600
Variable costs 90 200 400 690
Contribution margin SFr 210 SFr 300 SFr 400 SFr 910
Fixed costs:
Separable and avoidable SFr 90 SFr 100 SFr 120 SFr 310
Joint, allocated on sales dollar basis 60 100 160 320
Total �ixed costs SFr 150 SFr 200 SFr 280 SFr 630
Pro�it SFr 60 SFr 100 SFr 120 SFr 280
Questions:
1. The �irm is considering the introduction of a new Product M to replace Product J. Product M sells for SFr12 per unit, has variable costs of SFr5 per unit, and has separable �ixed costs of SFr104,000. How many units of Product M must be sold to maintain the existing income of SFr280,000?
2. Revenues of Product K could increase by 20% by reducing variable contribution margin to 45% and increasing separable and avoidable �ixed costs by SFr40,000. Should Zehnder do this? Show your logic.
3. Rank each product by total sales, variable contribution margin percentage, direct contribution margin percentage, and net pro�it percentage. Comment on how Zehnder might use each ranking.
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9-29. Adding a Department. Mayer’s Grocery Store is a small-town operation being threatened by a national discount store outlet being built nearby. Mayer Shamis, the owner, is studying the addition of a department to sell either garden supplies or beer and wine. He has talked to several other owners of similar stores and has reached the following conclusions:
1. A garden supplies department would generate sales of $40,000 per year with a gross pro�it of 60%. No other variable costs would be added. Additional �ixed costs would be $12,000. Grocery sales would increase by 5% because of increased traf�ic through the store.
2. A beer and wine department would generate sales of $60,000 per year with a gross pro�it of 40%. No other variable costs would be added, but �ixed costs would increase by $18,000. Grocery sales would increase by 8%.
The income statement for a typical year for grocery sales alone is as follows:
Sales $600,000
Cost of goods sold (variable) 240,000
Gross pro�it $360,000
Other variable costs 110,000
Contribution margin $250,000
Fixed costs 170,000
Operating income $80,000
Questions:
1. Re-compute the effects on income of adding each department. 2. Which department should be added? What qualitative issues appear important?
9-30. Outsourcing Decision. Gomer Corporation operates its own cafeteria for employees. The cafeteria prices are only 75% of the full costs of preparation. Management feels this is an important employee bene�it. Pyle, Inc. is offering to operate the cafeteria and promising to increase the quality of menu items, reduce prices, and reduce the needed subsidy. Pyle would use Gomer’s existing facilities and even transfer some of the current cafeteria employees to its staff. Pyle submitted a formal bid based on comparable services. As Gomer’s controller, you have summarized the next year’s budget for cafeteria operations and Pyle’s numbers from its proposal as follows:
Internally Managed Pyle, Inc. Managed
Food costs $ 500,000 $450,000
Preparation costs 200,000 180,000
Administrative overhead 300,000
Management fee _______ 200,000
Total cafeteria costs $1,000,000 $830,000
Cafeteria revenue 800,000 750,000
Operating subsidy $ 200,000 $ 80,000
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Question:
Comment on the numbers. Outline key issues that are of concern to you. What data will you need to collect and analyze to resolve the issues?
9-31. Elimination of a Department. The Breezy General Store is currently divided into three departments. Over the past several months, sales and pro�it have declined, although the situation is now considered stable. Department 2 has begun to show a loss, and the owner, Janie Feldman, is thinking of discontinuing it. The space could be rented to a chain shoe store, which would pay a �lat fee of $12,000 a month.
Below is last month’s income statement, considered to be typical. Sales salaries are �ixed but traceable to each department and could be avoided if the department were eliminated. Total �ixed administrative costs (allocated equally to all departments) are common costs.
Department 1 Department 2 Department 3 Total
Sales $185,000 $80,000 $135,000 $400,000
Costs:
Cost of goods sold $96,000 $44,000 $70,000 $210,000
Sales salaries 28,000 8,000 24,000 60,000
Administrative expenses 30,000 30,000 30,000 90,000
Total costs $154,000 $82,000 $124,000 $360,000
Operating income $31,000 $(2,000) $11,000 $40,000
Question:
Prepare an analysis to show Janie whether Department 2 should be discontinued and the space rented.
Case: Middlehurst House
Middlehurst House is a daycare center/preschool that operates as a partnership of George Friedman and Bill Compton. The center is in a city that has a large base of two-income families who have a need for quality day care. The two men started the center this year. Compton contributed $40,000 to get the business started—to purchase equipment and to operate through the early months. Friedman, who previously managed another center, is the director of the center and draws $2,000 per month for his services. Partnership pro�its and losses, after Friedman’s salary, are split 75% for Compton and 25% for Friedman.
Middlehurst House operates from 6 a.m. to 6 p.m., Monday through Friday. It is in a single building that has a capacity limit of 120 children and meets city and state regulations. At present, the center has six classes, all at maximum sizes, structured as follows:
Age Group
Number of Classes
Children per Class
Total Children
Monthly Tuition per Child
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Age Group
Number of Classes
Children per Class
Total Children
Monthly Tuition per Child
2 to 3 2 10 20 $320
3 to 4 1 15 15 280
4 to 5 1 15 15 280
5 to 6 2 15 30 260
Class sizes are determined by state law, which sets a limit on the number of children per instructor. The center uses one instructor per classroom.
Tuition is charged monthly. Minor adjustments are made on an individual basis. In October, the most recent month with data available, revenues were $21,500 ($22,600 less $1,100 adjustments). Monthly revenues should be rather stable since classes are full most of the time. Expenses for October were:
Salaries for instructors $ 9,600
Salary of director 2,000
Salary of part-time cook 900
Food expenses 2,200
Staff bene�its expenses 2,450
Supplies expenses 600
Occupancy and other administrative expenses 3,250
Total expenses $21,000
Fixed expenses are the salary of the part-time cook and occupancy and other administrative expenses. The salary of the director is �ixed—as a partnership, this is in reality a distribution of pro�its, but it is included in expenses for comparative purposes.
Food is $1.25 per student per day. Staff bene�its are 10% of salaries plus $200 per person for bene�it programs for instructors and the part-time cook. Variable supplies are $1 per student per month. Salaries for instructors average $1,600 per instructor per class.
Friedman wants to increase the quality of service by decreasing class sizes and also by expanding student enrollments. These alternatives are interrelated. Friedman thinks that class sizes are too large and that children are not getting the individual attention they require. Friedman surveyed parents of all 80 students to measure their support for a tuition increase tied to a reduction in class size. For children ages 2 to 5, most parents would support a 25% tuition increase, and nearly 50% would support a 50% increase. Of the 5-to-6 age group parents, nearly three fourths did not want any increase. The remainder said they would support a 25% increase but no more.
Proper class size is very subjective. However, Friedman feels that he could achieve a child/instructor ratio of 6 to 1 for the 2-to-3 age group, an 8 to 1 ratio for the 3-to-4 and 4-to-5 age groups, and a 10 to 1 ratio for the 5-to-6 age group.
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The center has easily maintained the 80-student level, with each class full. Friedman keeps in touch with waiting-list parents to make certain each is still interested. This list provides children when someone leaves the center. The current waiting list is as follows:
Age Group Number of Children Age Group Number of Children
2 to 3 5 4 to 5 4
3 to 4 7 5 to 6 11
Friedman does not start a new class unless more students are on the waiting list than are required per class. Obviously, enough students are on the 5-to-6 age group waiting list to start a new class. Lately, however, he has wondered if the center could make a pro�it by starting classes with fewer than the requisite number, taking the chance that new students would appear and could be added immediately.
Information from his various inquiries implies that a potential market for quality infant care (0 to 24 months) exists. Friedman doesn’t think this expansion would be pro�itable. However, he has never done an analysis of the situation and has not thought about an appropriate tuition. He believes that the infant/instructor ratio in his center should be no higher than 5 infants to one instructor. The center would have no food costs for the infants.
Compton will only agree to Friedman’s suggested changes if the center will continue to operate at or above the current pro�it level.
Questions:
1. Look at each decision separately, as incremental to the current situation, and evaluate the marginal pro�it:
a. If class size is decreased (keeping the same 80 students), what increase in tuition is necessary to keep the current monthly pro�it level?
b. Without regard to (a), is it pro�itable to create the new class from the waiting list? Explain.
c. Use the new fee structure as found in (a). Is it pro�itable to move to smaller class sizes, if new full classes are created and �illed to their new maximums using the waiting list? Show calculations.
d. Is a class for infant care pro�itable if tuition is the same as the proposed class tuition for the 2-to-3 age group?
2. Write a brief memo to Friedman and Compton highlighting any concerns that underlie the analyses you have performed in Part 1.
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Practice Problems in Action
Watch the video below for a step-by-step tutorial on how to solve the following problem using Excel. The video is best viewed in full-screen mode. For a transcript of the directions included in this tutorial video click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/BUS630_2e/Chapter-9_Tutorial- Transcript_FINAL.pdf) .
Problem This example uses a regional preschool. The owners are asking you to complete an incremental analysis with certain scenarios. Classes are grouped by age with one instructor per class.
The following costs were provided to you by the �inance department:
Instructor salaries/class $ 1,450
Staff bene�its % of salary 15%
Bene�its program per instructor $ 150
Current enrollment and age groups were provided by administration:
Age Group Current # of Classes Children per Class
2 to 3 2 10
3 to 4 1 14
4 to 5 1 14
5 to 6 2 20
The monthly tuition per child by age group was provided by the billing department:
Age Group Monthly Tuition per Child
2 to 3 $ 340
3 to 4 $ 300
4 to 5 $ 300
5 to 6 $ 295
The preschool would like to create a new student-to-instructor ratio as follows:
Age Group New Instructor Ratio (Students per 1 Instructor)
2 to 3 5
3 to 4 7
4 to 5 7
5 to 6 10
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So, for the age group 2 to 3, there would be 5 students for every 1 instructor, versus 10 per 1 instructor in the current class structure for 2- to 3-year-olds.
Question Look at each decision separately, as incremental to the current situation, and evaluate the scenario presented:
If class size is decreased to the new student-to-instructor ratio (keeping the same 88 students), what increase in tuition is necessary to keep the current monthly pro�it level?
Tutorial Video: Creating an incremental analysis
0:00 / 7:17
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Learning Objectives
After studying Chapter 10, you will be able to:
Explain the nature and importance of capital investment decisions.
Identify the relevant cash in�lows and out�lows in an investment proposal.
Use four different evaluation methods to evaluate investments.
Appreciate ethical issues relating to capital investment decisions.
Comprehend how income taxes and depreciation impact the cash �lows of capital investments.
Understand how the cost of capital is determined.
10 Capital Investment Decisions
VladTeodor/iStock/Thinkstock
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Evaluate investment decisions that include in�lation, working capital, uneven project lives, differing initial investments, and asset disposal gains and losses.
Understand the basic principles of time value of money.
Capital Investment Alternatives
Rose Stanley, President of Eddington Instruments, grabs her briefcase and heads for the airport. After clearing security, running to her gate, and just making her �light, Rose settles into her coach seat, in front of two screaming kids and behind two salespeople who apparently have just made the deal of the century. She opens her briefcase and �inds the Capital Spending Proposals �ile. The deadline for submitting proposals to her was yesterday. She plans to review these on her cross- country �light. The variety surprises her.
Engineering is pushing to integrate a newly announced semiconductor into an aging product. The new technology will push Eddington into new markets with great sales potential but against stiff competition. Adding space to the corporate headquarters will bring three administrative departments together, increase ef�iciency, and reduce operating expenses. Her Production Planning Manager proposes rearranging several work centers to improve production ef�iciency for a family of current products. Another project adds capacity to a specialized assembly operation. The Plant Manager requests funding for an air puri�ication system, which must be installed by year-end to meet new state air quality requirements. An information systems proposal would automate several manual operations, save personnel, and reduce inventory by an estimated 10%. Her Finance Manager is negotiating for controlling interest in a �irm with technical expertise that Eddington needs for new product development. Marketing has proposed a major jump in advertising spending for a product line that has not been meeting sales targets.
Rose clearly wants to get the “biggest bang for the bucks” from Eddington’s limited capital investment budget. A quick calculation shows her that this year’s investment dollars will fund about half of these proposals. Some proposals are risky, while others have predictable outcomes. Some are straightforward, but many include a host of extraneous issues. Also, �inancial data are overstated for some proposals and understated for others. Some generate immediate returns; others promise big cash �lows years from now.
This chapter extends the study of incremental analysis begun in Chapter 9 into multiperiod decisions, which are called capital investment decisions. This chapter discusses:
1. Identi�ication of relevant cash �lows in capital investments
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2. Techniques and methods for analyzing project data
Capital investment analysis is a planning task and is directly linked to budgeting, as discussed in Chapter 7. Capital budgeting is the process of evaluating speci�ic projects, estimating bene�its and costs of the projects, and selecting which projects to fund.
Capital budgeting depends on an understanding of the time value of money. For those who are unfamiliar with the time value of money or have not applied present values in �inancial accounting or other courses, section 10.8 explains the concept. Present value tables necessary for discounting future cash �lows are located in section 10.8.
Relevant revenues and operating costs for multiperiod decisions are assumed to be cash in�lows and cash out�lows, respectively. Since these decisions extend over a period of years, timing of these cash �lows is a major factor.
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10.1 The Importance of Capital Investment Decisions Capital investment is the acquisition of assets with an expected life greater than a year. These decisions attract managers’ interest for good reasons:
1. Long-term commitments. Capital decisions often lock the �irm into assets for many years. 2. Large amounts of dollars. Capital projects often involve large dollar amounts. From Ford Motor
Company with an annual investment budget of $7 billion to a small �irm buying a $50,000 truck, large relative dollar amounts get attention.
3. Key areas of the �irm. New products, new production technology, and research efforts are crucial to a �irm’s ongoing competitiveness.
4. Source of future earnings. Investing with foresight is the key to the �irm’s future pro�its and �inancial performance.
5. Scarce capital dollars. In most �irms, more demands exist for capital funds than the �irm can meet. Only the best opportunities should be funded.
Excellent analyses and decisions increase the �irm’s capacity, technology, ef�iciency, and cash generating power. Poor decisions waste resources, lose opportunities, and impact pro�its for many years.
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10.2 The Capital Investment Decision A capital investment generally includes a cash out�low, which is the investment, and cash in�lows, which are the returns on the investment. The decision maker expects cash in�lows to exceed cash out�lows. The typical investment project has cash out�lows at the beginning and cash in�lows over the life of the project.
Cash Flows
Cash �lows are the key data inputs in capital investment analyses. Cash has an opportunity cost, since it could be used to buy a productive or �inancial asset with earning power. Cash is a basic asset. Prices, costs, and values can all be expressed in cash amounts. If the decision impacts several time periods, cash- �low timing becomes a relevant factor.
Cash out�lows commonly include:
1. The cash cost of the initial investment plus any startup costs 2. Incremental cash operating costs incurred over the project’s life 3. Incremental working capital such as inventories and accounts receivable 4. Additional outlays needed to overhaul, expand, or update the asset during the project’s life 5. Additional taxes owed on incremental taxable income
Cash in�lows include:
1. Incremental cash revenues received over the project’s life 2. Reduced operating expenses received over the project’s life (A reduction of a cash out�low is
treated as a cash in�low.) 3. Cash received from selling old assets being replaced in the new project, net of any tax impacts 4. Released working capital, perhaps at the project’s end 5. Salvage value (net of taxes) realized from asset disposition at the project’s end
These relevant cash �lows occur after the “go” decision is made to proceed with the project. Therefore, we are estimating future cash �lows. Certain cash �lows are estimated based on current prices and known technology, whereas others are estimates based on vague facts and unproven methods. Often, cost savings and project bene�its are not easily quanti�ied. Much time and expense are spent to develop supporting forecast data. It is important to understand that the same cash-�low estimates are used regardless of the project evaluation method used.
Decision Criteria
Capital investment decisions are either:
Accept or reject or Select A or B or C, etc. (or some combination of these)
In the �irst type, we decide whether the return is acceptable or unacceptable. This is a screening decision. Is the return “good enough?” The second type is a preference or ranking decision—select the best choice from a set of mutually exclusive projects. By picking A, we reject B, C, and any other choices. One possible choice is to do nothing—the status quo.
Generally, projects are ranked on a scale of high to low returns. The highest-ranking projects are selected, until the capital investment budget is spent. Often, funds are limited; many acceptable projects
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will go unfunded. The �irm’s goal is to select projects with the highest returns. As in Chapter 9, pertinent nonquantitative factors may sway a decision and cause lower-ranked projects to be selected.
Time Perspectives
In the real world, every conceivable combination of cash-�low timing can exist. However, we assume a simpli�ied timeline. The present point in time is today, Year 0. This is when we assume investments are made—new assets acquired, old assets sold, and any tax consequences of these changes assessed. In real life, several years of cash out�lows may precede the start of a project’s operation.
Generally, annual time periods are used. Using shorter time periods is possible, such as one-month periods for monthly lease payments. Annual �lows of cash are assumed to occur at year-end due to the mathematics underlying the construction of the present value tables.
An Example—Equipment Replacement and Capacity Expansion
As an illustration, Clairmont Timepieces is considering a device costing $100,000 to replace an obsolete production device:
1. The new device’s expected life is �ive years and can probably be sold at the end of Year 5 for $10,000.
2. The vendor recommends an overhaul in Year 3 at a cost of $20,000. 3. Capacity will immediately increase by 1,000 units per year. Each unit sells for $55 and has $30 of
variable costs. 4. Additional inventory of $3,000 is needed and will be released at the project’s end (i.e., inventory
will be returned to the level it was at immediately prior to the purchase of the new production device).
5. Operating costs will be reduced by $15,000 per year. 6. The old device can be sold for $8,000 now, which is its book value. Alternatively, as another
option, it could be used for �ive more years with no salvage or book value at that time.
Remember that any cash revenue or cost that does not change is irrelevant and can be ignored. Any cash �low that differs among decision choices is relevant. Additional taxes or tax savings on incremental income or expenses are also relevant cash �lows. But, until income tax issues are discussed, taxation implications are ignored.
Formatting the Relevant Data
As in Chapter 9, adopting a uniform format for analysis of capital investments helps to organize data and to present it in a logical pattern. Using data from the previous example, the timeframe format shown in Figure 10.1 is used throughout our capital investment discussions.
Figure 10.1: Format for relevant capital investment data— Clairmont Timepieces
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Cash out�lows are displayed as negative amounts, and in�lows are displayed as positive amounts. Project years begin now (Year 0 or today), and are shown as columns. Speci�ic cash-�low items are shown as rows. The investments of $100,000 in equipment and $3,000 in inventory costs are reduced by the sale of old equipment for $8,000. The net initial investment is $95,000 and appears as a negative amount as it is a cash out�low. The additional 1,000 units of sales generate incremental contribution margin of $25,000, using a $55 sales price less a $30 variable cost per unit.
Remember that volumes of analytical support may be developed to back up each number in Figure 10.1. The $100,000 device cost would result from evaluations of many devices and negotiations with vendors. Estimates of additional revenues and variable costs come from marketing studies and capacity use. Estimates of cost savings come from production, industrial engineering, and cost accounting analyses.
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10.3 The Evaluation Methods The evaluation methods discussed here are:
1. Present value methods (also called discounted cash-�low methods) a. Net present value method (NPV) b. Internal rate of return method (IRR)
2. Payback period method 3. Accounting rate of return method
Nearly all managerial accountants agree that methods using present value (Methods 1a and 1b) give the best assessment of long-term investments. Methods that do not involve the time value of money (Methods 2 and 3) have serious �laws; however, since they are commonly used for investment evaluation, their strengths and weaknesses are discussed.
Net Present Value Method
The net present value (NPV) method includes the time value of money by using an interest rate that represents the desired rate of return or, at least, sets a minimum acceptable rate of return. The decision rule is:
If the present value of incremental net cash in�lows is greater than the incremental investment net cash out�low, approve the project.
Using the time value of money Tables 1 and 2 found at the end of this chapter, the net cash �lows for each year are brought back (i.e., discounted) to Year 0 and summed for all years. An interest rate must be speci�ied. This rate is often viewed as the cost of funds needed to �inance the project and is the minimum acceptable rate of return. To discount the cash �lows, we use the interest rate and the years that the cash �lows occur to obtain the appropriate present value factors from the present value tables. A portion of Table 1 appears below showing the present value factors (the shaded numbers), corresponding to an interest rate of 12%, for each year during the Clairmont Timepieces project’s life.
Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15% 16%
0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870 0.862
2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756 0.743
3 0.971 0.942 0.889 0.864 0.840 0.794 0.751 0.712 0.675 0.658 0.641
4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572 0.552
5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497 0.476
6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432 0.410
7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376 0.354
8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.327 0.305
9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284 0.263
10 0.905 0.820 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.247 0.227
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These present value factors are used in Figure 10.2 to discount the yearly cash �lows to their present values. In Figure 10.2, the net cash investment ($95,000) is subtracted from the sum of cash-in�low present values ($137,331). When the difference is positive, the project’s rate of return (ROR) is greater than the minimum acceptable ROR. If:
Present value of incremental net cash in�lows ≥ Incremental investment cash out�lows
then:
Project’s ROR ≥ Minimum acceptable ROR
Net present value is the difference between the present value of the incremental net cash in�lows and the incremental investment cash out�lows. If net present value is zero or positive, the project is acceptable because the project is earning the acceptable rate of return. When the sum is negative, the project’s ROR is less than the discount rate. If:
Present value of incremental net cash in�lows < Incremental investment cash out�lows
then:
Project’s ROR < Minimum acceptable ROR
If net present value is negative, the project should be rejected because its rate of return is below the minimum acceptable level.
The Interest Rate. What interest rate should be used for discounting the cash �lows? This rate has many names that help explain its source and use. Among them are:
1. Cost of capital—a weighted-average cost of long-term debt and equity funding. Only projects that can earn at least what the �irm pays for funds should be accepted. Later, we illustrate a calculation of cost of capital.
2. Minimum acceptable rate of return—a particular rate that is considered to be the lowest ROR that management will accept.
3. Desired rate of return, target rate of return, or required rate of return—a rate that re�lects management ROR expectations.
4. Hurdle rate—a threshold that a project’s ROR must “jump over” or exceed. 5. Cutoff rate—the rate at which projects with a higher ROR are accepted and those with a lower
ROR are rejected; often the rate where all available capital investment funds are committed.
A �irm will use one or more of these terms as its discount rate. While these terms sometimes produce different rates in the business world, we will use these terms interchangeably here. Generally, if a project’s ROR is below the chosen discount rate, it is rejected; above this rate, the project is acceptable. Still, whether it is funded depends on the availability of capital funds.
In the Clairmont Timepieces example, we assume that management has decided that 12% is the minimum acceptable rate of return. Calculations needed to obtain a net present value are shown in Figure 10.2. The net present value is a positive $42,331; therefore, the project earns more than a 12% ROR. The net present value method does not provide information about the project’s exact ROR; it merely informs whether the project is earning more than, less than, or equal to the minimum acceptable ROR.
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Figure 10.2: Net present value of capital investment cash �lows
If other discount rates had been selected, we would �ind the following net present values:
Percentage Present Value of Net Cash In�lows* − Investment = Net Present Value
16% $124,328 $95,000 $29,328
20 113,246 95,000 18,246
24 103,713 95,000 8,713
28 95,523 95,000 523
30 91,797 95,000 (3,203)
* If Excel is used, the present values will be slightly different due to the rounding of the present value factors used here.
Notice that, as the interest rate increases, the present values of the future cash �lows decrease. At 30% per year, the project’s net present value is negative, and the project is unacceptable. The project’s rate of return must be between 28 and 30%.
Project Ranking. Even though a project has a positive net present value, too many attractive projects may exist, given the investment dollars available. A ranking system is needed. We can rank projects by the amount of net present value each generates, but this ignores the relative size of the initial investments. An extension of the net present value method is the pro�itability index. It is found by dividing the present value of a project’s net cash in�lows by its net initial investment. The resulting ratio is cash in to cash out. The higher the ratio is, the more attractive the investment becomes. Notice that an acceptable project should have a pro�itability index of at least 1. The following projects are ranked by the pro�itability index.
Project Present Value of Net Cash
In�lows Initial
Investment Net Present
Value Pro�itability
Index Ranking
A $235,000 $200,000 $35,000 1.18 5
B 170,000 140,000 30,000 1.21 4
C 80,000 60,000 20,000 1.33 1
D 98,000 80,000 18,000 1.23 3
E 52,000 40,000 12,000 1.30 2
We would typically accept projects with the highest pro�itability index until we exhaust the capital budget or the list of acceptable projects.
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Internal Rate of Return (IRR) Method
The internal rate of return (IRR) is the project’s ROR and is the rate where the:
Net initial investment cash out�low = Present value of the incremental net cash in�lows
Without calculator or computer assistance, the speci�ic ROR is found by trial and error. We search for the rate that yields a zero net present value.
In the Clairmont Timepieces example, the internal rate of return was found to be between 28% and 30%. The net present value at 28% is positive and at 30% is negative. By interpolation, we can approximate a “more accurate” rate as follows:
Rate of Return Net Present Value Calculations
28% $523 Base rate = 28.00%
30 (3,203) ($523 ÷ $3,726) × 2% = 0.28%
2% difference $3,726 absolute difference Internal rate of return 28.28%
In most cases, however, knowing that the rate is between 28% and 30% is adequate.
Estimating the Internal Rate of Return. By using Table 2 and knowing certain project variables, we can estimate other unknown variables, including a project’s internal rate of return. This estimate requires that the annual net cash in�lows be an annuity (i.e., annual net cash �lows that are uniform). The variables and a sample set of data are:
Variable Example Data
A = Initial investment cash out�low $37,910
B = Life of project 5 years
C = Annual net cash in�low $10,000 per year
D = Internal rate of return 10%
E = Present value factor at 10% (Table 2) 3.791
If we know any three of A, B, C, or D, we can �ind E and the missing variable. A variety of questions can be answered:
1. What is the internal rate of return of the project? If A, B, and C are known, we can calculate E and �ind D as follows:
E = A ÷ C
$37,910 ÷ $10,000 = 3.791
On Table 2, we go to the 5-period (year) row and move across until we �ind 3.791 (E) in the 10% column (D). At 10%, the cash out�low ($37,910) equals the present value of the net cash in�lows (3.791 × $10,000). The internal rate of return is 10%.
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2. What annual cash in�low will yield a 10% IRR from the project? If A, B, and D are known, we can �ind E and calculate C. E is found in Table 2 by using �ive years and 10% ROR. The annual cash in�low is found as follows:
C = A ÷ E
$37,910 ÷ 3.791 = $10,000 per year
We need $10,000 per year in cash in�low to earn a 10% IRR.
3. What can we afford to invest if the project earns $10,000 each year for �ive years and we want a 10% IRR? If we know B, C, and D, we can �ind E and then calculate A. The investment is found by using the annual net cash in�low and 3.791 as follows:
A = C × E
$10,000 × 3.791 = $37,910
We can pay no more than $37,910 and still earn at least a 10% return.
4. How long must the project last to earn at least a 10% IRR? If we know A, C, and D, we calculate E and �ind B as follows:
E = A ÷ C
$37,910 ÷ $10,000 = 3.791
For a 10% IRR, 3.791 is on the 5-period row. The project’s life must be at least �ive years.
Most spreadsheet software and business calculators have built-in functions to �ind the internal rate of return. This simpli�ies the calculation burden that has limited its use in the past.
Project Ranking. Since each project has a speci�ic rate of return, ranking projects under the IRR method is relatively simple. All projects are listed according to their rates of return from high to low. The cost of capital or a cutoff rate can establish a minimum acceptable rate of return. Then, projects are selected by moving down the list until the budget is exhausted or the cutoff rate is reached.
Reinvestment Assumption. The internal rate of return method assumes that cash �lows are reinvested at the project’s internal rate of return. While this assumption may be realistic for cost of capital rates, it may be wishful thinking for projects with high internal rates of return. This issue, however, is best left to �inance texts and courses.
High Discount Rates. A concern exists about the use of high discount rates in present value methods. A project with signi�icant long-term payoffs may not appear favorable because the long-term payoffs will be discounted so severely. Even huge cash in�lows due 10 years or more into the future appear to be less valuable than minor cost savings earned in the �irst year of another project. High discount rates may encourage managers to think only short term; to ignore research, market innovations, and creative product development projects; and to ignore long-term environmental effects. Thus, positive or negative impacts can result from the wise or unwise use of accounting tools and policies.
Payback Period Method
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The payback period method is a “quick and dirty” evaluation of capital investment projects. It is likely that no major �irm makes investment decisions based solely on the payback period, but many ask for the payback period as part of their analyses. The payback period method asks:
How fast do we get our initial cash investment back?
No ROR is given, only a time period. If annual cash �lows are equal, the payback period is found as follows:
Net initial investment ÷ Annual net cash in�low = Payback period
If the investment is $120,000 and annual net cash in�low is $48,000, the payback period is 2.5 years. We do not know how long the project will last nor what cash �lows exist after the 2.5 years. It might last 20 years or 20 days beyond the payback point.
If annual cash �lows are uneven, the payback period is found by recovering the investment cost year by year. In the Clairmont Timepieces example:
Year Cash Flows Unrecovered Investment
0 $(95,000) $95,000
1 40,000 55,000
2 40,000 15,000
3 20,000 0
In Year 3, the cost is totally recovered, using only $15,000 of Year 3’s $20,000 (75%). The payback period is 2.75 years.
The payback method is viewed as a “bail-out” risk measure. How long do we need to stick with the project just to get our initial investment money back? It is used frequently in short-term projects where the impact of present values is not great. Such projects as ef�iciency improvements, cost reductions, and personnel savings are examples. Several major companies set an arbitrary payback period, such as six months, for certain types of cost-saving projects.
Using the Payback Reciprocal to Estimate the IRR. The payback period can be used to estimate a project’s IRR, assuming a fairly high ROR (over 20%) and project life that is more than twice the payback period. For example, if a $40,000 investment earns $10,000 per year for an expected 12 years, the payback period is four years. The reciprocal of the payback period is 1 divided by 4 and gives an IRR estimate of 25%. From Table 2 for 12 years, the present value factor (payback period) of 4 indicates a rate of return of between 22 and 24%. The payback reciprocal will always overstate the IRR somewhat. If the project’s life is very long, say 50 years, the payback reciprocal is an almost perfect estimator. (See the present value factor of 4.000 for 25% and 50 periods on Table 2.)
Ranking Projects. When the payback period is used to rank projects, the shortest payback period is best. Thus, all projects are listed from low to high. A �irm’s policy may say that no project with a payback period of over four years will be considered. This acts like a cutoff point. After that, projects would be selected until capital funds are exhausted. The major complaints about the payback period method are that it ignores:
1. The time value of money
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2. The cash �lows beyond the payback point 3. The timing of cash �lows within the payback period
These are serious de�iciencies, but the method is easily applied and can be a rough gauge of potential success.
Accounting Rate of Return Method
This method:
1. Ignores the time value of money 2. Presumes uniform �lows of income over the project’s life 3. Includes depreciation expense and other accounting accruals in the calculation of project
income, losing the purity of cash �lows
In fact, we only discuss this approach because many internal corporate performance reporting systems use accrual accounting data. Many companies use discounted cash �lows for investment decisions but report actual results using accrual income and expense measures.
The accounting rate of return (ARR) method attempts to measure the return from accrual net income from the project. When using the ARR method, depreciation expense on the incremental investment is subtracted from the annual operating net cash in�low. Accrual net income is arrived at by deducting all expenses, but only cash expenses have been deducted in obtaining annual net cash in�low. Therefore, noncash expenses such as depreciation expense must be deducted from annual net cash in�low to obtain accrual net income. Other accrual adjustments may also be made. The general formula is:
The average investment, the denominator, is the average of the net initial investment and the ending investment base ($0 if no salvage value exists). This is the average book value (i.e., net initial investment less its accumulated depreciation) of the investment over its life. Some analysts prefer to use the original cost of the investment or replacement cost as the denominator. The numerator is the annual incremental accrual net income from the project. To illustrate, assume the following:
Initial investment $110,000
Salvage value $10,000
Annual cash in�low $35,000
Project life 5 years
Depreciation expense $20,000
ARR calculations are:
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The 25% must be viewed relative to other projects’ ARR and cannot be compared to present value rates of return. For ranking purposes, projects are ranked from high to low. An arbitrary percentage may be set as a minimum rate.
Another problem with the ARR is the impression it gives of an increasing ROR on an annual basis as an asset grows older. A manager would see this project’s performance on the annual investment center responsibility report as follows:
Average Investment (Book Value) Project Net Income Annual ARR
Year 1 $100,000 $15,000 15.0%
Year 2 80,000 15,000 18.8
Year 3 60,000 15,000 25.0
Year 4 40,000 15,000 37.5
Year 5 20,000 15,000 75.0
The average annual book value declines each year, and net income is assumed to remain constant. As the asset gets older, the ARR increases. It is tempting for managers to reject any proposal that will make their performance reports look less favorable. This is particularly true when their bonuses are tied to accrual accounting performance numbers. Managers will be biased toward sticking with older assets with higher accounting rates of return. They forgo new investments that offer new technology, lower operating costs, and greater productivity.
Contemporary Practice 10.1: Capital Budgeting Practices in British Food Companies
A survey of 122 management accountants at British companies that manufacture food products and beverages revealed that “41 per cent of respondents used traditional accounting measures such as accounting rate of return and payback period to evaluate major capital projects, while the equivalent �igure for discounted cash �low models such as internal rate of return and net present value is only 19 per cent.”
Source: Abdel-Kader, M. & Luther, R. (2006). Management accounting practices in the British food and drinks industry. British Food Journal, 336–357.
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10.4 Ethical Issues and Pressures on Management In many corporate situations, managers are under pressure to earn high rates of return in the short run. All capital investment analyses depend on the credibility of future cash-�low estimates. Unlike past facts, which are measured very objectively, future values are based on predictions, opinions, judgments, and perhaps wishful thinking. The quality of decision making rests on a premise that future estimates are made objectively and in good faith. A manager trying to get a needed project approved may develop estimates that are too optimistic because of the manager’s enthusiastic support of the idea.
Company policies compound the problem by setting very high hurdle or cutoff rates that encourage proposal developers to overestimate future revenues and underestimate investment costs. Managers have been heard to say, “Show me the hurdle, and I’ll make the project jump over it.” In fact, a vicious cycle may develop: higher hurdles, more bias in estimates; higher hurdles, and so on.
To control these problems, many �irms have special analysts who evaluate proposals independent of the sponsoring managers. Others perform post-audits to compare actual results to the estimates. Tying responsibility for the project’s promises to the manager’s future evaluations may help solve some of these problems.
The second issue is the severe pressure on managers to show growth in immediate earnings. Key investment analysts and shareholders watch quarterly earnings announcements and other short-term information about the company to make almost daily buy and sell decisions. Capital investment proposals include a mix of short-term and long-term projects. Short-term projects often emphasize cost savings, which may be worthwhile but not strategically important. Long-term projects include research and development and new technology. Unfortunately, these projects often have long payback periods, but they offer signi�icant future potential. If hurdle rates are high, long-term projects will rarely rank as high as short-term projects. The long-run competitiveness and success of a �irm may be damaged severely if its managers are biased toward short-term rewards.
Japanese �irms, for a number of reasons, are said to have a much longer-term investment horizon. They are less concerned about the immediate pro�itability of new products and markets. Market penetration and market share are more important. This allows managers to develop a strategic plan that emphasizes the long-run success of the �irm.
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10.5 Taxes and Depreciation The illustrations have thus far ignored income taxes. Also, depreciation expense, being noncash, was considered only in the accounting rate of return method. These factors impact capital budgeting signi�icantly.
Income Taxes and Capital Investments
Except for nonpro�it organizations, the real world is a tax-paying world, and capital investment analysis must consider taxes. Taxation rules are complex and impact many cash �lows. Taxable income and gains include:
1. Incremental revenues minus incremental expenses 2. Incremental operating expense savings 3. Gains on sales of old assets now and of new assets at the project’s end
Incremental expenses and losses reduce taxes and include:
1. Incremental operating expenses 2. Losses on sales of old assets now and of new assets at the end of a project’s life
The tax rate should be the expected marginal tax rate for the future year being analyzed. The marginal tax rate is the tax rate applied to any incremental taxable income. For simplicity, we assume that the marginal income tax rate is 40% for all income tax-related issues. Clearly, income taxes reduce the ROR on capital projects by reducing net cash in�lows.
Depreciation Expense
The only role that depreciation expense plays in cash-�low-based capital investment analysis is as a deduction in calculating income taxes. If taxes are ignored or are not applicable, as in nonpro�it organizations, depreciation expense is also ignored. To simplify our depreciation expense and taxation discussions, we assume that: (1) straight-line depreciation is used, (2) depreciation expense calculations ignore salvage values, and (3) salvage values are net of tax consequences.
To understand the tax and depreciation expense impacts, let us look again at the Clairmont Timepieces example in Figure 10.2 and now apply a tax rate of 40% to the incremental operating cash �lows. For now, we ignore the effects of depreciation. This is shown in Figure 10.3.
Figure 10.3: Net present value analysis with taxes but without depreciation
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As Figure 10.3 shows, suddenly a very pro�itable project (just under 30% on a no-tax basis) now has a negative net present value using a 12% discount rate. We assume that the overhaul in Year 3 is a deductible expense, salvage value is net of taxes, and inventory recovery has no tax effects.
The Tax Shield
Depreciation expense is a noncash expense, provides a legitimate deduction for tax purposes, and creates a tax shield. By reducing taxable income, cash paid for taxes is reduced. Depreciation saves cash by reducing tax payments. Thus, if depreciation expense increases, tax payments decrease. Cash out�low is reduced. A reduced out�low has the same effect as an increased in�low.
The depreciation impact is seen in the Clairmont Timepieces example. The increase in depreciable assets is $92,000 ($100,000 minus $8,000) and is spread over �ive years. Currently, salvage value is ignored in most IRS depreciation calculations. Assuming straight-line depreciation, the incremental depreciation expense is $18,400 per year. Aftertax cash �lows, from Figure 10.1, are:
Year 1
Added contribution margin $25,000*
+ Operating cost savings 15,000*
Incremental cash in�low $40,000
− Depreciation expense −18,400
Taxable income $21,600
− Incremental taxes (40%) −8,640*
Aftertax project net income $12,960
+ Add back depreciation expense 18,400
Aftertax cash in�low $31,360
* Cash �lows
The project’s Year 1 aftertax pro�it, $12,960, and the incremental depreciation expense, $18,400, are summed to �ind the Year 1 aftertax cash in�low. Tax cash out�lows for the entire project are included in the Figure 10.4 analysis. The increased tax deduction for depreciation moves the net present value of the project from a negative $9,653 to a positive $16,879, a $26,532 change. This is the present value of the
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depreciation expense tax savings, as follows (the one dollar difference is due to rounding of present value factors):
(Depreciation Expense × Tax Rate × Present Value Factor (for 5 years at 12%) = Present Value of Tax Shield)
($18,400 × .040 × 3.605 = $26,533)
Figure 10.4: Net present value analysis with depreciation and taxes
Accelerated Depreciation Bene�its. The cash-saving power of depreciation can be increased by using accelerated depreciation to deduct, for income tax purposes, more depreciation earlier in a project’s life. Deferring taxes has a time value of money effect. By merely changing depreciation methods, the net present value can increase or decrease. This is strictly from speeding up or slowing the depreciation expense deductions and the time value of the tax deferrals. That is, having more depreciation expense earlier reduces taxable income, which in turn, reduces the cash out�low for taxes. This earlier reduction of cash out�low, which is tantamount to an increased cash in�low, increases the present value of cash �lows.
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10.6 Cost of Capital Throughout our discussions, cost of capital is mentioned frequently. Long-term money has a cost, either real as in interest paid on bonds payable or an opportunity cost as in the use of earnings retained in the business. A basic approach is explained here to show the source of this rate.
A weighted-average cost of capital pools a �irm’s long-term funds and is used because the relative amount of each fund’s source affects the average cost. Debt generally is less costly than equity since the creditor assumes less risk and interest is deductible for tax purposes. If a �irm has a pretax debt cost of 10% and a 40% tax rate, the after-tax cost is 6%. Dividends, on the other hand, are not deductible for tax purposes and are pro�it distributions to owners, not a business expense.
Assume that a �irm has the following long-term funds structure and cost of funds:
Book Value Mix
Percentage Pretax Cost
Aftertax Cost
Weighted Average
Bonds payable $10,000,000 25% 10% 6% 1.5%
Preferred stock 4,000,000 10 12 12 1.2
Common Stock 14,000,000 35 18 18 6.3
Retained earnings 12,000,000 30 18 18 5.4
Total long-term funds
$40,000,000 100% 14.4%
The pretax cost percentages come from �inancial markets calculations. The weighted-average cost of capital is 14.4% [(25% × 6%) + (10% × 12%) + (35% × 18%) + (30% × 18%)]. Often �inancially strong companies have low cost of funds. High risk, �inancially unstable, or new �irms often have high funds costs.
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10.7 Calculation Issues The variety of issues surrounding capital investment decisions is suf�icient that entire textbooks have been written about them. Here, we introduce a few of the more signi�icant complexities.
In�lation and Future Cash Flows
In�lation is a common economic problem. Over the past 40 years in the United States, annual in�lation rates have ranged from a high of over 12% to a low of under 2%. These levels are moderate compared to rates in many other countries. Yet, capital investment decisions should consider in�lationary impacts on future cash �lows.
While several approaches could be used to incorporate in�lation into the analysis, the approach we suggest is to build the impacts of in�lation into the expected future cash �lows. This allows the use of speci�ic in�lation rates for each cash-�low component. Also, rates can be changed for each future period.
To illustrate in�lation impacts on estimates of future cash �lows, assume that Kazen Motors plans to expand its engine diagnostic business. Equipment will cost about $120,000 and should last about three years. After three years, it is thought that greater on-board computer use will require more powerful testing technology. Annual revenues are expected to be $150,000, personnel costs are $60,000, and other support costs would be about $30,000. Kazen uses a 10% desired rate of return.
Economic forecasts indicate that in�lation will be 6% per year for the next few years. But Kazen feels that, at best, prices could be raised no more than 4% per year. Personnel costs will probably increase at a 10% rate, primarily because of bene�its costs. Other costs will increase at an average of 6% annually. The equipment, which has no salvage value, will be depreciated on a straight-line basis. Assume a 40% tax rate. Cash �lows related to the equipment are as follows:
Cash Flows:
Investment Life of the Project
Year 0 Year 1 Year 2 Year 3
Initial investment $(120,000)
Revenues $150,000 $156,000 162,240
Personnel costs (60,000) (66,000) (72,600)
Other costs (30,000) (31,800) (33,708)
Incremental taxes* ______ (8,000) (7,280) (6,373)
Net cash �lows $(120,000) $ 52,000 $ 50,920 $ 49,559
*Taxes in Year 1: ($150,000 − 60,000 − 30,000 − 40,000) × 0.4 = $8,000
Taxes in Year 2: ($156,000 − 66,000 − 31,800 − 40,000) × 0.4 = $7,280
Taxes in Year 3: ($162,240 − 72,600 − 33,708 − 40,000) × 0.4 = $6,373
Notice that depreciation, being based on the historical cost of the investment, is still $40,000 in each year. While all other revenues and costs have in�lation built into them, the tax law requires that the depreciation expense is always expressed in historical-cost dollars from the year of acquisition. Using historical cost-based depreciation in tax calculations often leads to higher tax payments since pro�its grow from in�lated revenues.
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It is dangerous to ignore in�lation. To do so assumes that all in�lation effects sum to zero, which is rarely the case. Certain cost areas, such as health care, have had unusually high increases in recent years. Forecasting these costs should include estimated in�lationary impacts to make cash-�low estimates credible.
Working Capital
When expansion occurs, inventories and receivables often grow. Financing working capital growth is an integral part of a project’s total investment. Unlike depreciable equipment and �ixed assets, working capital is committed and can probably be recovered at the end of the project. Often, working capital requirements grow slowly over time as sales increase. Incremental inventories and accounts receivable net of incremental accounts payable can easily be overlooked and omitted from a project’s analysis. In contrast, JIT projects often release working capital by reducing inventories, which can help �inance the project itself.
Assume that Belmar Athletics operates a chain of sporting goods stores in shopping malls. Opening a new store requires layout, equipment, and �ixtures costing about $450,000. In addition, about $200,000 of inventory is needed to stock a new store. Experience shows that inventory and other working capital needs will grow at about $20,000 per year for the �irst �ive years. If Belmar Athletics uses an eight-year timeframe for evaluating a store location, assumptions will be needed about the equipment salvage value and the recovery of the working capital investment. The �ixed assets’ salvage values are estimated to be $50,000 net of taxes, and the entire working capital investment (now $300,000) is thought to be recovered. The cash �lows would look like:
Life of the Project
Cash Flows: Today Year 1 Year 2 · · · Year 5 · · · Year 8
Initial construction $(450,000) $ 50,000
Working capital needs (200,000) $(20,000) $(20,000) · · · $(20,000) · · · 300,000
Working capital recovery is not automatic. Inventory may be obsolete, and receivables might not be collectible. A going-concern assumption can generally be made if the business is expected to continue past the timeframe cutoff.
Uneven Project Lives
When comparing projects, lives of each project may not match. How can a three-year solution to a problem be compared to a �ive-year or an eight-year solution? The decision must be viewed from the timeframe of the job to be done. Do we want a solution for three, �ive, or eight years? How long can the physical asset last? Often, technology changes make an asset’s economic life shorter than its physical life. A three-year solution may be sought, while an asset’s physical life might well be twice that long.
If the time period is based on the needs of the problem, the task is to �ind salvage or market values for assets at the end of the de�ined time period. If the time period is based on the physical lives of the proposed assets, different useful lives of the proposed solutions must be somehow matched. One approach is to use a shorter-lived project as the comparison time period. This requires �inding salvage or market values for assets at midpoints in their lives. While no speci�ic rule exists, the investment’s
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timeframe as de�ined by management seems to be the better choice. Management’s intent and common sense, rather than the physical lives of assets, should govern the time period choice.
Evaluation of Projects With Different Initial Investments
Up to this point, most of the illustrations have assumed that a single investment alternative existed. The �irm had to decide whether or not to invest in that project. Actually, a �irm may have several alternatives but still have to select only one. In such a case, care must be exercised in using the internal rate of return method, because the project with the highest internal rate of return may not be the most desirable. This can happen in those cases where the dollar investment is not the same. The dollar amount of the return from a larger investment, in many cases, will exceed the dollar return from a smaller investment having a better internal rate of return.
Assume that Behar Transit Company must choose between two delivery vans. Each has an estimated life of �ive years with annual returns as follows:
Van I Van II
Net investment $75,000 $100,000
Net cash in�low for each of 5 years 26,000 33,000
Investments are expected to earn a desired rate of return of at least 12%. Van II requires an investment of an additional $25,000 versus Van I. The approximate internal rate of return is computed for each alternative and for the incremental investment as follows:
Van I Van II Incremental (II – I)
Net investment $(75,000) $(100,000) $(25,000)
Annual return 26,000 33,000 7,000
Payback period 2.885 3.030 3.571
Nearest PV factor on Table 2 for 5 periods 2.864 2.991 3.605
Nearest IRR given on Table 2 22% 20% 12%
It appears that Van I should be selected because the internal rate of return is higher. The additional $25,000 investment needed by Van II yields a much lower rate of return: 12%. But, if the rate of return on the incremental investment is greater than the hurdle rate of return, the larger investment could still be made. In this example, an additional $7,000 per year is returned on an additional investment of $25,000. The rate of return on the incremental investment barely meets the 12% desired rate of return.
In another situation, Van I could be a Phase I of a pair of sequential jobs and Van II could be Phases I and II combined. Phase I may be executed without Phase II but not vice versa. Advocates of Phase II would clearly argue that both phases be approved at one time. However, as we have seen, Phase II has an IRR of about 12%. If the cutoff rate is 15%, Phase I and the combined phases are acceptable. But Phase II by itself is unacceptable. Breaking down projects into their subcomponents can give useful insight into the yields on incremental investments.
Gains and Losses on Asset Disposals
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If assets are sold at more or less than their book values, gains or losses appear with tax implications. The book value is an asset’s original cost minus its accumulated depreciation. In the business world, accounting book values and tax cost bases often differ. In our discussions here, unless speci�ically mentioned, these two amounts are assumed to be the same. If the sale is for more than the book value, a gain occurs; if for less, a loss occurs.
Gains and losses on disposals and their impacts on cash �lows arise at two points in the capital investment decision:
1. Old assets may be sold at the same time as a new asset is acquired 2. New assets may be sold at the end of the project’s expected life
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10.8 The Time Value of Money Dollars promised in the future are not equal to dollars received now. When given a choice, we all prefer getting $100 today versus $100 two years from now. Dollars due in different time periods should be valued on a uniform scale that recognizes the time value of money. Present value converts future dollars into current dollar equivalents. Future value converts all dollars into equivalent dollars as of some future date. To �ind these values, we need an interest rate and the number of time periods between today and the future cash �lows.
Money has earning power. Dollars today grow to larger sums through earning interest on the principal plus earning interest on interest. The investment principal plus compound interest is the future value (FV). The future value of $100 in two years, with interest compounded at the rate of 10% annually, is $121. The formula for the future value of $1 is:
FV = (1 + i)n where i = interest rate
n = number of years
In the example, the future value is computed as follows:
FV of $1 = (1.10)2 = $1.21
FV of $100 = $100 × $1.21, or $121
An investor who is happy with a 10% ROR looks at the receipt of $121 in two years as equivalent to $100 today, assuming certainty. This investor is indifferent between the $100 today or $121 in two years.
The interest rate in�luences the values. If a decision maker has a choice of investments, the preferred choice is the investment with the highest ROR. The reason, of course, is that the investment with the highest ROR will yield the largest future amount or require the smallest current investment. For example, an alternative investment will earn a 15% ROR. Assuming certainty, the future value in two years of the $100 at 15% is:
$100 × (1.15)2 = $100 × 1.3225 = $132.25
Since $132.25 is larger than $121, the project earning 15% is preferred to the 10% project.
Present Value of Money
Because decisions are made today and because future cash �lows come in many different patterns and time periods, present values of future dollars are more useful and easier to analyze. It is conventional to use present value analysis.
How much money must we invest today to earn a given dollar amount in the future? Or, given an investment, how much will be earned in the future? Or, given an investment and a set of future cash in�lows, what is the ROR? Answers to these questions can be found by computing the present value of the future cash �lows and comparing it with the amount invested.
The present value (PV) of a future value can be computed by multiplying the future value by the present value of $1. The present value of $1 is:
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PV of $1 = 1 ÷ (1 + i)n
Assume, for example, that $121 is needed in two years, and the rate of interest is 10%. How much must be invested today to have $121 after two years? We �irst determine the present value of $1 due in two years with interest compounded annually at 10%:
PV of $1 for 2 years at 10% = 1 ÷ (1.10)2 = 0.826
Next, we multiply by the future value:
PV of $121 for 2 years at 10% = $121 × 0.826 = $100 (rounded)
The computation can be viewed as:
$121 ÷ 1.10 = $110 is the value at the end of Year 1.
$110 ÷ 1.10 = $100 is the investment at the start of Year 1, or today.
This is summarized as follows:
$121 ÷ (1.10)2 or [1 ÷ (1.10)2] × $121 = $100
The process of reducing a future amount to a present value is called discounting. The present value is sometimes called the discounted value. The rate of interest is the discount rate. The 0.826 is called the present value factor or discount factor.
It is seldom necessary to calculate either future values or present values as done here. Calculators and spreadsheet software easily perform these functions. Tables 1 and 2, found at the end of this chapter, give present value factors for various discount (interest) rates for various time periods expressed in years. Table 1 gives the present value of $1 to be received at the end of the various time periods at interest or discount rates shown across the top row of the table. Thus, it is a tabulation of the factor 1 ÷ (1 + i)n, where n is the number of years and i is the discount rate. The factor for two years at 10% is 0.826, and the present value (PV) of $121 to be received in two years is calculated as follows:
PV = $121 × 0.826 = $100 (rounded)
The discount factors appearing in Tables 1 and 2 are rounded to the third digit, which is suf�icient precision for most capital investment problems.
Present Value of a Series of Future Cash Flows
Often, a series of future cash in�lows are earned from an investment instead of one cash in�low. As an example, a machine costing $3,500 today is forecast to generate cash in�lows of $1,000 each year for �ive
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years. The time interval for most decisions is annual, but any time interval (a day, week, month, quarter, etc.) can be used as long as the interest rate (i) is adjusted to correspond to the time period.
Calculating present values depends on whether the cash �lows series are equal or unequal amounts. An annuity refers to a series of equal cash �lows. In either case, however, the underlying concepts are the same. The present value of a series is the sum of the present values of the individual amounts. The present value of these �ive annual receipts of $1,000 using a 10% discount rate is computed as follows:
Year Computation Explanation
1 $1,000 × (1 ÷ 1.10) = $909 PV of $1,000 received at the end of Year 1
2 1,000 × [1 ÷ (1.10)2] = 826 PV of $1,000 received at the end of Year 2
3 1,000 × [1 ÷ (1.10)3] = 751 PV of $1,000 received at the end of Year 3
4 1,000 × [1 ÷ (1.10)4] = 683 PV of $1,000 received at the end of Year 4
5 1,000 × [1 ÷ (1.10)5] = 621 PV of $1,000 received at the end of Year 5
$3,790 PV of an annuity of $1,000 for 5 years
The present value can also be computed as follows:
$1,000 × [1/1.10 + 1/(1.10)2 + 1/(1.10)3 + 1/(1.10)4 + 1/(1.10)5] = $3,790
The decimal equivalents of the fractions can be found in Table 1 and applied to the annual cash in�low:
0.909 + 0.826 + 0.751 + 0.683 + 0.621 = 3.790
$1,000 × 3.790 = $3,790
Note that the factor, 3.791, can be found on Table 2 using the 10% column and the 5-period row. The factors in Table 2 are the sums of the present value factors in Table 1. The difference between 3.790 and 3.791 is due to rounding. The following calculations using interest rates of 8%, 10%, and 12% for �ive years illustrate this point.
8% 10% 12%
Years Table 1 Table 2 Table 1 Table 2 Table 1 Table 2
1 0.926 0.909 0.893
2 0.857 0.826 0.797
3 0.794 0.751 0.712
4 0.735 0.683 0.636
5 0.681 0.621 0.567
Total 3.993 3.993 3.790* 3.791* 3.605 3.605
* Difference due to rounding.
When calculating, it is easier to add the annual factors and make one computation. Thus, Table 2 is more convenient for evaluating equal cash �lows. If the annual cash-�low amounts are not equal, it is necessary
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to use Table 1.
Present Value Analysis Applied
Assume that we sell machinery and offer �inancing to our customers using long-term notes payable. When a contract is signed, the customer makes two promises:
1. To pay the principal amount (the face value of the note) at maturity 2. To pay interest periodically at the rate stated in the contract
We can either hold the note (earning interest and collecting the principal at the end of the contract) or sell the contract to an investor to get the cash for the sale now. The contract’s market value depends on several factors, including the market rate of interest for similar contracts. The sum of the present values of the two promises is the contract’s market price. As the market rate of interest rises, the contract’s value declines, and vice versa.
To illustrate, assume that Hillcrest Corp. sells a $100,000 machine. The buyer signs a ten-year $100,000 contract with an interest rate of 10%, paid annually. This contract speci�ies the following cash payments:
Year Interest at 10% Payment of Principal Total Cash Out�low
1 $10,000 $10,000
2 10,000 10,000
. . . . . . . . . . . . . . . . . . . . . . .
9 10,000 10,000
10 10,000 $100,000 110,000
Suppose that the current market rate of interest is 12%. In this case, investors are not willing to buy the contract at face value, because they could earn 12% elsewhere. To sell the contract, Hillcrest must price the contract below face value. Selling at a price below face allows the investor to increase the rate of return by paying less for the two promises.
Promise 1: $100,000 × 0.322 (10 periods at 12% from Table 1) $32,200
Promise 2: $ 10,000 × 5.650 (10 payments at 12% from Table 2) 56,500
Proceeds from sale of the contract $88,700
Discount $11,300
The investor that purchases the contract from Hillcrest at $88,700 will earn 12% interest on the $88,700 invested. The 12% earned is usually called the yield or the effective rate of interest. An effective interest rate or yield to maturity is the rate of interest earned regardless of the compounding period or the stated interest rate.
Likewise, if the current market rate of interest is 8%, an investor will pay a premium for a contract with a 10% interest rate. The selling price and premium are determined as follows:
Promise 1: $100,000 × 0.463 (10 periods at 8% from Table 1) $46,300
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Promise 2: $ 10,000 × 6.710 (10 payments at 8% from Table 2) 67,100
Proceeds from sale of the contract $113,400
Premium $13,400
Present Value Tables
Table 1 Where:
Present Value of $1 P = 1/(1 + i)n P = Present Value Factor i = Interest Rate n = Number of Periods
Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15%
0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870
2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756
3 0.971 0.942 0.889 0.861 0.840 0.794 0.751 0.712 0.675 0.658
4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572
5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497
6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432
7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376
8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404. 0.351 0.327
9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284
10 0.905 0.820 0.616 0.614 0.558 0.463 0.386 0.322 0.270 0.247
11 0.896 0.804 0.650 0.585 0.527 0.429 0.350 0.287 0.237 0.215
12 0.887 0.788 0.625 0.557 0.497 0.397 0.319 0.274 0.208 0.187
13 0.879 0.773 0.601 0.530 0.469 0.368 0.290 0.229 0.182 0.163
14 0.870 0.758 0.577 0.505 0.442 0.340 0.263 0.205 0.160 0.141
15 0.861 0.743 0.555 0.481 0.417 0.315 0.239 0.183 0.140 0.123
16 0.853 0.728 0.534 0.458 0.394 0.292 0.218 0.163 0.123 0.107
17 0.844 0.714 0.513 0.436 0.371 0.270 0.198 0.146 0.108 0.093
18 0.836 0.700 0.494 0.416 0.350 0.250 0.180 0.130 0.095 0.081
19 0.828 0.686 0.475 0.396 0.331 0.232 0.164 0.116 0.083 0.070
20 0.820 0.673 0.456 0.377 0.312 0.215 0.149 0.104 0.073 0.061
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Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15%
21 0.811 0.660 0.439 0.359 0.294 0.199 0.135 0.093 0.064 0.053
22 0.803 0.647 0.422 0.342 0.278 0.184 0.123 0.083 0.056 0.046
23 0.795 0.634 0.406 0.326 0.262 0.170 0.112 0.074 0.049 0.040
24 0.788 0.622 0.390 0.310 0.247 0.158 0.102 0.066 0.043 0.035
25 0.780 0.610 0.375 0.295 0.233 0.146 0.092 0.059 0.038 0.030
30 0.742 0.552 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.015
35 0.706 0.500 0.253 0.181 0.130 0.068 0.036 0.019 0.010 0.008
40 0.672 0.453 0.208 0.142 0.097 0.046 0.022 0.011 0.005 0.004
45 0.639 0.410 0.171 0.111 0.073 0.031 0.014 0.006 0.003 0.002
50 0.608 0.372 0.141 0.087 0.054 0.021 0.009 0.003 0.001 0.001
∞ 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Periods (n) 16% 18% 20% 22% 24% 25% 30% 40%
0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1 0.862 0.847 0.833 0.820 0.806 0.800 0.769 0.714
2 0.743 0.718 0.694 0.672 0.650 0.640 0.592 0.510
3 0.641 0.609 0.579 0.551 0.524 0.512 0.455 0.364
4 0.552 0.516 0.482 0.451 0.423 0.410 0.350 0.260
5 0.476 0.437 0.402 0.370 0.341 0.328 0.269 0.186
6 0.410 0.370 0.335 0.303 0.275 0.262 0.207 0.133
7 0.354 0.314 0.279 0.249 0.222 0.210 0.159 0.095
8 0.305 0.266 0.233 0.204 0.179 0.168 0.123 0.068
9 0.263 0.225 0.194 0.167 0.144 0.134 0.094 0.048
10 0.227 0.191 0.162 0.137 0.116 0.107 0.073 0.035
11 0.195 0.162 0.135 0.112 0.094 0.086 0.056 0.025
12 0.168 0.137 0.112 0.092 0.076 0.069 0.043 0.018
13 0.145 0.116 0.093 0.075 0.061 0.055 0.033 0.013
14 0.125 0.099 0.078 0.062 0.049 0.044 0.025 0.009
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Periods (n) 16% 18% 20% 22% 24% 25% 30% 40%
15 0.108 0.084 0.065 0.051 0.040 0.035 0.020 0.006
16 0.093 0.071 0.054 0.042 0.032 0.028 0.015 0.005
17 0.080 0.060 0.045 0.034 0.026 0.023 0. 012 0.003
18 0.069 0.051 0.038 0.028 0.021 0.018 0.009 0.002
19 0.060 0.043 0.031 0.023 0.017 0.014 0.007 0.002
20 0.051 0.037 0.026 0.019 0.014 0.012 0.005 0.001
21 0.044 0.031 0.022 0.015 0.011 0.009 0.004 0.001
22 0.038 0.026 0.018 0.013 0.009 0.007 0.003 0.001
23 0.033 0.022 0.015 0.010 0.007 0.006 0.002 0.000
24 0.028 0.019 0.013 0.008 0.006 0.005 0.002 0.000
25 0.024 0.016 0.010 0.007 0.005 0.004 0.001 0.000
30 0.012 0.007 0.004 0.003 0.002 0.001 0.000 0.000
35 0.006 0.003 0.002 0.001 0.001 0.000 0.000 0.000
40 0.003 0.001 0.001 0.000 0.000 0.000 0.000 0.000
45 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000
50 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000
∞ 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Present Value Tables
Table 2 Where:
Present Value of $1 Received Periodically for n Periods
P = [1 − (1/(1 + i)n]/i
P = Present Value Factor i = Interest Rate n = Number of Periods
Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14%
0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877
2 1.970 1.942 1.886 1.859 1.833 1.783 1.736 1.690 1.647
3 2.941 2.884 2.775 2.723 2.673 2.577 2.487 2.402 2.322
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Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14%
4 3.902 3.808 3.630 3.546 3.465 3.312 3.170 3.037 2.914
5 4.853 4.713 4.452 4.329 4.212 3.993 3.791 3.605 3.433
6 5.795 5.601 5.242 5.076 4.917 4.623 4.355 4.111 3.889
7 6.728 6.472 6.002 5.786 5.582 5.206 4.868 4.564 4.288
8 7.652 7.325 6.733 6.463 6.210 5.747 5.335 4.968 4.639
9 8.566 8.162 7.435 7.108 6.802 6.247 5.759 5.328 4.946
10 9.471 8.983 8.111 7.722 7.360 6.710 6.145 5.650 5.216
11 10.368 9.787 8.760 8.306 7.887 7.139 6.495 5.938 5.453
12 11.255 10.575 9.385 8.863 8.384 7.536 6.814 6.194 5.660
13 12.134 11.348 9.986 9.394 8.853 7.904 7.103 6.424 5.842
14 13.004 12.106 10.563 9.899 9.295 8.244 7.367 6.628 6.002
15 13.865 12.849 11.118 10.380 9.712 8.559 7.606 6.811 6.142
16 14.718 13.578 11.652 10.838 10.106 8.851 7.824 6.974 6.265
17 15.562 14.292 12.166 11.274 10.477 9.122 8.022 7.120 6.373
18 16.398 14.992 12.659 11.690 10.828 9.372 8.201 7.250 6.467
19 17.226 15.678 13.134 12.085 11.158 9.604 8.365 7.366 6.550
20 18.046 16.351 13.590 12.462 11.470 9.818 8.514 7.469 6.623
21 18.857 17.011 14.029 12.821 11.764 10.017 8.649 7.562 6.687
22 19.660 17.658 14.451 13.163 12.042 10.201 8.772 7.645 6.743
23 20.456 18.292 14.857 13.489 12.303 10.371 8.883 7.718 6.792
24 21.243 18.914 15.247 13.799 12.550 10.529 8.985 7.784 6.835
25 22.023 19.523 15.622 14.094 12.783 10.675 9.077 7.843 6.873
30 25.808 22.396 17.292 15.372 13.765 11.258 9.427 8.055 7.003
35 29.409 24.999 18.665 16.374 14.498 11.655 9.644 8.176 7.070
40 32.835 27.355 19.793 17.159 15.046 11.925 9.779 8.244 7.105
45 36.095 29.490 20.720 17.774 15.456 12.108 9.863 8.283 7.123
50 39.196 31.424 21.482 18.256 15.762 12.233 9.915 8.304 7.133
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Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14%
∞ 100.000 50.000 25.000 20.000 16.667 12.500 10.000 8.333 7.143
Periods (n) 15% 16% 18% 20% 22% 24% 25% 30% 40%
0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1 0.870 0.862 0.847 0.833 0.820 0.806 0.800 0.769 0.714
2 1.626 1.605 1.566 1.528 1.492 1.457 1.440 1.361 1.224
3 2.283 2.246 2.174 2.106 2.042 1.981 1.952 1.816 1.589
4 2.855 2.798 2.690 2.589 2.494 2.404 2.362 2.166 1.849
5 3.352 3.274 3.127 2.991 2.864 2.745 2.689 2.436 2.035
6 3.784 3.685 3.498 3.326 3.167 3.020 2.951 2.643 2.168
7 4.160 4.039 3.812 3.605 3.416 3.242 3.161 2.802 2.263
8 4.487 4.344 4.078 3.837 3.619 3.421 3.329 2.925 2.331
9 4.772 4.607 4.303 4.031 3.786 3.566 3.463 3.019 2.379
10 5.019 4.833 4.494 4.192 3.923 3.682 3.571 3.092 2.414
11 5.234 5.029 4.656 4.327 4.035 3.776 3.656 3.147 2.438
12 5.421 5.197 4.793 4.439 4.127 3.851 3.725 3.190 2.456
13 5.583 5.342 4.910 4.533 4.203 3.912 3.780 3.223 2.469
14 5.724 5.468 5.008 4.611 4.265 3.962 3.824 3.249 2.478
15 5.847 5.575 5.092 4.675 4.315 4.001 3.859 3.268 2.484
16 5.954 5.668 5.162 4.730 4.357 4.033 3.887 3.283 2.489
17 6.047 5.749 5.222 4.775 4.391 4.059 3.910 3.295 2.492
18 6.128 5.818 5.273 4.812 4.419 4.080 3.928 3.304 2.494
19 6.198 5.877 5.316 4.843 4.442 4.097 3.942 3.311 2.496
20 6.259 5.929 5.353 4.870 4.460 4.110 3.954 3.316 2.497
21 6.312 5.973 5.384 4.891 4.476 4.121 3.963 3.320 2.498
22 6.359 6.011 5.410 4.909 4.488 4.130 3.970 3.323 2.498
23 6.399 6.044 5.432 4.925 4.499 4.137 3.976 3.325 2.499
24 6.434 6.073 5.451 4.937 4.507 4.143 3.981 3.327 2.499
25 6.464 6.097 5.467 4.948 4.514 4.147 3.985 3.329 2.499
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Periods (n) 15% 16% 18% 20% 22% 24% 25% 30% 40%
30 6.566 6.177 5.517 4.979 4.534 4.160 3.995 3.332 2.500
35 6.617 6.215 5.539 4.992 4.541 4.164 3.998 3.333 2.500
40 6.642 6.233 5.548 4.997 4.544 4.166 3.999 3.333 2.500
45 6.654 6.242 5.552 4.999 4.545 4.166 4.000 3.333 2.500
50 6.661 6.246 5.554 4.999 4.545 4.167 4.000 3.333 2.500
∞ 6.667 6.250 5.556 5.000 4.545 4.167 4.000 3.333 2.500
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Summary & Resources
Chapter Summary Capital investment decisions are critical to the �irm’s long-term success. The relevant data for making investment decisions are incremental cash �lows, using criteria established in Chapter 9. Capital investments generally have multiperiod cash �lows, requiring the use of the time value of money. The opportunity cost of cash to be received in the future can be a signi�icant variable in measuring returns.
Four methods are discussed to evaluate the cash �lows. Two methods use present values for all cash �lows:
1. Net present value, where a rate of return is set and decisions are made based on whether the net present value is positive or negative
2. Internal rate of return, where the rate of return is found by setting the initial investment equal to the present value of future net cash in�lows
Two other methods discussed that do not use the time value of money are the payback period and the accounting rate of return methods.
Rarely are funds available to �inance all attractive projects. Projects are selected based on rankings of their relative attractiveness. Taxes on pro�its from capital investments must be calculated and do affect the ROR of projects. The cost of capital is often used to develop a minimum acceptable rate of return.
Computational issues such as uneven lives, working capital needs, incremental investment analysis, and in�lationary impacts on forecasts are examined.
Key Terms
accelerated depreciation Depreciation methods that charge larger amounts of depreciation in the early years of an asset’s life and relatively smaller amounts to the later years.
accounting rate of return (ARR) method A method of calculating a rate of return on a capital investment project in which the average annual net income from the project is divided by the average book value of the investment.
annuity A series of equal cash �lows received or paid over equal time intervals.
capital budgeting The process of evaluating, selecting, controlling, and �inancing capital investments.
capital investment The cash out�low needed to acquire long-term assets or to obtain access to cash in�lows in future periods.
capital investment decisions A decision of whether to acquire assets with an expected life in excess of one year.
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compound interest Interest on the principal plus the previously earned interest.
cost of capital The weighted average cost, expressed as a percentage, of obtaining long-term �inancial resources for an organization.
cutoff rate The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.
desired rate of return A target rate of return on capital investments as selected by top management for determining the minimum rate of return acceptable.
discount factor The multiplier used to determine the present value.
discount rate The interest rate used in reducing a future amount to a present value.
discounted value The value now for an amount to be received in the future; the amount to be paid now to settle a debt that becomes due in the future.
discounting The process of reducing a future amount to a present value using a speci�ic interest rate.
effective interest rate The actual rate of interest earned in one year, regardless of the compounding period associated with the stated interest rate.
face value The principal amount due at maturity.
future value The compound amount of any principal plus interest at the end of a speci�ic time period, using a speci�ic interest rate.
going-concern assumption Can generally be made if the business is expected to continue past the timeframe cutoff.
hurdle rate The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.
in�lation General increases in the prices of goods and services.
internal rate of return (IRR)
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The rate of return that equates the present value of the future cash in�lows with amount of the capital investment outlay.
marginal tax rate The tax rate that would be applied to the next dollar of taxable income.
market rate of interest The effective yield that is currently earned on similar types of �inancial instruments.
minimum acceptable rate of return The lowest rate of return that a capital investment project can earn and still be approved.
net initial investment The net out�low of cash, a commitment of cash, or the sacri�ice of an in�low of cash that occurs at the beginning of a project.
net present value The difference between the investment and the present value of future returns discounted at a speci�ic interest rate.
net present value method The capital investment evaluation method that discounts future cash �lows to arrive at present values.
payback period The amount of time required to recover the net initial investment.
payback period method A quick way to evaluate potential capital investments by asking only how long it will take to recover the net initial investment.
payback reciprocal The percentage obtained by dividing the payback period into 1.
premium Amount in excess of the principal or face amount that an investor will pay for a �ixed-rate instrument because the coupon rate is higher than the current market rate.
present value The value now for an amount to be received in the future; the amount to be paid now to settle a debt that becomes due in the future.
pro�itability index The ratio of the present value of net cash in�lows divided by the net initial investment.
required rate of return The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.
target rate of return The minimum acceptable rate of return set by management that a capital investment project can earn and still be approved.
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tax shield The amount of taxes saved because of the tax deductibility of an expenditure.
time value of money The concept that a future sum of money is of less value than the same dollar amount today.
weighted-average cost of capital The cost of debt capital and equity capital weighted by their respective proportions in the total long- term capital structure.
working capital Current assets minus current liabilities.
yield to maturity The actual rate of interest earned in one year regardless of the compounding period associated with the stated interest rate.
Problem for Review Pam Williams, owner of a self-storage business, has just received an offer that is worth $600,000 after taxes for the storage buildings. She is interested in another investment opportunity that can probably yield an annual discounted return of 15% after taxes. The storage business is expected to continue to yield an annual cash in�low, before taxes, of $170,000 for a period of 15 years. The book value of the storage buildings is $660,000, and straight-line depreciation is used for tax purposes. Zero salvage value is predicted. A 40% tax rate applies.
Question:
Should the offer to sell the storage business be accepted? Explain.
Solution:
First, solve for the net aftertax cash �low if the business is kept:
Cash �low before taxes $170,000
Minus depreciation (44,000) ($660,000 ÷ 15 years)
Taxable cash �low $126,000
Taxes (40%) (50,400)
Aftertax cash �low $ 75,600
Plus depreciation 44,000
Net aftertax cash �low $119,600
Investment Life of the Project
Year: 0 1 15
Purchase offer ($600,000)
Net cash �low $119,600 . . . $119,600
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Investment Life of the Project
PV – Years 1 to 15 699,301
(15%, 15 years): $119,600 × 5.847
NPV $ 99,301
Since the PV of the �lows is greater than the offer of $600,000, the business should not be sold.
Questions for Review and Discussion 1. Why is timing important in a capital investment decision? What is meant by the time value of
money? 2. Could the net present value method and the internal rate of return use the same interest rate?
Explain. 3. Are the returns from an investment the same as the accounting pro�it? Explain. 4. What are the advantages and disadvantages of the accounting rate of return method? 5. Explain the difference between the internal rate of return method and the net present value
method. 6. How can project rankings using the internal rate of return and the pro�itability index differ? 7. Explain the tax shield. Tie this explanation to the comment: “Depreciation is a source of cash.” 8. Why is an initial investment in additional inventory different than an investment in machinery?
Explain the difference in cash �lows. 9. What is the advantage of accelerated depreciation over straight-line depreciation in a capital
investment decision? 10. Knowing the cost of capital is a necessary part of present value analysis. What does it represent?
Explain one way to measure it. 11. How can in�lation can be incorporated into capital investment analysis? 12. What problem arises if alternative investments have different useful lives? Identify at least one
solution.
Exercises 10-1. Determining the Life of an Investment. Arborvista Electronics is considering expanding its business by adding one more store in Amsterdam. The building and its operating contents will cost 1 million euros and generate about €200,000 in cash in�lows each year after taxes. The manager, Sarah Keren, feels the investment should not be made unless the store realizes a 10% rate of return on the cash invested.
Question:
For how many years must the store operate to earn a 10% return?
10-2. Four Methods. Avondale Company purchased a farm tractor for $100,000. The cash in�low from using the tractor is expected to be $30,000 per year for eight years. Avondale uses a 15% cutoff rate.
Question:
Use straight-line depreciation where needed, and ignore taxes. What is the payback period, the estimated IRR, the NPV, and the ARR?
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10-3. Payback Method. Elbein Company purchased a machine for $125,000 and will depreciate it on a straight-line basis over a �ive-year period with an aftertax salvage value of $15,000. The related cash operating savings, before income taxes, is expected to be $50,000 a year.
Questions:
1. Find the payback period, ignoring taxes. 2. Assume that Elbein’s effective income tax rate is 40% and that salvage value is ignored when
calculating depreciation. What is the payback period?
10-4. Different Capital Investment Methods. Warrensville Center Company plans to acquire equipment costing $600,000. Depreciation on the new equipment would be $100,000 each year for six years. The annual cash in�low before income tax from this equipment has been estimated at $210,000. The tax rate is 40%.
Questions:
1. Find the payback period. 2. Find the ARR using the average investment. 3. Find the NPV if Warrensville’s minimum acceptable rate of return is 16%. 4. Estimate the IRR from Table 2 (e.g., between 10 and 12%).
10-5. Investments With Uneven Cash Flows. Glenmont Consolidated has data on two $100,000 investment opportunities. With only $100,000 in cash available, the owners must decide which is the better opportunity. The controller has gathered the following data:
Investment 1: $30,000 of cash in�low for each of the �irst three years and $90,000 for each of the last three years.
Investment 2: $80,000 of cash in�low in the �irst year, $60,000 in the next four years, and $40,000 in the sixth year.
Question:
If a 14% ROR is needed, which investment will be preferred? Why?
10-6. Equipment Replacement. By replacing an old refrigeration unit, Sheila Marshall of Victoria Estates Produce in Liverpool, U.K., thinks that sales from the greater capacity will increase by £100,000 per year and that cash operating costs will decline by £60,000 per year. The new refrigerator will cost £350,000. Her variable contribution margin is 40%. The old equipment is fully depreciated but can be sold for £8,000. The new refrigerator will use straight-line depreciation, has a �ive-year life, and is expected to have a salvage value of £40,000. Ignore taxes.
Question:
Format the cash �lows for the refrigeration unit proposal.
10-7. Net Returns and Discounted Rate of Return. The Eastway Company is considering new equipment that can reduce personnel costs by an estimated $60,000 a year. The new equipment is also expected to generate annual intangible customer service bene�its of $70,000. The new equipment will cost $400,000 and will be depreciated on a straight-line basis for tax purposes. The asset will have no
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residual value at the end of ten years, the estimated life of the equipment. Income tax is estimated at 40%.
Questions:
1. Determine the annual net cash in�low from the proposed investment. 2. Will the investment earn an 18% aftertax rate of return? 3. Comment on the NPV.
10-8. Uneven Cash Flows. The following projects of YABI Enterprises each require an $80,000 investment.
Cash in�lows:
Project
98-A4 98-G3 98-K1 98-P6 98-S4
Year 1 $20,000 $10,000 $40,000 $60,000
Year 2 20,000 10,000 30,000
Year 3 20,000 15,000 40,000 10,000
Year 4 20,000 15,000 $160,000 (60,000)
Year 5 20,000 25,000 40,000
Year 6 20,000 25,000 40,000
Year 7 20,000 30,000 40,000
Year 8 20,000 30,000 80,000
Questions:
1. For each project, �ind the payback period. 2. For each project, �ind the ARR. 3. For each project, �ind the NPV (using a 15% discount rate).
10-9. New Business. Wrenford Co. purchased a new machine for $50,000 to expand capacity. Sales are expected to increase by 20%. The only additional �ixed expense is the depreciation on the new machine (straight-line over �ive years with no salvage value). The income statement for the past year is:
Sales $300,000
Variable expenses (180,000)
Fixed expenses (100,000)
Net income before taxes $20,000
Taxes (40%) (8,000)
Net income after taxes $12,000
Questions:
1. What is the expected annual aftertax cash in�low from the new machine? 2. Find the NPV using a hurdle rate of 15% and the payback period.
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10-10. Equipment Replacement. By replacing present equipment with more ef�icient equipment, Belvoir Company estimates that cash operating costs can be reduced by $65,000 a year. In addition, increased sales volume can result in a larger contribution margin of $25,000 a year without considering the ef�iciency savings. Depreciation of $50,000 per year will be taken on new equipment. Depreciation on present equipment is $10,000 per year. The income tax rate is 40%.
Question:
What is the estimated incremental annual aftertax cash in�low on this investment?
10-11. Find the Missing Values. The table below compares six projects for Cedar Corporation, but it is incomplete.
Internal Rate of Return
Initial Investment
Life of the Project
Annual Net Cash In�low Percentage
Present Value Factor (Table 2)
Project 1
$118,932 6 years $34,000 ? % ?
Project 2
? 5 years 12,000 ? % 3.605
Project 3
68,000 15 years ? 16 % ?
Project 4
84,750 ? years 15,000 12 % ?
Project 5
? ? years 20,000 20 % 2.991
Project 6
111,925 20 years ? 8 % ?
Question:
Provide the missing values for these projects.
10-12. Gains and Losses on Disposal. Hinsdale Enterprises is considering the purchase of a new machine for $200,000. It would have a �ive-year life. The company would sell for $50,000 its old machine, which cost $180,000 and has a book value of $20,000. Gains, losses, and pro�its have a tax rate of 40%. The new machine will require about $30,000 less in raw materials inventory to operate.
Question:
What is the net cash out�low for the investment?
10-13. Comparing Alternatives. Superior Company is considering a new popper for one of its portable caramel popcorn stands. The analysis is narrowed to the “Bang” or the “Pow.” Information on the two devices is:
Bang Pow
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Bang Pow
Purchase price $90,000 $60,000
Annual cash in�lows 34,000 24,000
Salvage value in 5 years 8,000 5,000
Useful life 5 years 5 years
Either device will do the job equally as well. Superior uses a 16% cost of capital. Ignore taxes.
Questions:
1. Which machine has the higher NPV? Is this a proper basis for making this investment decision? 2. Using the pro�itability index, which machine is more attractive? 3. If Superior has $180,000 to invest in popping machines, what should it do? Why?
10-14. In�lation and Investment Analysis. Lavista Health Spas is evaluating an expansion of its existing facilities this fall. The proposal calls for a six-year building rental contract at $10,000 a year. Equipment purchases and facility improvements are expected to cost $60,000. Straight-line depreciation is used. Other cash operating expenses are estimated at $25,000 annually. Based on past experience, the company thinks new revenues should be $50,000 annually. Lavista Health Spas will not expand unless the project covers its 14% cost of capital. The company’s effective tax rate is 40%.
In�lation is a concern. The controller, Evie Weinreich, thinks that revenues and cash expenses will in�late by 5% per year. Round the discount rate to the next highest rate available in Table 2.
Question:
Using NPV, suggest whether the expansion project should be adopted.
10-15. Multiple Projects. Marvin Gross manages a temporary hiring service and is considering several investments for his business. He expects a 16% ROR. Ignore taxes. The basic facts about three opportunities are:
a. More of�ice space. The space will cost $400,000, earn a net cash in�low of $120,000 per year after taxes, last 5 years, have no salvage value, and be depreciated using straight-line.
b. An opportunity to run a training program. The project will earn $50,000 per year and have a life of �ive years.
c. New computer equipment. Marvin thinks the cost of the equipment needed is $60,000. The expected cash in�low per year is $12,000.
Questions:
1. What is the new present value of Investment A (more of�ice space)? 2. What is the most Marvin should pay for upfront preparations for Investment B (an opportunity
to run a training program) and still meet his ROR expections? 3. How long must the new computer equipment in Investment C last (in years) to meet Marvin’s
ROR expectations?
10-16. Unequal Lives. Having given the matter some thought, you decide that you would be equally happy buying and driving any of the following cars:
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a. A Supreme Deluxe and trading every sixth year. b. A Premium Fairmont and trading every third year. c. An Economy Delight and trading every second year.
You have decided to base your decision on the present value of the expected future costs. You have predicted your costs as follows:
Supreme Deluxe Premium Fairmont Economy Delight
Original cost $30,000 $20,000 $15,000
Market value at trade in time 8,000 8,000 8,000
Annual cash operating costs 2,400 2,000 1,500
Overhaul, fourth year 2,000 0 0
Overhaul, second year 0 1,000 0
You believe that you will stick with this approach for at least six years. Your minimum desired rate of return is 10%. Ignore taxes.
Question:
Select the alternative that promises the greatest �inancial advantage.
Problems 10-17. Relevant Costs. Aussie Auto Wash Company has just installed a special machine for washing cars in its Perth outlet. The machine cost A$20,000. Its operating costs, based on a yearly volume of 100,000 cars, total A$15,000, exclusive of depreciation. After the machine has been used one day, a salesperson offers a different machine that promises to do the same job at a yearly operating cost of A$9,000, exclusive of depreciation. The new machine will cost A$24,000, installed. The “old” machine is unique and can be sold outright for only A$8,000, less A$2,000 removal cost. The old and new machines will have a four-year useful life and no residual value. Sales, all in cash, will be A$150,000 per year, and other cash expenses will be A$110,000 annually, regardless of this decision.
Questions:
1. Ignore taxes. Calculate net income for each of the four years assuming that the new machine is not purchased and then assuming that it is purchased. Sum the net incomes for the four years for each alternative. What should be done?
2. Ignore taxes, and consider the time value of money. If a 15% return on investment is desired, what should be done?
10-18. Value of a Business. Miramar, Inc., makes and sells candy in large lots for other �irms that package and sell the candy under various brand names. The �irm could acquire a small candy exporting �irm that has sold about 800,000 boxes of candy annually to Korea and Japan. To operate the �irm, Miramar would have to hire specialized sales reps for $1,200,000 annually, including travel and entertainment expenses. Additional packaging machinery costing $1,600,000 must be acquired. The machinery would last �ive years, have no salvage value, and be depreciated on a straight-line basis.
Other data are as follows:
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a. Variable costs are $0.80 per box. b. Selling price on the export business is $4 per box. c. Annual cash costs of operating the new machinery are $320,000. d. Tax rate is 40%. e. Cost of capital is 16%.
Question:
On the basis of this information and a �ive-year time horizon, what is the most Miramar should pay for this investment opportunity?
10-19. Investment Returns and Sales Volume. Judy Yank, whose uncle whispered “plastics” into her ear soon after she graduated from college years ago, founded Maple Leaf Plastics, Inc. Judy is considering an investment of $2,000,000 in a new product line. Depreciation of $200,000 is to be deducted in each of the next ten years. Salvage value is estimated at zero. A selling price of $50 per unit is decided upon; unit variable cost is $30. The sales division believes that a sales estimate of 50,000 units per year is realistic. Joseph Samuels, the controller, states that a solid market exists for only 20,000 units a year. Projects must meet a minimum rate-of-return requirement of 15%. Income tax is estimated at 40% of income before tax.
Questions:
1. Evaluate the project using each of the sales volume estimates. Use the NPV method. 2. At what volume will the project earn exactly a 15% return?
10-20. Sell or Use Equipment. An offer of $130,000 has been received for equipment that Lancashire Products has been using to make certain parts. The equipment is fully depreciated but can be used for �ive more years. After �ive years, it is expected to have little, if any, value.
The variable cost of producing the parts is $10 per unit. A total of 10,000 units are needed each year. If the parts are not manufactured, the company must buy them from an outside supplier at a cost of $15 per unit. Also, if the parts are not produced, the space occupied by the equipment can be rented for $12,000 per year. Income tax is estimated at 40% of the income before tax. The company uses a 12% hurdle rate on this type of investment.
Question:
Prepare a recommendation for Lancashire’s president on the proposed equipment sale.
10-21. Expanding a Product Line. Sutherland Company makes of�ice equipment, such as tables, desks, computer equipment consoles, and work tables. The sales manager, Blossom Newman, is trying to decide whether to expand the relatively new computer equipment console product line. The average desk will sell for $300 and has a variable cost of $140 per unit. Volume is expected to be 4,000 units per year for �ive years. To make the desks, the �irm will have to buy additional machinery that will cost $900,000, has a �ive-year life, and has a $100,000 salvage value net of taxes. Straight-line depreciation is used, and salvage value is ignored in depreciation calculations. Additional �ixed cash operating costs will be $200,000 per year. Sutherland has a 40% tax rate, and its cost of capital is 16%.
Questions:
1. Using NPV, determine whether the computer console line should be expanded. 2. Compute the payback period.
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3. Determine the approximate IRR that the �irm expects to earn on the investment. Ignore salvage value.
10-22. Equipment Replacement Concerns. The molding department of Stonehaven, Inc. has been investigating the acquisition of new equipment costing $100,000. Cash savings before income taxes from the use of this equipment are estimated to be $40,000 per year for ten years. At the end of �ive years, the new equipment must be overhauled at a cost of $35,000. The new equipment will have no salvage value after ten years. The new machine would replace an old machine that would need a $30,000 overhaul now, and again in �ive years, if it is not replaced. The old machine is fully depreciated but can still function. To remove the old machine, environmental precautions (mainly an asbestos problem) will cost the �irm $40,000. The rate used in evaluating investments is 10%. The income tax rate is 40%. Stonehaven uses straight-line depreciation.
Questions:
1. Calculate the NPV. Make a recommendation. 2. If the asbestos will need to be removed within two years anyway, how does this impact your
answer to Part 1? Comment.
10-23. Ranking Investment Alternatives. Grosvenor Industries has designated $1.2 million for capital investment expenditures during the upcoming year. Its cost of capital is 14%. Any unused funds will earn the cost of capital rate. The following investment opportunities along with their required investment and estimated net present values have been identi�ied:
Project Net Investment NPV Project Net Investment NPV
A $200,000 $22,000 F $250,000 $30,000
B 275,000 21,000 G 100,000 7,000
C 150,000 6,000 H 200,000 18,000
D 190,000 (19,000) I 210,000 4,000
E 500,000 40,000 J 250,000 35,000
Questions:
1. Rank the projects using the pro�itability index. Considering the limit on funds available, which projects should be accepted?
2. Using the NPV, which projects should be accepted, considering the limit on funds available? 3. If the available investment funds are reduced to only $1,000,000:
a. Does the list of accepted projects change from Part 2? b. What is the opportunity cost of the eliminated $200,000?
10-24. Comparing Unequals. Data relating to three possible investments are as follows:
X Y Z
Cost $34,000 $25,000 $75,000
Annual cash savings 8,111 7,458 14,011
Useful life - years 10 5 20
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Questions:
1. Ignoring taxes, rank the investments according to their desirability using the payback period, IRR, NPV with a discount rate of 12%, and pro�itability index.
2. Comment on the impact that the unequal lives have on the rankings. 3. Comment on the impact that the unequal investments have on the rankings.
10-25. Equipment Replacement. Houston Mill Company owns a specialty truck with the following attributes:
Book value $55,000
Current market value 40,000
Expected salvage value (after �ive-year remaining useful life) 0
Annual depreciation expense, straight-line method 11,000
Annual cash operating costs 18,000
The �irm’s cost of capital is 14%, and a 40% tax rate is applicable to all taxation items.
The �irm plans to replace the truck with one costing $80,000 and having an expected salvage value net of taxes of $5,000, annual cash operating costs of $3,000, and a useful life of �ive years. Straight-line depreciation of $16,000 per year would be taken on the new truck. Additionally, because the new truck is more dependable, the �irm could reduce its repair parts inventory by $15,000.
Question:
Determine whether the new truck should be bought. Use whatever capital investment methods you believe will best present the facts to Houston Mill’s management.
Case: Stewart Machining
Stewart Machining purchased a new grinding machine one year ago at a cost of $68,000. The machine has been working very satisfactorily, but the shop manager, Jack Tudy, has just received information on an electronically controlled grinder that is vastly superior to the machine that he now uses. While both machines can meet all required existing quality standards and tolerances, the new machine’s quality potential can far exceed the old machine’s capabilities. Comparative data on the two machines follow:
Present Machine Proposed New Machine
Purchase cost new (including installation costs) $70,000 $90,000
Salvage value today 35,000
Salvage value at end of life 5,000 10,000
Annual costs to operate 95,000 75,000
Estimated useful life when new 7 years 6 years
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Jack makes a few quick computations and exclaims, “Wow! We need that machine and its capabilities. But, no way can I sell it upstairs. When the boss sees the loss on the old machine, he’ll have kittens.” He’s looking at this:
Remaining book value of the old machine $60,000
Salvage value now of the old machine 35,000
Net loss from disposal (before tax deduction of the loss) $25,000
Stewart Machining uses straight-line depreciation and ignores salvage value in its depreciation calculations. Sales from the grinding operation are expected to remain unchanged at $300,000 per year inde�initely. Other cash costs of the grinding operation total $80,000 annually. The corporate tax rate is 40%.
Questions:
1. Prepare summary income statements covering the next six years for the grinding operation, assuming that:
a. The new machine is not purchased b. The new machine is purchased
2. What do you recommend? Show any needed additional analysis. 3. Comment on the reality of the $25,000 loss Jack has calculated. Can or should this be
ignored? 4. Comment on why introducing new technology is dif�icult to justify to management. 5. Develop a policy that would encourage investment in new technology and yet would
avoid wasting scarce capital investment money.