Module 2
Cost Analysis and Estimation
a. Differential Analysis
We start by describing the general approach of differential analysis and
identifying decision situations in which it is appropriate. We then illustrate its use with
two general applications, pricing and production decisions. Every decision that a manager
makes requires comparing one or more proposed alternatives with the status quo. (If there
is only one alternative and the status quo is unacceptable, there really is no decision to
make.) The task is to determine how costs in particular and profi ts in general will be
affected if one alternative is chosen over another. This process is called differential
analysis. Although decision makers are usually interested in all differences between
alternatives, including fi nancial and nonfi nancial ones, we focus on fi nancial decisions
involving costs and revenues. Differential analysis is used for both short-run decisions,
such as the ones we discuss in this, and long-run decisions, such as those discussed in the
Appendix to the book. Generally, when the term short run is applied to decision horizons
over which capacity will be unchanged, one year is used for convenience.
One important distinction between short-run and long-run decisions is whether the
timing of cash receipts and cash disbursements is important, that is, whether the time
value of money is a signifi cant factor. Short-run decisions affect cash fl ow for such a
short period of time that the time value of money is immaterial and hence ignored. Thus,
the amount of cash fl ows is important for short-run analysis, but the timing of the fl ows
is assumed to be unimportant. If an action affects cash fl ows over a longer period of time
(usually more than one year), the time value of money is considered, as discussed in the
Appendix to this book.
Decisions by companies to enter markets in China involve long-run differential
analysis. Decisions by automobile companies to offer incentives and rebates to boost
sales are generally made as if they are short run (companies often discover, however, that
these decisions have long-run pricing implications). Differential costs change in response
to alternative courses of action. Both variable costs and fi xed costs may be differential
costs. Variable costs are differential when a decision involves possible changes in
volume. For example, a decision to close a plant reduces variable costs and usually some
fi xed costs. All of the affected costs are termed differential. On the other hand, if a
machine replacement does not affect either the volume of output or the variable cost per
unit, variable costs are not differential.
An important category of costs to identify when making decisions includes costs
that were incurred in the past and cannot be changed regardless of the decision made.
These costs are called sunk costs and are not relevant for the decision. By defi nition,
they cannot be differential because they will be the same for all decisions. Examples of
sunk costs include material and equipment already purchased, for which there are no
markets for used or preowned goods. As the examples in this are presented, you will fi nd
that differential analysis requires examining the facts for each option relevant to the
decision to determine which costs will be affected. Differential and variable costs have
independent meanings and applications and should not be considered interchangeable.
Although we are focusing on differential costs, the information presented to
management can show the detailed costs that are included for making a decision, or it can
show just the differences between alternatives, the first two columns show the total
operating profi t under the status quo and the alternative. This part of the presentation is
referred to as the total format. The third column shows only the differences; this
presentation is called the differential format. An advantage of the total format is that, fi
rst, all the information is available so it is easy to derive the differential format if desired.
Second, the total format provides information to managers about the total resources
required if one alternative is chosen. The advantage of the differential format is that it
highlights the differences between alternatives.
The differential approach is useful for many decisions that managers make about
pricing because it provides information about the likely impact of these decisions on
profit. We learn in economics that prices are determined by supply and demand. Why do
we study pricing decisions in cost accounting? Managers make pricing decisions in part
to determine whether they wish to participate in the market, that is, whether to make their
products and services available. This is where the supply curve comes from. Thus, we do
not say that managers (or fi rms) set the price; we say that they decide at what price they
would be willing to enter the market.
In making pricing decisions, it is tempting to consider all costs incurred by the fi
rm, divide them by total volume, and consider the resulting number a minimum price.
The terms full cost or full product cost describe a product’s cost that includes both the
variable costs of producing and selling the product and a share of the organization’s
fixed costs. Sometimes decision makers use these full costs, mistakenly thinking that they
are variable costs, and fall victim to the full-cost fallacy. For example, during the fi rst
year of business an employee of U-Develop claimed that accepting a special order from a
customer for 40 cents a copy would be a mistake. “Since our variable costs are 36 cents
per print and our fi xed costs are $1,500 per month, our total costs for the month without
the special order are $5,100 for 10,000 prints. That is 51 cents per print ($5,100 ÷
10,000), which is more than the 40 cents per copy offered by the customer. We’d be
losing 11 cents per print!”
By considering fi xed costs in the analysis, the employee might be including
irrelevant information. If the fi xed costs will be incurred whether the special order is
accepted or rejected, these costs should not bear on the decision. Instead, the employee
should focus on the variable costs of 36 cents per print in deciding whether to accept the
special order from the customer. This is a common mistake in short-run decisions. All
costs must be covered in the long run or the company will fail. In the short run, it will be
profi table to accept the order because the price of 40 cents per print exceeds variable
costs of 36 cents per print, assuming that this price does not affect other business at the
company. Full product costs serve a wide variety of important purposes, but they are
generally not relevant to the type of short-run operating decision described in this
example.
The differential approach particularly helps in making decisions regarding special
orders where the order will not affect other sales and is not expected to recur.
Determining which costs are relevant depends on the decision being considered. Each
alternative is stated as a branch of a decision tree and then the value of each alternative is
determined. Finally, the alternative with the highest value is chosen.
U-Develop now has a machine in a stand-alone kiosk where
customers can bring various digital photo media (cartridges, sticks, etc.) and make paper
prints of their pictures. The machine is usually idle about two hours each day. The art
teacher at the local high school asks U-Develop to allow the students in the photography
club to come in during idle periods to print pictures taken for a school contest. U-Develop
has idle capacity adequate for this job, which will not affect other sales. The teacher, who
has a limited budget, asks Jamaal Kidd, the U-Develop owner, for a special price of 40
cents a print for the 500 pictures the students have taken. The regular price is 50 cents.
The best economic decision is to accept the order because the company will gain
$100 from it. Fixed costs are not affected by the decision because they are not differential
in this situation. Therefore, they are not relevant. The differential approach to pricing
works well for special orders, but some criticize its use for pricing a firm’s regular
products. Critics suggest that following the differential approach in the short run leads to
underpricing in the long run because the contribution to covering fixed costs and
generating profits will be inadequate.
A second criticism of the differential approach is that it may be diffi cult to sell a
product to a customer at a reduced price on a particular day when capacity utilization
happens to be low if that customer might return on another day when capacity utilization
happens to be high. For example, many analysts worry that the U.S. auto industry’s cycle
of discounting cars will be diffi cult to break, even after capacity is cut to be more in line
with demand. We see similar behavior in the airline industry, where customers
strategically withhold purchases until the last minute, expecting carriers to discount fares.
The root of the problem is that pricing is dynamic, not just a static optimization of profi ts
during the period of low demand.
Others respond to these criticisms in two ways. First, the differential approach
does lead to correct short-run pricing decisions. Once the fi rm has set plant capacity and
incurred fi xed costs, the fi xed costs become irrelevant to the short-run pricing decision.
Clearly, airlines understand this with their discount fares. The fi rm must attempt to set a
price that at least equals the differential, or variable, costs.
Second, in both the short and long runs, the differential approach indicates only
the minimum acceptable price. The fi rm always can charge a higher amount, depending
on its customers and competitors. Some of these issues are pursued in this questions and
exercises. The U-Develop example also illustrates a limitation in using fi nancial analyses
for many business decisions. There are several benefi ts that are diffi cult to quantify and
are, therefore, excluded from the analysis. By offering this discount to the school club,
Jamaal is encouraging an interest in photography and contributing to the development of
the students. These are factors that Jamaal can and should consider before deciding
whether to accept the offer.
Most fi rms rely on full-cost information reports when setting prices. Full cost is
the total cost to produce and sell a unit; it includes all costs incurred by the activities that
make up the value chain. Typically, the accounting department provides cost reports to
the marketing department, which then adds appropriate markups to determine benchmark
or target prices for all products the fi rm normally sells. This approach is often called
cost-plus. Using full costs for pricing decisions can be justifi ed in three circumstances:
When a fi rm enters into a long-term contractual relationship to supply a product,
most activity costs depend on the production decisions under the long-term contract.
Therefore, full costs are relevant for the long-term pricing decision. Many contracts for
developing and producing customized products and those entered into with governmental
agencies specify prices as full costs plus a markup. Prices set in regulated industries such
as electric utilities also are based on full costs.
Firms initially can set prices based on full costs and then make short-term
adjustments to refl ect market conditions. Accordingly, they adjust the prices of the
product downward to acquire additional business. Conversely, when demand for their
products is high, fi rms recognize the greater likelihood that the existing capacity of
activity resources is inadequate to satisfy all of the demand. Accordingly, they adjust the
prices upward based on the higher incremental costs when capacity is fully utilized.
When used in pricing decisions, the differential costs required to sell and/or
produce a product provide a fl oor. In the short run, differential costs may be very low, as
when selling one additional seat on an already scheduled airline fl ight or allowing one
more student into an already scheduled college course. In the long run, however,
differential costs are much higher than in the short run. For an airline, long-run
differential costs include the costs to buy and maintain the aircraft and to pay crew
salaries, landing fees, and so forth. In the long run, these costs must be covered. To
simplify this type of analysis, the full product costs to make and/or sell a product are
often used to estimate long-run differential costs. Hence, a common saying in business is:
I can drop my prices to just cover variable costs in the short run, but in the long run, my
prices have to cover full product costs.
To this point, we have discussed differential analysis and its usefulness for short-
run and long-run pricing decisions. Several other approaches are used, however, to
establish prices based on costs. In addition to the cost-plus or full-cost approach
described earlier, two approaches—life-cycle product costing and pricing and target
costingfrom target pricing—are discussed here. In general, these approaches are
especially useful in making long-run pricing decisions. Life-Cycle Product Costing and
Pricing The product life cycle covers the time from initial research and development to
the time at which support to the customer is withdrawn. For pharmaceuticals, this time
span may be several years. For some electronic goods, it may be less than one year.
Managers estimate the revenues and costs for each product from its initial
research and development to its fi nal customer support. Life-cycle costing tracks costs
attributable to each product from start to fi nish. The term cradle-to-grave costing
conveys the sense of capturing all life-cycle costs associated with a product. Life-cycle
costs provide important information for pricing. For some companies, such as Merck and
Pfi zer in pharmaceuticals and Boeing and Airbus in aircraft, the development period is
relatively long, and many costs are incurred prior to manufacturing.
A product life-cycle budget highlights for managers the importance of setting
prices that will cover costs in all value-chain categories, not just in the production
through customer service categories. To be profi table, companies must generate enough
revenue to cover costs incurred in all categories of the value chain. Life-cycle costing is
becoming increasingly important as environmental regulations that require fi rms to “take
back” and dispose of the product at the end of the life cycle are adopted. These
regulations give literal meaning to the phrase “cradle-to-grave.” The costs of recycling
used products are especially important for certain companies— for example, refrigerator
manufacturers, such as Whirlpool and GE, and producers of toner cartridges for printers,
such as Hewlett-Packard and Epson. These fi rms need to consider these additional costs
at the end of the useful life of the product in making pricing decisions.
As described in the Business Application feature, Take-Back Laws in Europe,
these laws make the costs of recycling and disposal of products the responsibility of the
manufacturer. This, in turn, can affect product design as manufacturers trade off the cost
of manufacture and disposal. For example, someFmaterials may be easier to work with in
manufacturing the product but are more diffi cult to dispose of or recycle.
Target Costing from Target Pricing Simply stated, target costing is the concept of
“price-based costing” instead of “cost-based pricing.” A target price is the estimated price
for a product or service that potential customers will be willing to pay. A target cost is the
estimated long-run cost of a product or service whose sale enables the company to
achieve targeted profi t. We derive the target cost by subtracting the target profi t from
the target price. For instance, assume that Dell can sell an MP3 player for $200 and wants
profi ts of at least $20; this means that Dell needs to fi nd a way to limit costs to $180.
Target costing is widely used by companies including Mercedes Benz and Toyota in the
automobile industry, Panasonic and Sharp in the electronics industry, and Apple and
Toshiba in the personal computer industry.
b. Legal Issues Relating to Costs and Sales Prices
Laws in many countries, including the United States, require managers to take
costs into account when they set sales prices. For example, managers will face charges of
predatory pricing if they set prices below costs. Predatory pricing is the practice of setting
the selling price of a product at a low price with the intent of driving competitors out of
the market or creating a barrier to entry for new competitors. For the practice to be
predatory, managers must set the price below cost and intend to harm competition. In
many countries, including the United States, predatory pricing is anticompetitive and
illegal under antitrust laws.
At fi rst, you might wonder what is wrong with setting prices low and intending to
harm competition. It sounds like free enterprise, and setting prices low is normally good
for consumers. The legal problem arises when prices are set suffi ciently low to drive
competitors out of the market or keep competitors out of the market. With little
competition left in the market, the company that has set predatory prices is able to act like
a monopolist and hit consumers with high prices. From the consumers’ point of view,
they benefi t in the short run when the “predators” set prices low, but these same
consumers suffer in the long run when they face monopoly prices.
One usually fi nds evidence of predatory pricing when larger companies drive out
smaller companies. For example, a small airline recently added several routes to compete
with one of the large, international airlines. In response, the large airline dropped its
prices below those of the small airline. The small airline went bankrupt and stopped fl
ying those routes. The large airline then raised its prices. To qualify as predatory pricing,
the “predator” must drop its prices below costs. In theory, pricing below marginal costs is
irrational because the marginal revenue from each unit sold is less than the marginal cost.
Why would a manager set prices below marginal cost, thereby incurring a loss on each
unit sold? Regulators argue that managers who set prices below marginal costs are likely
to do so to drive out competition so they can later raise prices to recoup the losses. If you
combine the act of setting prices below costs with intent to harm competition, then you
have predatory pricing.
Price fixing is the agreement among business competitors to set prices at a
particular level. Generally, the idea is to “fi x” prices at a level higher than equilibrium
prices in competitive markets. The Organization for Petroleum Exporting Countries
(OPEC) provides us with a daily reminder of the effects of price fi xing. OPEC sets
prices for its members that are likely above equilibrium prices in a competitive market for
oil. Price fi xing is a particular legal and ethical problem because it is not universally
illegal. In many developing countries, price fi xing is not illegal. Companies with
business units in both developed and developing countries face different sets of rules
depending on where managers are doing business. OPEC, for example, operates legally
in setting oil prices because its activities are not illegal in its member countries. Managers
must be particularly alert to price fi xing because the activities that law enforcement offi
cials regard as illegal include even informal or unspoken agreements to fi x prices. This
appears to be the case in recent allegations of price fi xing in the market for dynamic
random access memory (DRAM) chips. Companies from Germany, South Korea, and
Japan were charged with price fi xing in their U.S. operations.
c. Use of Differential Analysis for Production Decisions
A make-or-buy decision is any decision by a company to acquire goods or services
internally or externally. A restaurant that uses its own ingredients in preparing meals
“makes”; one that serves meals from frozen entrees “buys.” A steel company that mines
its own iron ore and processes it into pig iron makes; one that purchases it for further
processing buys. The make-or-buy decision is often part of a company’s long-run
strategy. Some companies choose to integrate vertically (own the fi rms in the supply
chain) to control the activities that lead to the fi nal product; others prefer to rely on
outsiders for some inputs and specialize in only certain steps of the total manufacturing
process. Aside from strategic issues, the make-or-buy decision is ultimately a question of
which fi rm in the value chain can produce the product or service at the lowest cost.
Whether to rely on outsiders for a substantial amount of materials depends on
both differential cost comparisons and other factors that are not easily quantifi ed, such as
suppliers’ dependability and quality control. Although make-or-buy decisions sometimes
appear to be simple one-time choices, frequently they are part of a more strategic analysis
in which top management makes a policy decision to move the company toward more or
less vertical integration.
Suppose that U-Develop’s volume is projected to be 100,000 prints. If it is
expected to be more than 80,000 prints, the preceding analysis indicates that U-Develop
should continue to produce them. However, that analysis has not considered the
opportunity cost of using the facilities to process prints. Recall that opportunity costs are
the forgone returns from not employing a resource in its best alternative use.
Theoretically, determining opportunity cost requires considering every possible use of the
resource in question. If U-Develop has no alternative benefi cial use for its facilities, the
opportunity cost is zero, in which case the previous analysis would stand.
Suppose, however, that the facilities to process prints could be used to take
passport and visa photos. This new service would provide a $2,000 differential
contribution. If the passport and visa service is the best alternative use of the facility, the
opportunity cost of using the facility to process prints is $2,000. In that case, U-Develop
would be better off outsourcing the processing and using the facilities to offer the
passport and visa service, as shown by the two alternative analyses of the problem.
Determining opportunity cost is typically very diffi cult and involves considerable
subjectivity. Opportunity costs are not routinely reported with other accounting cost data
because they are not the result of completed transactions. Some opportunity costs, such as
the alternative use of plant facilities as just described, can be estimated in monetary
terms; others, like the loss of control over production, might not be so readily quantifed.
When a benefit is forgone, it is not possible to determine whether the opportunity cost
estimate is realistic. The fact that they are difficult to estimate or subject to considerable
uncertainty does not mean opportunity costs should be ignored (as they often are).
Opportunity costs can represent a substantial part of the cost of an alternative, and the
financial analyst has to be aware of the forgone opportunities when preparing the
analysis.
The discrepancy between what is shown on the product line financial statements
and the differential analysis stems from the assumptions about differential cost. The
financial statement presented was designed to calculate department profits, not to identify
the differential costs for this decision. Thus, managers relying on operating profit
calculated after all cost allocations, including some that are not differential to this
decision, would incorrectly conclude that the product line should be dropped. Financial
statements prepared in accordance with generally accepted accounting principles do not
routinely provide differential cost information. Differential cost estimates depend on
unique information that usually requires separate analysis. The financial statement that
was prepared on a contribution margin basis clearly reveals the revenues and variable
costs that are differential to this decision. A separate analysis was required, however, to
determine which fixed costs were differential. It is possible, of course, to prepare reports
that reflect each division’s contribution to companywide costs and profits. This segment
margin would include division revenues less all direct costs of the division and would
exclude allocated costs.
Dropping a product line in some companies is equivalent to closing a business
unit. For example, many auto assembly plants are used for specific models and if those
models are dropped, managers will consider closing the plant. In the analysis of U-
Develop’s product line decision, we focused primarily on the financial aspects of the
decision. When a business unit is closed, important nonfinancial impacts need to be
considered. Plant closures, for example, have serious effects for the employees and
communities involved. For example, when General Motors phased out the Oldsmobile
brand, Lansing, Michigan, suffered thousands of job cuts. These nonfinancial
considerations are often so important that they outweigh the financial issues.
Another common managerial decision is determining what products or services to
offer. This choice directly affects costs. Many companies are capable of producing a
large variety of goods and services but may be limited in the short run by available
capacity. For instance, U-Develop had to decide whether to use its limited space to
continue to sell prints or expand its sale of frames. In another case, staffing issues may
cause a hospital to decide between adding a new intensive care unit and expanding its
obstetrics ward. We usually think of product choices as short-run decisions because we
have adopted the definition that in the short run, capacity is fixed, but in the long run, it
can be changed. In the long run, the constraints on available capacity can be overcome by
capacity addition, but, in the short run, capacity limitations require choices.
U-Develop can sell 150 metal frames or 150 wooden frames or any combination
totaling 150 to break even. The contribution margin of each product is the same, so the
profit-volume relationship is the same regardless of the mix of products produced and
sold. U-Develop’s objective is to maximize the contribution from its sale of frames, but
which should it produce, metal or wood? Without knowing either U-Develop’s maximum
production capacity or the amount of that capacity used to produce one product or the
other, we might say that it doesn’t matter because both products are equally profitable.
But because capacity is limited, that answer is incorrect if U- Develop uses its capacity at
a different rate for each product.
Suppose that U-Develop’s capacity is limited to 200 machine-hours per month.
This limitation is known as a constraint. Further assume that machines may be used to
produce either two metal frames or one wooden frame per machine-hour.
d. The Theory of Constraints
Organizations often have constraints, or limits, on what they can accomplish. The
theory of constraints (TOC) is a management method for dealing with constraints that is
based on the ideas. In the face of constraints, the optimal product mix is that which
maximizes contribution margin per unit of constraining resources as we just saw in the
previous section. When we considered the problem of U-Develop in the previous section,
we had to adapt to a resource that was fully utilized in the short run, for example, a
machine that was operating full time. In other situations, the constraint might be a
personwith unique skills who is working full time (and perhaps even overtime) or a key
supplier who is delivering all of a key input that is possible.
These constraints can create imbalances in which the constrained resource is
working full time while other, complementary resources are less than fully utilized and
cannot be redeployed in the specialized task that is constrained. In effect, this means that
the “cost” of operating the constrained resource can be thought of as the marginal cost of
operating that resource plus the additional costs of idle capacity of other resources. In the
theory of constraints, we learn that maximizing the output of the constrained resource is
the best route to increased marginal revenues. Even if one could increase the output of
other processes it would not matter (and would produce no incremental revenue) because
the constrained resource is acting as an impediment that limits the system’s ability to
produce output.
When decision makers consider alternative investments, the “benefi ts” associated
with increased bottleneck output are much greater than what those managers might
estimate if they were to consider only the specific bottleneck resource. Decision makers
also must consider the cost of idle resources that are being constrained by the bottleneck.
Our example of metal and wooden frames was an example of a single constraint
(machine time) in a small fi rm. Consider now a large, complex organization and you can
imagine that the number of constraining resources is much greater and that managing
these constraints would be more complicated. An important insight of the theory is that
the organization is made up of many processes and that optimizing production at each
machine (locally) is unlikely to result in the optimal production schedule for the entire
organization (globally).
A thorough treatment of the theory of constraints is beyond the scope of this
book, but the essence of the theory can be described by considering two concepts:
bottlenecks and throughput contribution. 2 The theory of constraints focuses on
increasing the excess of differential revenue over differential costs when faced with
bottlenecks. A bottleneck is an operation where the work required to be performed limits
production. In other words, the bottleneck is the constraining resource. With multiple
parts of a production process, each operation depends on the preceding operations. One
operation cannot be started until the previous one has completed its work.
The objective of the theory of constraints is to maximize throughput contribution
given investments and operating costs. The theory of constraints assumes a short-run time
horizon and few variable costs. In most versions of the theory, only materials, purchased
parts, piecework labor, and energy to run machines are considered variable. Most direct
labor and overhead costs are assumed fixed. This is consistent with the ideas that the
shorter the time period, the more costs are fixed and that the theory of constraints focuses
on the short run. Generally, this assumption about cost behavior seems reasonable, but it
is important to remember that the approach is ultimately to maximize the contribution
margin (the difference between price and all variable costs) per unit of the constraining
resource.
e. Basic Cost Behavior Patterns
The most important characteristic of costs for decision making is how they behave
— how they vary with activity is the key distinction for decision making. Therefore, the
basic idea in cost estimation is to estimate the relation between costs and the variables
affecting costs, the cost drivers. We focus on the relation between costs and one
important variable that affects them: activity level. Activities can be measured by volume
(for example, units of output, machine-hours, pages typed, miles driven), by complexity
(for example, number of different products, number of components in a product), or by
any other cost driver.
You already know the key terms for describing cost behavior: variable costs and
fixed costs. You also know that variable costs change proportionately with activity levels
but fixed costs do not where TC refers to total costs, F refers to fixed costs that do not
vary with activity levels, V refers to variable costs per unit of activity, and X refers to the
volume of the activity. In practice, we usually have data about the total costs incurred at
each of the various activity levels, but we do not have a breakdown of costs into fixed
and variable components because accounting records typically accumulate costs by
account, not by behavior. What we need to do is to use the information from the accounts
to estimate cost behavior.
Text messaging is a common add-on service to mobile phones, but how profitable
is it for the phone companies? In September 2008, the chairman of the Senate Antitrust
Committee sent letters to four major telecommunications companies asking for
information about prices and costs. His interest was prompted by a price increase from
$.10 to $.20 for the pay-per-use service.
Although the companies did not discuss the costs of text messaging in their
responses, the variable cost can be estimated by the engineering method. First, how does
a text message use the carriers’ resources? A text message initially travels wirelessly
from a handset to the closest base-station tower and is then transferred through wired
links to the digital pipes of the telephone network, and then, near its destination, is
converted back into a wireless signal to traverse the final leg, from tower to handset.
How does sending a text message impact the network? In the wired portion of its
journey, a file of such infinitesimal size is inconsequential. Srinivasan Keshav, a
professor of computer science at the University of Waterloo in Ontario, said, “Messages
are small. Even though a trillion seems like a lot to carry, it isn’t.”
What does this mean for the costs? Professor Keshav said that once a carrier
invests in the centralized storage equipment—the cost of storing a terabyte now is only
$100 and dropping—and the staff to maintain it, its costs are basically covered.
“Operating costs are relatively insensitive to volume,” he said. “It doesn’t cost the carrier
much more to transmit a hundred million messages than a million.” In other words, the
variable costs are close to zero. What are the implications for pricing? With no
incremental fixed or variable costs associated with the texting product, carriers profit
from offering unlimited messaging at an affordable rate. Once one understands that a text
message travels wirelessly as a stowaway within a control channel, one sees the carriers’
pricing plans in an entirely new light. The most profitable plan for the carriers will be the
one that collects the most revenue from the customer: unlimited messaging, for which
AT&T and Sprint charge $20 a month and T-Mobile, $15.
f. What Methods Are Used to Estimate Cost Behavior?
Results are likely to differ from method to method. Consequently, it is a good idea
to use more than one method so that results can be compared. Large differences in cost
estimates suggest it is worthwhile to conduct additional analysis. If the estimates are
similar, you may have more confidence in them. In practice, operating managers
frequently apply their own best judgment as a final step in the estimation process. They
often modify the estimate submitted by the controller’s staff because they have more
knowledge of the process and, more important, they bear ultimate responsibility for all
cost estimates. These methods, therefore, should be seen as ways to help management
arrive at the best estimates possible. Their weaknesses as well as their strengths require
attention.
How might you begin to help Charlene estimate the cost of a new center? One
approach is to start with a detailed step-by-step analysis of what needs to be done, that is,
the activities the store staff would conduct to operate the center. Probably the first thing
you would want to know is the size of the center. Because this is a service firm, the size
can be easily represented by the time it takes employees to provide repair service.
Charlene estimates that the new center will average about 480 hours monthly. Once you
determine the size of the center, you can turn to the other necessary activities. Examples
might be renting the office where the repairs will take place, using lights and other
utilities, providing administrative support, or using supplies such as gloves and screws.
You would then estimate the times or costs for each of these activities. The times
required for each step requiring labor (administrative support, for example) would be
multiplied by an estimated wage rate. Other costs, such as office rent, would be estimated
from local market information. The estimate you just made is an engineering estimate.
In practice, labor time estimates might come from a time and motion study.
Engineering estimates of the supplies required for typical repairs can be obtained from
manufacturers’ manuals and the experience of computer technicians. Other costs are
estimated similarly; for example, the size and cost of the building needed to house the
reception and service operation can be estimated based on area rental costs and space
requirements. One advantage to the engineering approach is that it can detail each step
required to perform an operation. This permits comparison with other centers in which
similar operations are performed and enables the company to review its productivity and
identify specific strengths and weaknesses. Another advantage to this approach is that it
does not require data from prior activities in the organization. Hence, it can be used to
estimate costs for totally new activities.
A company that uses engineering estimates often can identify where “slack”
exists in its operations. For example, if an engineering estimate indicates that 4,000
square feet of floor area are required for an assembly process, but the company has been
renting 6,000 square feet in other centers, the company might find it beneficial to
rearrange the plan to make floor space available for other uses or look for smaller rental
space. A difficulty with the engineering approach is that it can be quite expensive to use
because it analyzes each activity involved in the business. Another consideration is that
engineering estimates are often based on optimal conditions. Therefore, when evaluating
performance, bidding on a contract, planning expected costs, or estimating costs for any
other purpose, it is important to recognize that the actual work conditions will be less
than optimal.
One approach to estimating costs that includes the realities of downtime, missed
work, machine repair, and the other factors that often cause engineering estimates to be
less than realistic is to look at results from existing activities. For example, accountants
often use the account analysis approach to estimate costs. This method calls for a review
of each cost account used to record the costs that are of interest, and the identification of
each as fi xed or variable, depending on the relation between the cost and some activity.
Identifying the relation between the activity and the cost is the key step in account
analysis. For example, in estimating the production costs for a specified number of units
within the range of present manufacturing capacity, direct materials and direct labor costs
are generally considered variable, and building occupancy costs are generally considered
fi xed. The identifi cation depends on the accountant’s judgment and experience.
Engineering estimates and account analysis are valuable approaches to estimating
costs, but they have important limitations. Engineering estimates often omit
inefficiencies, such as downtime for unscheduled maintenance, absenteeism, and other
miscellaneous random events that affect all fi rms. Account analysis is often based on last
period’s costs alone and is subject to managers focusing on specific issues of the previous
period even though these might be unusual and infrequent. One approach to dealing with
both random and unusual events is to use several periods of operation or several locations
as the basis for estimating cost relations. We can do this by applying statistical theory,
which allows for random events to be separated from the underlying relation between
costs and activities.
When using statistical approaches to cost estimation, we need to ensure that the
activity levels of the past are relevant for the activity levels estimated. Extrapolations
beyond the upper and lower bounds of past observations are highly subjective. Suppose,
for example, that the highest activity level observed at any center is 600 repair-hours per
month and we wish to predict the cost of a center with 800 repair-hours per month. An
estimate may be highly inaccurate simply because the past data do not reflect cost
behavior with output of more than 600 repair-hours. The level of activity for which a cost
estimate may be valid is the relevant range. It should include only those activity levels for
which the assumed cost relations used in the estimate are considered to hold. Thus, when
past data are used, the relevant range for the projection is usually between the upper and
lower limits of past activity levels for which data are available.
Although the use of past data for future cost estimation has limitations, it works
quite well in many cases. In many estimates, past data are adequate representations of
future cost relations, even if the forecasted level of activity is somewhat outside the
relevant range. Moreover, reliance on past data is relatively inexpensive; it could be the
only readily available, cost-effective basis for estimating costs. Past data do show the
associations that held in prior periods and at least can be a meaningful starting point for
estimating costs as long as their limitations are recognized.
When you begin a statistical analysis of costs and activities, it is helpful to begin
by graphing the costs against activities using a scattergraph. This visual representation of
the data provides a quick indication of the fixed-variable relation of costs and activities
and can indicate whether the relation seems to change at certain activity levels. To
prepare the graph, we fi rst obtain the relevant data. For example, if estimates of
manufacturing overhead are to be based on machine-hours, we must fi rst obtain data
about past manufacturing overhead and related machine-hours.
The number of observations to include depends on the availability of the data, the
variability within the data, the relative costs and benefits of obtaining reliable data, and
the length of time the current process has been in operation. A common rule of thumb is
to use three years of monthly data if the physical processes have not changed
significantly within that time. If the company’s operations have changed significantly,
however, data that predate the change may be misleading because you will be estimating
the relation for two different processes. If cost and activity levels are highly stable, a
shorter time period could be adequate. Data for the past 15 months were collected for a
representative center of 3C to estimate variable and fixed overhead. These data are
presented and plotted in Once all data points were plotted, a line was drawn to fi t them
as closely as possible and was extended to the vertical axis on the scattergraph.
The slope of the line represents the estimated variable costs per unit, and the
intercept with the vertical axis represents an estimate of the fixed costs. The slope is
referred to as the variable cost per unit because it represents the change in costs that
occurs as a result of changes in activity. The intercept is referred to as the fixed cost
because it represents the costs incurred at a zero activity level given the existing capacity
if the relation plotted is valid from the data points back to the origin. Note that there are
no observations of cost behavior around the zero activity level in this example, so the
data do not indicate the costs that would be incurred if the activity level were zero.
Rather, they provide an estimating equation useful within the relevant range. Preparing an
estimate on the basis of a scattergraph is subject to a high level of error, especially if the
points are scattered widely. Determining the best fi t is often a matter of “eyeball
judgment.” Consequently, scattergraphs are usually not used as the sole basis for cost
estimates but to illustrate the relations between costs and activity and to point out any
past data items that might be significantly out of line.
Although the high-low method is easy to apply, use it carefully to ensure that the
two points chosen to prepare the estimates represent cost and activity relations over the
range of activity for which the prediction is made. This is one reason to prepare the
scattergraph. The highest and lowest points could represent unusual circumstances. When
this happens, you should choose the highest and lowest points that appear representative.
The scattergraph can be used graphically to illustrate cost-activity relations based
on past experience and provides a useful visual display of the cost-volume relation.
However, because it offers only a rough approximation of the relation, we recommend
using the scattergraph in conjunction with other cost estimation methods, especially those
that rely on statistical approaches. Although the high-low method allows computation of
estimates of the fixed and variable costs, it ignores most of the information available to
the analyst.
With computational tools included in many calculators or in spreadsheets such as
Microsoft Excel ® , the additional cost of using all the data instead of two points is quite
small. Regression techniques are designed to generate a line that best fi ts a set of data
points. Because the regression procedure uses all the data points, the resulting estimates
have a broader base than those based on a few select points (such as the highest and
lowest activity levels). In addition, regression techniques generate information that helps
a manager determine how well the estimated regression equation describes the relations
between costs and activities. Regression analysis also permits the inclusion of more than
one predictor, a feature that can be useful when more than one factor affects costs. For
example, variable overhead can be a function of both direct labor-hours and the amount
of direct material processed. We leave the description of the computational details and
theory to computer and statistics courses; we will focus on the use and interpretation of
regression estimates. We describe the steps required to obtain regression estimates using
Microsoft Excel in Appendix A.
The most important step in obtaining regression estimates for cost estimation is to
establish the existence of a logical relation between activities and the cost to be
estimated. These activities are referred to as predictors, X terms, independent variables,
or the right-hand side ( RHS ) of a regression equation. The cost to be estimated can be
called the dependent variable, the Y term, or the left-hand side (LHS) of the regression
equation. Although regression programs accept any data for the Y and X terms, entering
numbers that have no logical relation can result in misleading estimates. The accountant
or cost analyst has the important responsibility of ensuring that the activities are logically
related to costs.
Although the prediction of overhead costs in the previous example, with its R2
of .828, was considered good, management might wish to see whether a better estimate
can be obtained using additional predictor variables. In such a case, they examine the
nature of the operation to determine which additional predictors might be useful in
deriving a cost estimation equation.
The adjusted R-squared (R2 ) is the correlation coefficient squared and adjusted
for the number of independent variables used to make the estimate. This adjustment to R2
recognizes that as the number of independent variables increases, R2 (unadjusted)
increases. Statisticians believe that adjusted R2 is a better measure of the association
between X and Y than the unadjusted R2 value when more than one X predictor is used.
The correlation coefficient for this equation is .953, and the adjusted R2 is .892. This is
an improvement over the results obtained when the regression equation included only
repair-hours. Improved results can be expected because some overhead costs may be
related to parts cost (for example, administrative support) but not to repair-hours.
Preparing a cost estimate using this multiple regression equation requires not only
the estimated repair-hours for the new center but also the estimated parts cost. The
additional data requirements for multiple regression models can limit their usefulness in
many applications. Of course, in planning for the new center’s activity, 3C probably has
already estimated parts cost and repair-hours, and in such a situation the added costs of
obtaining data could be quite low.
Although our focus in this is on cost estimation, we could also use the regression
results to test whether a particular factor is related to cost. In other words, we could test
whether the factor is a cost driver. For example, in the analysis on the previous page, we
could examine the t -statistics for each of the coefficients to determine if they are both
signifi cant. (In Appendix A, where we discuss the use of Excel for estimating the
regression, we see that they are both significant.) If the analysis showed, for example,
that parts cost was not significant, we would conclude that repair-hours is the better cost
driver.
Advances in easy-to-use computer software, especially spreadsheet software, have
greatly simplified regression analysis and made it available to more people.
Consequently, regression methods have been increasingly used (and misused). In
particular, analysts can be tempted to enter many variables into a regression model
without careful thought of their validity. The results can be misleading and potentially
disastrous. Some of the more common problems with using regression estimates include
attempting to fit a linear equation to nonlinear data, failing to exclude outliers, including
predictors with apparent, but spurious, relations to the dependent variable, and using data
that do not fit the assumptions of regression analysis.
The effect of attempting to fit a linear model to nonlinear data is likely to occur
when the fi rm is operating near its capacity limits. Close to maximum capacity, costs
increase more rapidly than activity because of overtime premiums paid to employees,
increased maintenance and repair costs for equipment, and similar factors. The linear cost
estimate understates the slope of the cost line in the ranges close to capacity. One way to
overcome the problem is to define a relevant range of activity, for example, from 25
percent to 75 percent capacity, and use the range for one set of costestimating regression
equations. A different equation could be derived for the levels between 81 and 100
percent capacity. Another approach is to model the nonlinearity explicitly by including
the squared value of an independent variable as well as the variable itself. However, this
approach does not provide a constant unit variable cost estimate; the estimate is different
at each level of activity.
Because regression minimizes the sum of the squared deviations from the
regression line, observations that lie a signifi cant distance away from the line could have
an overwhelming effect on the regression estimates. This type of problem can easily arise
in accounting settings. Suppose that a year’s worth of supplies was purchased and
expensed entirely (but not used) within a single month or a large adjustment was made
for underaccruing payroll taxes. The accounting records in such cases are clearly
abnormal with respect to the activity measure. An inspection of the scattergraph can often
reveal this problem. When an extreme outlier appears in the data set, scrutiny of the
output from the regression analysis will rarely identify it. Instead, a plot of the regression
line on the data points is usually needed. If multiple predictors are used, an outlier will be
even more diffi cult to fi nd. The best way to avoid this problem is to examine the data in
advance and eliminate highly unusual observations before running the regression.
It is sometimes tempting to include many variables in the regression and let the
program “fi nd” relations among the variables. This can lead, however, to spurious
relations. For example, a relation between variable 1 and variable 2 could appear to exist,
when, in fact, variable 3, which was left out of the analysis, explains the situation. An
obvious example is estimation of a regression to explain direct materials cost by using,
say, direct labor costs as the independent variable. The association will typically be quite
high, but both are driven by output.
Regression analysis is a powerful tool for analyzing and estimating costs, but it
relies on several important assumptions. If the assumptions are not satisfi ed, the results
of the regression will not be reliable. Two important assumptions that are often not satisfi
ed in estimating costs are that (1) the process for which costs are being estimated remains
constant over time and (2) the errors in estimating the costs are independent of the cost
drivers.
Businesses today change processes frequently as part of continuous improvement
efforts. Regression analysis assumes, however, that the process remains the same. This
situation leaves the cost analyst with two choices. The analyst can restrict the data to a
short period and thereby assume the process has remained the same. However, the
estimates will not be as reliable because there are relatively few observations.
Alternatively, the analyst can use a longer period. As long as the process has not changed,
the estimates will be more reliable (since they are based on more information), but the
analyst then risks using estimates that might not be meaningful if the process has
changed. These trade-offs indicate that using regression analysis for estimating costs
requires care in the selection and use of the data. It is not enough to rely on a spreadsheet
program to generate the results; the analyst must be assured that the data being used are
appropriate for regression analysis.
A regression estimate is only an estimate. Computerized statistical techniques
sometimes have an aura of truth about them. In fact, a regression estimate can be little
better than an informal estimate based on plotted data. Regression has advantages,
however. It is objective, provides a number of statistics not available from other methods,
and could be the only feasible method when more than one predictor is used. We
recommend that users of regression (1) fully understand the method and its limitations;
(2) specify the model, that is, the hypothesized relation between costs and cost predictors;
(3) know the characteristics of the data being used; and (4) examine a plot of the data.
g. Learning Phenomenon
You might recall the fi rst time that you used a spreadsheet program on a
computer. While you might have been slow at fi rst, your speed improved as you gained
more experience. In the same way, companies fi nd that experience—or learning—affects
labor costs. Specifi cally, the more experience that workers have performing a task, the
less time they spend on it. As we discussed in the previous section, cost estimation
methods assume that the process for which costs are being estimated has notchanged. If,
because of learning, for example, the process has changed, we need to incorporate that
change in our estimation methods.
The learning phenomenon refers to the systematic relationship between the
amount of experience in performing a task and the time required to perform it. This can
occur when companies introduce new production methods, make new products (either
goods or services), or hire new employees. For example, the effect of learning on the cost
of aircraft manufacturing is well known. Manufacturers of products for the aerospace
industry, such as General Electric and Boeing (see the Business Application discussion
on learning curves), recognize the effect of learning on the production cost of a new
product by writing contracts that establish a lower cost for consecutive units produced.
For example, the second unit produced has a lower production cost than the fi rst unit, the
third unit produced has a lower production cost than the second unit, and so on.
Assume that the company’s engineers have found a systematic relation between
the time required to produce units and the volume of units produced. These engineers
estimate that the time required to produce the second unit is 80 percent of the time
required to produce the fi rst unit. Further, the time to produce the fourth unit is 80Fper
cent of the time to produce the second unit, and so forth. (What is the time to produce the
eighth unit? Answer: 80 percent of the time to produce the fourth unit.)
This is called an 80 percent learning curve. 1 If the time to produce the fourth unit
was 70 percent of the time to produce the second unit, then the relationship would be
called a 70 percent learning curve. If the time to produce the fourth unit was 90 percent of
the time to produce the second unit, then the relationship would be called a 90 percent
learning curve. You get the idea. Now assume that the fi rst unit takes workers 100 hours
to produce. Then, given an 80 percent learning curve, the second unit will require 80
hours to produce ( 80 percent 100 hours). The fourth unit will require 64 hours ( 80
percent 80Fhours), and so forth, as shown in the table that follows.
Assume that Generic Electric Company is considering producing a new
navigational device for NASA. NASA has indicated it will pay $500,000 per unit for the
device. Generic Electric engineers and cost management analysts estimate the cost to
Generic Electric to produce the fi rst four units of the device to be $600,000 per unit. At
fi rst, Generic Electric decides not to produce the device because the unit cost exceeds the
unit price. However, NASA assures Generic Electric that it will order 40 units of the
device. After considering the learning phenomenon for the device, Generic Electric
realizes that the average cost per unit will drop to $400,000for 40 units. For four units,
producing the device is unprofi table. For 40 units, however, it is profi table because the
learning phenomenon reduces the time and costs for units 5 through 40 suffi ciently to
bring the average cost down to $400,000 per unit.
Elite State University (not its real name) developed labor time and cost
expectations for clerical activities that were subject to the learning phenomenon. For
example, employees were expected to answer an inquiry about the status of an
application to the university’s law school in one minute. Management observed that time
spent on these activities systematically exceeded expectations. Upon investigating the
problem, management found high personnel turnover, which meant that the activities
were often being performed by inexperienced people. As a result, the university never
experienced the expected benefi ts of learning. After changing personnel practices to
reduce turnover, the university had more experienced people in jobs. These experienced
people performed the activities faster than less experienced people, and the time spent on
activities now met expectations.
h. How Is an Estimation Method Chosen?
Each of the methods discussed has advantages and disadvantages. Probably the
most informative estimate of cost behavior results from using several methods discussed
because each has the potential to provide information that the others do not. We have
discussed a variety of cost estimation methods ranging from the simple account analysis
method to sophisticated techniques involving regression analysis. Which of these
methods is best? In general, the more sophisticated methods yield more accurate cost
estimates than the simpler methods do. However, even a sophisticated method yields only
an imperfect estimate of an unknown cost behavior pattern.
If a company’s operations have followed a particular pattern in the past and that
pattern is expected to continue in the future, using the relation between past costs and
activity to estimate future costs can be useful. Of course, if the relation changes, it could
be necessary to adjust the estimated costs accordingly or explicitly consider the changes
when developing the estimates. Analysts must be careful when predicting future costs
from historical data. In many cases, the cost-activity relation changes. Technological
innovation, increased use of automation, more mechanized processes, and similar
changes have made the past cost-activity relations inappropriate for prediction purposes
in many organizations. For example, switching to a just-in-time inventory system will
alter the relation between materials-handling costs and volume because the intermediate
storage step is eliminated. In other cases, the costs change so dramatically that old cost
data are worthless predictors of future costs. Because of the high variation in costs,
companies using preciousmetals or relying on labor in developing countries have found
that past cost data are not very helpful in predicting future costs. Although accountants
can adjust the data, the resulting cost estimates tend to lose their objectivity as the
number of adjustments increases.
Cost estimation is a critical aspect of decision-making in management, as it
provides insight into the potential financial implications of various choices. However,
relying on a single method for cost estimation may not capture the full spectrum of
potential costs accurately. This is why employing multiple estimation methods can offer a
more comprehensive understanding of the likely range of costs that may result from a
particular decision. In the case of 3C, a company utilizing four different estimation
methods observed variations in manufacturing overhead estimates. While these estimates
may be close, the differences highlight the inherent variability in estimating costs. It's
challenging to definitively determine which method is superior, as each method may have
its strengths and limitations depending on the context and underlying assumptions.
By considering the range of estimates provided by multiple methods, management
gains valuable insights into the potential variability and uncertainty associated with cost
projections. This broader perspective enables them to make more informed decisions and
assess the level of confidence in the estimated costs. Additionally, it facilitates a more
thorough evaluation of whether additional cost data should be collected to refine the
estimates further.
Furthermore, the consistency or divergence in decision outcomes based on
different cost estimates can inform management about the adequacy of existing
information. If decisions remain consistent across all estimates, it suggests that the
available data sufficiently support the decision-making process. However, if there are
discrepancies in decisions based on different estimates, it may signal the need for further
investigation or data gathering to enhance the accuracy of cost projections.
