Management 122
Fall 2001
Handout 2
Operational Decision Making
Introduction
This section of the course will focus on the question of how to use accounting
information to make a variety of decisions regarding how to operate a company. The
types of decisions we will consider include what price to charge, how many brands to
produce, whether to produce a component internally or buy it from another company, and
essentially any strategic decision in the firm.
The types of decisions that need to be made, and the circumstances in which they
need to be made, will vary enormously from one situation to another. Therefore, it is
essential to have a solution methodology that works in every conceivable case. I advise
you to follow the steps listed below. If you practice using this approach, you should be
capable of analyzing almost any business decision you might encounter.
1. Make sure that you fully understand the economic environment
The context in which the decision is being made is crucial. Understand the firm’s
operations as well as the nature of the economic markets in which it participates,
both sales and purchases.
2. Identify the precise nature of the decision
Clarify exactly what the company is proposing and how it directly impacts the
business.
3. Identify the firm’s objectives
At the most basic level, this is always the same: maximize profit (revenue - total
cost). Always start at that basic level and then determine what factors in this
company affect its profit.
4. Identify the economic effects of the decision
Having identified the direct effects of the decision in step 2 and the profitdetermining factors in step 3, you should ascertain all the ways (direct and
indirect) in which the decision impacts those profit factors. Systematically trace
all the economic effects through the firm.
5. Make sure that you’ve seen the intangible as well as the tangible effects
Effects on outlays are easy to identify. However, there is another type of cost,
opportunity cost, that is frequently missed, yet is often critical. Given the ease
with which you can miss opportunity costs of a decision, you should make a
special effort to ferret them out. There can also be some subtle effects (such as
downward shifts in demand if lower quality materials are used) that are easily
missed absent a special effort to find them.
6. Aggregate all the effects and determine the choice that maximizes the objective
Determine the net effect of the decision on the firm’s profit. This is the most
straightforward step.
7. What do you need to know that you don’t?
You don’t always have all the information needed to make a proper decision.
Recognizing what you don’t know that is important is essential. This can have
several benefits. You might be in a position to acquire the needed information
through research, or if the missing information is regularly needed, change the
accounting system to collect it routinely. Even if the information cannot be
acquired, the ambiguity caused by the missing information should be
acknowledged in your analysis, so that management knows how reliable your
conclusions are. In this class, you obviously can’t get any information that I don’t
provide you (except possibly on the group assignments), but I will often ask you
to identify information deficiencies that could impact your analyses.
8. Make sure that you’ve answered the question that needs answering
This admonishment might seem unnecessary, but it can help avoid embarrassment.
Many people will lose track of the original issue during the process of
determining the solution (even I do this sometimes).
9. Communicate your findings
Organize your analysis in a clear manner. State your conclusions concisely and
unambiguously. Provide intuition for your results that will help to persuade the
reader. (Understanding the analysis in an intuitive manner is not only good for
communication with others, but will greatly facilitate the solution process itself.)
Part 1: Differential Cost and Revenue Analysis
Step 4 of the decision making procedure involves a determination of the economic
effects of a decision. A valuable tool in this part of the process is the concept of
differential cost and revenue. Differential cost and revenue analysis involves structuring
the decision as a choice between two alternatives, one typically being the default or status
quo choice and the other being the alternate choice. A large variety of decisions can be
thought of in this way.
Differential analysis involves a review of all the costs and revenues in the
business. Some of these costs and revenues will be the same under the alternate choice as
under the status quo. These costs and revenues can be ignored as they are nondifferential, aka sunk. Other costs and revenues are differential and will change if the
alternate choice is adopted. Compute the difference in each of these costs and revenues,
add the differential revenues and subtract the differential costs. The total is the
differential profit. If it is negative, then the alternate is a bad idea and the status quo
should be maintained. If the differential profit is positive, then the alternate is a good
idea and should be adopted.
A word of caution: don’t be too quick to dismiss costs and revenues as nondifferential, as there might be subtle effects of the decision that aren’t immediately
obvious (remember step 5). Also, the distinction between differential and nondifferential costs and revenues is context-specific and will differ from one type of
decision (e.g. changing the price) to another (e.g. buying a new machine) as well as from
one company to another for the same type of decision (although there will probably be
little difference in that case).
This approach to decision analysis has several benefits. First, it allows you to
dismiss the unimportant and focus on the important. If something doesn’t matter, then it
is best to throw it away. Otherwise, it can distract us from the important issues and can
be a source of error. Non-differential costs and revenues don’t matter, so it is desirable to
filter them out of the analysis. Another benefit of the differential analysis approach is
that it provides structure. By reviewing each cost and revenue to see whether it is
differential, you are less likely to overlook an important effect of the decision.
Part 2: Demand and Supply Cross-Elasticities in Differential Analysis
When a company produces multiple products, it is important to recognize that the
products should not be analyzed in isolation. Decisions affecting one product will often
indirectly affect the other products as well. If differential analysis suggests that an action
will increase profitability for one product, it is possible that it will induce a larger
reduction in profit of the other products, leaving the company as a whole worse off. This
is a scenario that can be avoided by carefully considering how the various products in a
particular company interact.
There are four basic types of cross-product interactions, based on two criteria:
whether the relationship is supply-driven or demand-driven, and whether the products are
substitutes or complements. Supply-driven relationships involve interactions in the
process of producing the products by the firm while demand-driven relationships involve
interactions in the process of selling the products by the firm. Products A and B are
substitutes if an increase in sales (production) of A leads to a decrease in demand for
(supply of) B. A and B are complements if an increase in sales (production) of A leads to
an increase in demand for (supply of) B. The type and magnitude of these interactions
can be characterized in terms of demand and supply cross-elasticities. This is accounting,
not economics, so we won't worry about how to compute the elasticities, but the basic
concepts are critical to our analysis (these types of issues will often fall into step 7 of the
decision making process, in which we know that a cross-elasticity probably exists but we
don’t have a measure of it). Each of the four types of cross-product interactions are
discussed below.
1. Demand complementarity (loss leader, foot in the door)
In this scenario, if we sell one of our products, it improve the chances we will sell
another of our products, either because of the nature of consumer preferences, or
because the first product sale creates a relationship with the customer that can be
exploited with later product sales (getting a foot in the door). The company might
maximize profits by under-pricing the product and losing money on it in order to
increase sales of other products which have positive margins. The product that is
deliberately sold at a loss is called a loss leader. An extreme example of
preference-driven complementarity is left shoes, sales of which are critical to
sales of right shoes (and vice versa). The foot in the door strategy is exemplified
by Microsoft, whose operating system software, DOS and especially Windows,
gave the firm an advantage in marketing application software, the most profitable
part of its business.
2. Demand substitutability (cannibalism)
The reverse situation from 1) above occurs when the sale of one product reduces
demand for another product (it cannibalizes the other product's market). This
typically happens when a firm sells many similar products. For example, a car
dealer might offer several models, each with a variety of different options. A
potential customer is unlikely to purchase multiple vehicles regardless of how
many models he likes, so the sale of one is likely to come at the expense of the
sale of another car. The prospect of cannibalism suggests that the optimal amount
of product diversity is lower and optimal prices are higher than would be
indicated by examination of each product individually. One note of caution. The
firm must have some market power (i.e. the company cannot be facing perfect
competition) for this to be an issue. If the company has a small presence in its
market, it is unlikely that any of its products will materially harm sales of the
others, although they might hurt competitors' sales.
3. Supply complementarity (synergies, joint costs)
Synergies arise when production of one product provides expertise that will be
useful in production of another product. Philip Morris is in a better position to
introduce a new brand of cigarettes at a lower cost of production than a start-up
firm would be, because Philip Morris has considerable knowledge and experience
manufacturing other brands of cigarettes. Another variation of supply
complementarity that we've seen before is joint costs. In computer recycling,
plastic and gold are complementary because you can't produce one without the
other. If supply complementarities exist, products that in isolation appear to lose
money could actually contribute favorably to the firm's overall profitability.
4. Supply substitutability (joint capacity)
This is the scenario discussed in the Nov. 2 textbook reading assignment.
Multiple products share a joint capacity constraint (such as a limit on the number
of machine hours that can be used), so that a reduction in the production of one
product will allow an increase in production of another product. In this case, the
opportunity cost of using the constrained resource (in this case, machine hours)
should be factored into differential cost analysis. We call that opportunity cost
the shadow price of the resource that is being used. One thing to remember about
joint capacity constraints is that in the long run, they can and should be relaxed if
the cost of adding capacity is less than the shadow price of the additional
capacity.
Part 3: Multi-Period Decision Making
When a decision affects more than one point in time, with some effects occurring at
different times than other effects, you cannot simply add the differential revenues and
subtract the differential costs. Since a dollar of cost today is more detrimental than a
dollar of cost next year, an adjustment to the differential costs and revenues must be
made prior to their aggregation. The adjustment involves converting each differential
effect to its present value (by dividing by [1 + d]t where d is the discount rate and t is the
number of years in the future at which the effect occurs) and then aggregating the effects
to determine the net present value (NPV) of the proposed decision, which is the
differential profit.
One of the most common applications of NPV is to investment (or research and
development) decisions in which a firm spends money at the present to provide it with
capacity (or technical capability) to produce and sell a product in future years. The costs
are immediate while the benefits take time to be realized.
One of the major issues in investment decision making is the choice of discount rate, d.
If d is set too low, the company will approve unprofitable investments, while if d is set
too high, the company will pass on some desirable opportunities. The choice of discount
rate is fully at the discretion of management, but should be based on the following
formula:
d=i+b+r+s
where i is the risk free rate of return set by the market and the same for every project in
every firm;
b is the company’s default premium set by the market and the same for every project in
the firm;
r is the project’s risk premium which reflects the increase (or decrease) in the firm’s
overall riskiness if the project is approved; r is typically negative if the project is safer
than the firm’s typical activities or if the project will hedge those activities;
and s is the scarcity premium which is positive if the company has limited investment
funds; s will reflect the fact that accepting this project will force the company to pass up
other positive NPV projects (an opportunity cost) for a lack of cash (the constrained
resource) to fund those projects; s is the most difficult component of the discount rate to
assess.
When cash is constrained, NPV analysis is complicated by the need to determine the
correct scarcity premium (a type of shadow price). Remember when we discussed supply
substitutability. We determined that the proper basis for choosing among alternative uses
of a constraining resource was to maximize the contribution per unit of the scarce
resource used. In the investment context, the contribution is NPV, calculated without
taking account of the scarcity premium. The constraining resource is cash to invest in the
project, so the contribution per unit of scarce resource is NPV / initial investment, which
is known as the NPV Index (NPVI). The decision rule for selecting investment projects
is to approve the projects with the highest NPV Index.
The NPV Index decision rule is optimal if the cash shortfall faced by the company is
temporary. If, on the other hand, the firm anticipates a long-term funding constraint,
NPV Index is less useful. Consider two alternative projects, both costing $100. A
produces $30 per year for fifteen years, starting next year. B produces $150 next year
only. With a discount rate of 20%, the NPVI of A is 0.403 and the NPVI of B is 0.25.
That suggests A to be preferable. However, A ties up the firm’s money for fifteen years,
while B only ties it up for one year. Thus A continues to create opportunity costs each
year for fifteen years while B only creates opportunity cost this year.
An alternative to NPVI is needed to account for the higher opportunity cost of long-term
projects relative to short-term projects when cash is tight for long periods of time. Such
an alternative is the internal rate of return (IRR), which is defined as the discount rate that
would be required for a project to have NPV = 0. The higher the IRR, the better the
project. Selecting projects with the highest IRRs is the optimal strategy under certain
assumptions when funding constraints are permanent. Consider the example in the
previous paragraph. A has an IRR of 29.4%, and B has an IRR of 50%.
Exercises
Exercise H2(E1): CVP and Capacity Setting
A manufacturer has the following costs:
fixed costs of $5,000,000 related to its corporate headquarters (administration)
and marketing activities (unrelated to the number of plants);
semi-fixed costs of $3,000,000 per plant (the firm can select as many plants as it
desires -- each plant has a capacity of 50,000 units);
and variable costs of $80 per unit.
Semi-fixed costs and 75 percent of variable costs are related to manufacturing. All other
costs relate to marketing and administration.
The firm's marketing department estimates that it faces the following demand
schedule displaying the number of units it can sell at various prices:
$350
$300
$250
$220
30,000
50,000
80,000
100,000
a) What is the contribution margin if the company charges $300 per unit?
b) What price should the firm charge so that it maximizes its profit?
c) Assume the demand schedule is only an estimate, and that actual sales demand could
be 80 percent, 100 percent, or 120 percent of the estimate, with an equal chance of each
outcome. What price leads to the greatest profit if demand is at the low end of the range?
d) What price leads to the greatest profit if demand is at the high end of the range?
e) If you managed this company and needed to set the price before discovering whether
demand is strong, weak, or average, what price would you charge and why?
Exercise H2(E2): Generic Cola
Private label brands (or generic brands) are versions of products that grocery or drug
stores sell at prices that are lower than name brands in an effort to engage in price
discrimination. In recent years, private labels have captured significant market share in a
large number of product markets, including soft drinks. At present, virtually all grocery
and drug store chains offer a large number of private label products.
Safeway, the nation’s second largest grocery store chain and owner of Vons, comes to the
president of Pepsi-Cola Co. with the following offer. Safeway will purchase a sufficient
quantity of syrup to produce 100 million liters of private label cola (nearly identical to
Pepsi in both ingredients and manufacturing processes) for $4 million per month.
Safeway would then contract with General Bottlers, a joint venture partially owned by
Pepsi, to combine the syrup with carbonated water and place it in 2-liter bottles to be sold
at Safeway and Vons stores throughout the country. The contract would last one year and
start in two months.
The Pepsi-Cola plant that would be used to produce the syrup for Safeway, if the offer is
accepted, has the following cost structure for this month. It is capable of producing
sufficient syrup for 1.6 billion liters of soft drinks per month. Currently, the plant is
producing Pepsi (800 mil. liters), Diet Pepsi (500 mil. liters), Slice (100 mil. liters), and
Mug Root Beer (100 mil. liters). All amounts are millions of dollars.
Sugar
Aspertame (artificial sweetener)
Other flavorings
Direct labor
Plant rent
Machine depreciation and maintenance
Supervisory staff
Inspections
Allocated corporate overhead (including marketing)
7.2
5.9
7.5
12.3
7.0
9.6
6.4
2.8
72.0
Idle equipment neither wears out nor requires maintenance. Each product has its own
inspection station. Introducing production of the private label brand would require a
special equipment modification costing $2.4 million.
What is Pepsi’s estimated differential profit of accepting Safeway’s offer? Be clear about
the assumptions you are making in deriving this estimate.
If you are the president of Pepsi-Cola, do you accept this offer?
Exercise H2(E3): Product Varieties
Tonka manufactures Play-Doh modeling compound in four varieties: red, white, blue,
and yellow. The firm is contemplating elimination of yellow Play-Doh. As an
accountant, you have been asked whether this is a good idea.
Tonka sells Play-Doh to a group of distributors. That set of distributors will not change if
yellow Play-Doh is eliminated. However, part of the firm’s plant could be transferred to
another Tonka subsidiary (the one that produces toy trucks), reducing capacity costs by
20 percent. Unit costs are the same for all Play-Doh colors. Monthly sales of each color
except yellow are currently $100,000. Sales of yellow are only $60,000. The price per
can is the same for each color.
Tonka’s Play-Doh plant uses ABC to allocate costs. Including direct labor and materials
in unit costs, the following are the plant’s monthly costs by category in the hierarchy:
Capacity costs
Product costs
Customer costs
Batch costs
Unit costs
$100,000
20,000
40,000
55,000
90,000
Three batches are required for each color per month except yellow, which requires two
(for a total of 11 bataches).
a) What is the profit for yellow Play-Doh, assuming that capacity, product, and customer
costs are allocated equally to all the colors, and batch costs are allocated in proportion to
the number of batches?
b) Based on the above information, what is the estimated effect on profit of the proposal
to drop production of yellow Play-Doh?
Exercise H2(E4): Cross-elasticity Scenarios
Following is a sequence of scenarios. Identify which type(s) of cross-elasticity (if any) is
likely to exist in each case. How would you amend your analysis of the proposed
decisions to account for the possible cross-elasticities that you have identified?
a) An aerospace firm manufactures two products: missiles for the U.S. Air Force and
small jet airplanes for use by corporate executives. The company's plant has 300,000
square feet, and due to their sizes, its products require a lot of space for assembly. The
company has the opportunity to bid on a contract to produce an additional 1000 missiles
over five years. Variable costs are $400,000 per missile and additional fixed costs
required to fulfill the contract would be $50 million per year. Fortunately, the plant need
not be expanded to fulfill the contract. The company plans to bid $800 million for the
contract.
b) A company manufactures several different sizes of garbage bags to be sold by grocery
and drug stores. The company is considering expanding its product line to include 1 cu.
ft. bags for very small trash cans. However, management is aware that a similar venture
by a company whose only other product was trash cans lost money.
c) It’s 1957. You are the president of General Motors. One of your engineers has
proposed using new “space age” materials in production to enhance durability, extending
average car life from 4 to 6 years. The increase in cost per car would be less than 5
percent. Even if that additional cost is passed through to consumers, should GM adopt
this plan for the next model year, sales would immediately increase 10 percent since
many people will appreciate the enhanced value.
d) UCLA is considering an increase in the number of undergraduate accounting courses
that it offers, adding classes in management accounting controls, tax planning, and
international accounting. These courses could be used to meet the requirements of the
accounting minor. AGSM estimates that each class would attract 50 students. 40
students would provide the school with sufficient revenue to cover the costs of offering
each course.
e) The partners at a major public accounting firm (take your pick) have the following
problem: due to fierce competition, the firm is often forced to bid less than its costs to
win the contract to perform an audit. To stop this crazy situation, some of the partners
want to impose a restriction that each bid must be high enough to guarantee a profit. The
firm also provides consulting and tax services.
Exercise H2(E5): Play-Doh II
Refer to the situation in H2(E3).
What cross-product dependencies (there could be more than one) might exist in this case,
and not have been reflected in the information above, that would affect the profitability
(or lack thereof) of the plan to eliminate yellow Play-Doh. Qualitatively, how would
each cross-product dependency affect profitability of the plan, and how might you
acquire information about each that would allow you to make quantitative assessments?
Exercise H2(E6): Integrated Problem
Your division produces two brands of cleaning agents: Powerful and Super Powerful.
Your factory can produce a total of 300,000 gallons per month of the two products
combined. In January, you chose to produce and sell 100,000 gallons of each product,
giving the firm a 60 percent market share. The sales prices were $4.00 per gallon for
Powerful and $6.00 per gallon for Super Powerful. The income statement for January (in
$ thousand) is as follows:
Sales
Cost of Goods Sold
Gross Profit
Marketing and Administration
Variable
Fixed
Net Income
Powerful
Super Powerful
Total
400
350
50
600
430
170
1,000
780
220
30
60
40
90
70
150
(40)
40
0
Fixed M&A expense is allocated to products on the basis of revenue.
The unit cost of manufacturing is displayed in the following table:
Powerful
Super Powerful
Direct materials
Direct labor
Variable manufacturing
overhead
Fixed manufacturing overhead
1.50
0.20
0.60
1.80
0.25
0.75
1.20
1.50
Total unit cost
3.50
4.30
Both variable and fixed manufacturing overhead are allocated to products on the basis of
direct labor cost. Initially assume that you cannot change the sales prices of the products.
a) The unprofitability of the Powerful line is a major concern to the company. You have
been asked to study the prospect of closing down the line. You have discovered an
opportunity to transfer use of half of the factory to another division in the company,
reducing capacity to 150,000 per month. Such an action would reduce your division’s
fixed manufacturing overhead by $90,000 per month (this overhead would become the
responsibility of the other division).
Given the information provided above, what would be the estimated effect on profit of
the plan to close the Powerful product line? Does this suggest that you should close the
line?
b) What additional information (up to 3 items) would you like to gather before deciding
whether this is a good idea? Explain how each would potentially affect your decision.
Note that these items need not be limited to cross-elasticities.
c) Assume that you decide to retain the Powerful product line. You now have the
opportunity to change the sales price of each product. The marketing department has
commissioned two surveys: each one to estimate the demand curve for one of the
products. The results of the surveys follow:
Powerful
Super Powerful
Price
Sales
Volume
Price
Sales
Volume
3.25
3.50
3.75
4.00
4.25
4.50
4.75
180,000
150,000
125,000
100,000
80,000
60,000
45,000
4.50
5.00
5.50
6.00
6.50
7.00
7.50
170,000
140,000
120,000
100,000
85,000
70,000
55,000
i) Based on these demand schedules, what price should you charge for each product to
maximize its profit?
ii) Assume that you have the opportunity to transfer part of your factory, as discussed in
a) above. What price should you charge for each product?
iii) Is there a flaw in the marketing department’s method of estimating demand? If so,
what is it and how is it likely to distort the decision making process in this case?
Exercise H2(E7): Upgrading Equipment
You are a widget manufacturer facing the following situation. Manufacturing technology
is making rapid improvements. You can buy new equipment this year for $200,000
(including installation) that will reduce your variable operating costs, but will increase
your annual maintenance cost. However, you can also wait until next year when even
better equipment will be available. If you wait, you can buy equipment for $200,000 that
will further reduce variable operating costs, but will also further increase maintenance
costs.
If you adopt new technology, variable costs go down, providing an incentive to cut the
sales price and increase volume. You must take that into account in making a decision.
The following table illustrates the differences in operations using the three technologies:
Old equipment
This year’s equipment
Next year’s equipment
Variable cost
/ widget
10
8
6
Maintenance
cost
50,000
60,000
80,000
Production /
sales volume
50,000
55,000
60,000
Price
20
19
18
There is no salvage value for any of the equipment. Three years from now the widget
market will disappear. Depreciation is computed on a straight-line basis over the useful
life of the assets (which ends in three years for everything). There are no taxes, and the
discount rate is 10 percent.
Assume that the changes in operating cash flows begin in the year after new equipment is
purchased.
Should you acquire new technology? If so, when?
Exercise H2(E8): Investment Alternatives
Two investments are available to a company. The first investment, based on traditional
technology, will cost $50,000 and generate payoffs of $10,000 per year for ten years.
The second investment, based on experimental technology, will cost $100,000 and
generate $25,000 per year for twenty years, starting two years from now, assuming the
technology is successful. There is an 80 percent chance that it will be successful, but if
not, the company receives no payoffs in the future. There is no way to determine in
advance whether the second investment will be successful.
You may obtain five additional pieces of information to help you decide whether to
invest in neither, one, or both projects. What do you consider the five most important
pieces of information, and how would each influence your decision?
The information must be researchable, not a derived number like NPV. You can
calculate NPV if you have the right information.
Exercise Solutions
Exercise H2(E1)
a) Contribution Margin =
(Price - Variable Cost per Unit) * Volume =
(300 - 80) * 50,000 =
$11,000,000.
b) The following table displays profit at various prices:
Price
Contribution margin
Fixed / semi-fixed costs
Profit
350
300
250
220
8.1 million
11 million
13.6 million
14 million
8 million
8 million
11 million
11 million
100,000
3 million
2.6 million
3 million
Remember that there is 1 plant for prices of $350 and $300 and 2 plants for prices of
$250 and $220.
Both $300 and $220 maximize profit.
c) The following table displays profit at various prices:
Price
Contribution margin
Fixed / semi-fixed costs
Profit
350
300
250
220
6.48 million
8.8 million
10.88 million
11.2 million
8 million
8 million
11 million
11 million
(1,520,000)
800,000
(120,000)
200,000
$300 maximizes profit.
d) The following table displays profit at various prices:
Price
Contribution margin
Fixed / semi-fixed costs
Profit
350
300
250
220
9.72 million
11 million
16.32 million
14 million
8 million
8 million
11 million
11 million
1.72 million
3 million
5.32 million
3 million
$250 maximizes profit. Note that at $220 and $300, it is better to sell less than is
demanded since profits would be lower if another plant is opened.
e) $250 maximizes expected profit (average over the three possible scenarios), but is
risky. $300 might be better if you want to avoid losing money under any circumstances.
The optimal choice depends on the firm’s financial circumstances.
Exercise H2(E2)
What are the differential effects of the proposed production of syrup for Safeway? That
depends on various assumptions. Based on the assumptions given below, for a year, the
impact (in $ thousands) is
Revenue
Sugar
Other flavorings
Direct labor
Depreciation and maintenance
Inspections
Equipment modification
Profit
48,000
(8,640)
(6,000)
(9,840)
(7,680)
(8,400)
(4,800)
2,640
The proposal appears to generate a positive differential profit. Of course, different
assumptions (which could be equally plausible), might lead to a different conclusion.
Assumptions: the Safeway cola is regular, not diet; the cost driver for inspections cost is
the number of inspection stations; the contract will not be extended beyond a year, at the
end of which time, the equipment will need to be remodified at a cost of $2.4 million.
Other considerations: how much benefit Pepsico receives from General Bottlers’
contract to bottle the Safeway cola; whether the company will want to use the excess
capacity at the plant to expand production of its products over the next year (potential
opportunity cost); whether the contract will lead to an erosion of demand for Pepsico
drinks by consumers substituting the private label brand.
Exercise H2(E3)
a) Total costs of yellow Play-Doh =
(capacity + product + customer costs) / 4 +
(batch costs) / (total number of batches) * (number of yellow batches) +
(unit costs) / [total production (sales) volume] * [yellow production (sales) volume] =
(100,000 + 20,000 + 40,000) / 4 + 55,000 / 11 * 2 + 90,000 / 360,000 * 60,000 =
$65,000.
Yellow profit = Revenue - total cost = 60,000 - 65,000 = ($5,000).
b) What are the differential effects of dropping yellow?
Revenue
Capacity costs
Product costs
Customer costs
Batch costs
Unit costs
(60,000)
20,000
5,000
--10,000
15,000
Total
(10,000)
The proposal to drop yellow Play-Doh would appear to be unprofitable.
Exercise H2(E4)
a) Demand cross-elasticities seem unlikely in this case since the customers for the two
products are not the same. Supply substitutability seems a strong possibility if missile
production would crowd out potential plane production in the assembly plant. To
account for this, the firm should estimate a shadow price for lost plane production by
calculating the reduction in plane contribution margin that will be caused by the
missile contract and add that amount to the estimated costs of the contract. Supply
complementarity is also possible: the firm might gain some expertise manufacturing
missiles that could be applied to airplane production in the future. Factoring that
possibility into the analysis is relatively subjective and would depend on past
experience in the industry to speculate about the potential amount of synergy.
b) Demand substitutability is likely since some customers probably buy the company’s
large bags for their small cans and those sales would be lost. A marketing survey
would be helpful in determining the severity of lost sales. On the other hand, supply
complementarity might imply that the firm will be more successful than the trash can
company that tried to make small bags and failed. To incorporate this possibility, the
company should carefully review the operations plan and budget/performance data
from the failed venture (if the other company is willing to divulge the information)
and discuss it with the operations people in this firm to see if they can spot ways to
streamline the operation and reduce its costs, since they have greater expertise in
making trash bags than that other company.
c) In 1957, General Motors was part of a small oligopoly of domestic firms that
completely controlled the U.S. auto market. If all the American firms built shoddy
cars that died quickly, consumers had no choice but to return to the dealer every few
years to get a new one. GM wouldn’t want to upset such a sweet situation. Sure, the
new materials would enhance sales now, but at the cost of fewer sales in four years
(demand substitutability), especially if Ford and the other manufacturers followed suit
(which they would since GM’s innovation probably couldn’t be patented, and even if
it could, the others were probably holding back some of their own quality
improvements). Thus the company would not be willing to incur a small cost to
increase auto longevity and might even have been willing to incur a small cost to
decrease longevity. Indeed, the U.S. auto makers designed their vehicles to have
very short lives until foreign competition forced them to substantially improve
quality.
d) Discuss in class.
e) Discuss in class.
Exercise H2(E5)
Demand substitutability is plausible since some people might not really care what color
their Play-Doh is. That would make the proposal more profitable since overall demand
would fall less than assumed.
Demand complementarity is also likely since some people will prefer to use the different
colors together (either to create new colors or to create multi-colored things). Indeed,
Play-Doh markets the four different colors as a single product, suggesting the plausibility
of this notion. In that case, the proposal would be less profitable than estimated because
demand for the remaining colors would decline.
Supply complementarity (synergy) is possible, although it is difficult to perceive the
exact mechanism by which it would affect the company’s profits in this case. If synergy
exists, it will make the proposal less profitable.
Supply substitutability exists (the shift to Tonka trucks) and is already accounted for in
the analysis. However, the way it is considered is incorrect. The proper measure of the
differential effect is not the cost that is reallocated to the truck division, but the
opportunity benefit of the transferred space to the truck division.
Exercise H2(E6)
a) What are the differential costs and revenues? You lose the revenue on Powerful, as
well as its variable costs: direct materials, direct labor, variable overhead, and variable
M&A. Also, fixed overhead falls by $90,000, since you can transfer part of the plant. In
summary, the differential effect on profit is
Sales
Direct materials
Direct labor
Variable overhead
Fixed overhead
Variable M&A
Total
(400)
150
20
60
90
30
(50)
The plan to eliminate Powerful appears to reduce profits.
b) There are several valid choices. We will discuss them in class. Answering this
question requires you to identify pieces of information that
1) could be collected in a reasonable, cost effective way, and
2) would change the analysis in a clear and potentially material way.
c)
i) What is the total cost as a function of the volume of Powerful (P) and Super Powerful
(S)?
Cost = 420,000 + 2.6P + 3.2S.
What is the contribution margin for each product at each price (price - variable cost) x
volume?
Powerful
Super Powerful
Price
Contribution Margin
Price Contribution Margin
3.25
3.50
3.75
4.00
4.25
4.50
4.75
117,000
135,000
143,750
140,000
132,000
114,000
96,750
4.50
5.00
5.50
6.00
6.50
7.00
7.50
221,000
252,000
276,000
280,000
280,500
266,000
236,500
Maximum profit occurs at the prices that maximize contribution margin, as long as
capacity is not exceeded. That occurs at prices of $3.75 for Powerful and $6.50 for Super
Powerful. Total profit, after deducting fixed costs, is $4,250. Total volume is 210,000.
ii) If half the plant is transferred, total cost becomes 330,000 + 2.6P + 3.2S. However,
the contribution margin maximizing prices are not feasible, since capacity is only
150,000. Higher prices on one or both products must be charged to stay within capacity.
Since, at prices higher than (3.75, 6.50), contribution margin increases with volume
(decreases with price), you will want to come very close to full capacity. Considering
this, only two combinations need to be checked, (4.25, 7.00) and (4.50, 6.50). Of these
two, (4.25, 7.00) generates the higher total contribution margin ($398,000). At those
prices, profit is $68,000. Since that is higher than the $4,250 in profit if you don’t
transfer half of the plant, the optimal choice is to make the transfer.
iii) Discuss in class. Carefully read the paragraph in c) that discusses how the demand
schedules were developed, and think about the implicit assumptions that the marketing
department is making in using this approach. In what ways are those assumptions likely
to be false?
Exercise H2(E7)
Annual operating cash flow using each technology is
volume * (price - variable cost / widget) - maintenance cost:
Old equipment
This year's equipment
Next year's equipment
50,000 * (20 - 10) - 50,000 =
55,000 * (19 - 8) - 60,000 =
60,000 * (18 - 6) - 80,000 =
450,000
545,000
640,000.
There is also a cash outflow of 200,000 in the year that technology is purchased (year 0 in
the case of this year's technology and year 1 in the case of next year's technology). Also,
the year 1 operating cash flow in the case of purchasing next year is the operating cash
flow for the old technology (with total cash flow that year being 200,000 lower to reflect
the investment cost).
Year by year differential cash flows are (in thousands):
This year’s equipment
Next year’s equipment
0
(200)
0
1
95
(200)
2
95
190
3
95
190
Discounting these to time 0 based on a 10 percent discount rate yields:
This year’s equipment
Next year’s equipment
0
(200)
0
1
86
(182)
2
79
158
3
71
143
NPV
36
119
The maximum NPV occurs if we purchase the equipment next year, so that is the optimal
choice.
Exercise H2(E8)
Discuss in class. There are many possible choices, e.g. the interest rate the company pays
on its debt.
Previous Exam Questions and Solutions
I -Choice of Product Quality) Your company produces two types of widgets: A and B.
B is the higher quality version. Its machining process is more meticulous, and it requires
two inspections per production run (A only requires one) to ensure that a sufficiently low
number of flawed widgets is sold. You use an ABC system to allocate overhead. The
system is based on the following four activities, with their allocation bases and total cost:
Depreciation and maintenance
Sq. feet of production
space
Production runs
Inspections
Quantity of widgets
Machine setup
Quality control
Inventory storage
$200,000
$200,000
$280,000
$50,000
Following are the quantities of each of the allocation bases for the two widget types:
Sq. ft.
Runs
Inspections
Widgets
Type A
Type B
2000
6
6
30000
2000
4
8
20000
In addition to overhead, each type of widget incurs direct material and labor in the
following amounts per widget:
Direct materials
Direct labor
Type A
Type B
$3
$5
$4
$8
Your company’s R&D department has developed a way to produce type B widgets using
high-quality materials. This approach would have the following effects:
only one inspection per production run would be needed for an acceptable rate of
flawed widgets,
direct materials costs would double, and
direct labor would increase by 15 percent since the new materials are more
difficult to process.
a) What would be the effect on profit of using the new materials?
b) What do you think are the two most important considerations, outside those provided
in the information above, that would possibly be relevant to the decision in a), and why?
Solution - I)
a) What are the differential effects on profit of changing materials?
Quality control
Direct materials
Direct labor
80,000
(80,000)
(24,000)
Total
(24,000)
The switch to higher quality materials would appear to reduce profits.
b) There are a variety of possible good answers for this question. For example, an
improvement in materials quality could have non-quantified benefits such as increased
customer satisfaction (due to the final product being more reliable) or reduced
maintenance cost for equipment (due to less damage from flawed units) that would make
adoption more attractive. The key to receiving full credit on this question is to clearly
(and briefly) identify a credible connection between the decision (changing quality) and
some variable (such as customer satisfaction) that is of interest to the decision maker and
is not already accounted for in the above analysis.
II) These questions continue the story of the San Bernardino Valley Spring Water
Company. Refer to the information provided in exam problem I in handout 1.
c - Pricing) The owner of the firm is not happy with the company’s results and wants to
make changes in the operations of the Big Bear water. One idea is to change the price.
The Big Bear shop faces the following estimated demand schedule:
Price
1.50
1.75
2.00
2.25
2.50
Quantity
18,000
14,000
10,000
8,000
6,000
The following are true:
the plant’s rent is determined by a lease that lasts for five more years;
the company has no opportunity to change its production facilities;
maintenance costs are determined by the salary of the company’s maintenance
person ($2,000) who could be converted to half-time (savings of $1000) if
machine hours fall below 150;
machine hours are proportional to bottles produced;
the plant’s machines can run a maximum of 200 hours per month;
supervision costs are independent of the number of bottles produced of each type;
the supervisor can be converted to part-time work (less than 200 hours per month)
with a proportional savings of his salary if he isn’t needed for as much time;
the equipment is alternated roughly weekly between the two water varieties (one
batch of each) with no change in this pattern in response to changing volume;
if only one type of water is produced, the machines only need to be reset once per
month;
transportation occurs whenever the plant produces a truckful of bottles (2000) for
either shop;
transportation costs include the driver’s wages (hourly) and fuel;
the two water varieties share five common materials (including two types of
plastic, water, sugar, and carbon dioxide) and have five unique materials
(flavorings such as methane in swamp water and ammonia in bog water) in each.
advertising involves ads in community newspapers ($3,000 in Santa Monica,
$4,000 at Big Bear) and on L.A. radio stations ($5,000);
the Big Bear shop incurs variable selling cost of 15 cents for each bottle it sells;
the Santa Monica shop incurs variable selling cost of 20 cents for each bottle it
sells;
and the owner lives in Pacific Palisades, two miles northwest of Santa Monica.
Based on differential analysis, what is the optimal price to charge for water at the Big
Bear shop?
Are there any unknown or non-quantifiable effects that are relevant to this decision?
Please list three, explaining the effects, how they should impact the analysis, and how
you would propose to estimate the magnitude.
d - Decision Making) Another alternative that the president is considering is to close the
Big Bear shop. Relative to the status quo of charging $2.00 per bottle at the store, what is
the differential profit of closing the shop?
Are there any unknown or non-quantifiable effects that are relevant to this decision?
Please list three, explaining the effects, how they should impact the analysis, and how
you would propose to estimate the magnitude. At least two effects should differ from
those chosen in (c).
Given the information provided (and ignoring the non-quantifiable effects you’ve
identified), what should the president do?
Solutions - II)
c) The decision requires a determination of the per-bottle variable cost of Big Bear
water. Variable cost includes direct materials, direct labor, transportation, and selling
cost:
Direct materials
Direct labor
Transportation
Selling
Total variable cost
Santa Monica
0.04
0.16
0.06
0.20
0.46
Big Bear
0.04
0.16
0.03
0.15
0.38
The company should choose the price generating the highest contribution margin of Big
Bear water. A complication is the existence of an opportunity cost, the loss of Santa
Monica water if machine hours for Big Bear water exceeds 80 hours (which would bring
total machine hours to the limit of 200). The firm can produce up to 13,333 bottles of
Big Bear water without a problem. Every bottle of Big Bear beyond 13,333 requires that
the firm sacrifice the sale of a bottle of water in Santa Monica generating an opportunity
cost of ($1.80-0.46)=1.34.
Price
1.50
1.75
2.00
2.25
2.50
CM/bottle
1.12
1.37
1.62
1.87
2.12
Quantity
18,000
14,000
10,000
8,000
6,000
Big Bear CM
20,160
19,180
16,200
14,960
12,720
Opportunity cost
6,254
894
0
0
0
Net
13,906
18,286
16,200
14,960
12,720
$1.75 is the optimal price. Profits will increase by $2,086.
There are several good answers to the question about unknown or non-quantifiable
effects. For example:
If the price of Santa Monica water can be changed simultaneously, that could
reduce the opportunity cost of cutting the Big Bear price to the point of reaching
capacity. The loss of sales in Santa Monica as a result could be cushioned by
raising the price there to bring demand down to the new level of supply. The
extent to which prices in Santa Monica could be increased can be found be
performing a demand survey similar to the one performed for the Big Bear store.
Transportation costs are being underallocated to Big Bear. More fuel is
consumed and more driving time spent traveling on twisting mountain roads than
on Interstate 10. Since transportation is a variable cost, this misallocation affects
the contribution margin calculations above, making a lower price seem more
attractive than it really is. This problem could be fixed by tracking time and fuel
consumption on both routes, at least for some test runs, to better estimate the
relative costs of the two.
Demand complementarity might exist between the two types of water.
Vacationers at Big Bear might try the water there, enjoy that rich bog flavor, and
upon returning to the Westside, decide to try the Santa Monica water. Cutting the
price at Big Bear could lead to an increase in demand in Santa Monica, improving
the company’s profits. This possibility could be examined by surveying Santa
Monica customers to discover why they decided to try the product. Such a survey
could have other marketing benefits as well.
While a common answer of students, supply substitutability is not a good choice since
that issue is known and quantified in the solution given above. Another common choice,
demand substitutability, is also dubious because the markets are geographically
segregated. It is unlikely that anyone would travel to Big Bear to get slightly cheaper
water rather than go to Santa Monica.
d) What will change if Big Bear water is eliminated? Big Bear revenue will disappear,
direct labor and materials will fall, maintenance will fall (since machine hours < 150),
supervision will fall (supervision reduced to120 hours / month), setups will fall (from 10
to 1 batches), materials handling will fall (from 15 to 10 materials), transportation will
fall, Big Bear advertising will be eliminated, and the Big Bear shop will be eliminated.
Differential profit is:
Revenue
Direct materials
Direct labor
Plant maintenance
Supervision
Machine setups
Materials handling
Transportation
Advertising
Big Bear shop operations
Profit
(20,000)
400
1,600
1,000
2,400
2,250
667
300
4,000
8,000
617
Eliminating Big Bear will increase profits by $617.
The optimal decision, excluding non-quantifiable effects, is to retain the Big Bear shop
and cut prices to $1.75.
Once again, there are several possible answers to the unknown effects question, including
some of the possible answers in part c), and some new ones. The misallocation of
transportation costs and demand complementarity still apply, if somewhat differently.
New issues could include:
synergy between swamp and bog water production and marketing. This would
make elimination of the Big Bear shop less attractive. Estimating synergy is
extremely difficult. You could interview the staff and get their opinions on how
important the synergies are.
the owner’s home in Pacific Palisades. Eliminating the Big Bear operation could
reduce the owner’s travel time, providing significant benefits (since owners’ time
is always valuable). Estimation should be straightforward, just ask the owner
what the value is.
III - Investment Analysis) As a senior vice president of a major consumer products
corporation, you have been asked to review the following investment and advise the CEO
whether it should be pursued. The investment involves buying a bottle manufacturer and
making it a subsidiary of your beer division. The acquisition will benefit the firm by
providing a reliable internal source of bottles. The acquisition price will be $3,500,000.
The bottle company has assets of $2,500,000 and debt of $1,000,000 which must be paid
off by the parent corporation (for a total of $4,500,000 in cash outlays). If the transaction
occurs, the beer division will also acquire an asset called goodwill of $2,000,000 to
reflect the premium paid for the bottler. That goodwill must be amortized over five
years, resulting in an expense of $400,000 per year. The company will also have
depreciation of $200,000 per year for the next ten years on the bottler's property, plant,
and equipment. The company would have to make some changes at the bottling plant in
the first year following the acquisition to optimize it for producing bottles for its beer
plant. Those changes will cost $300,000.
On the plus side, the bottling plant will produce 20 million bottles per year at a
variable cost of $0.12 per bottle and a fixed outlay cost of $1,500,000 per year.
Currently, the beer division pays $0.25 per bottle and has sufficient volume that it can use
as many bottles as the bottling plant can produce. The bottling plant is expected to
operate for another ten years before it becomes obsolete. At that point, it can be scrapped
and the land sold, yielding $1,000,000.
If the firm buys the bottler, the transaction will take place on January 2, at the
beginning of the next fiscal year. By convention, costs and benefits received throughout
a year are treated for present value purposes as occurring at the end of that year.
a) Assuming that there are no taxes and the firm's discount rate is 10 percent, should the
corporation buy the bottling company?
b) Funds are tight at the corporation, and for the next year, the firm will have to carefully
ration its cash. What information would you need to have to decide under these
circumstances whether the investment is warranted?
c) You are the senior vice president in charge of the beer division, which is why you
must make a recommendation to accept or reject this opportunity. Your division is
treated as an investment center, and your bonus depends on the residual income the
division generates. Also, you suspect that you might be in line to succeed the president
when he retires in two years. The firm's cost of capital is 10 percent and it computes RI
based on end of year net book value of assets. What is your recommendation?
Solutions - III)
a) The decision should be based on NPV which depends on each year's cash flow:
Time 0: Outflow of acquisition price and assumed debt = ($4.5 million).
Time 1: Difference between bottling plant operating cash cost of 20 million x $0.12 +
$1.5 million and cost of buying the bottles from external supplier of 20 million x $0.25,
for a net cash flow effect of $1.1 million; in addition, there is a cost of optimizing the
plant of $300,000 yielding a total effect of $800,000.
Time 2-9: Each year the company saves $1.1 million, as calculated above.
Time 10: In addition to the $1.1 million savings, the company can sell the land yielding
$1 million, resulting in total cash flow of $2.1 million.
Each of these cash flows must be converted to present value by dividing by (1+0.10)t
where t is the time period. Summing the present values yields the net present value of
$2.37 million.
Since the NPV is positive, this seems to be a beneficial transaction.
b) You need to know what alternative investment projects the company has. You also
need to know how long the cash constraint will persist to know what measure to use in
comparing projects, NPVI or IRR.
c) The calculation of RI involves the determination of the effect of the transaction on
profit and the effect on investment (assets).
In year 1, as noted above, the transaction leads to an increase in operating cash flow of
$800,000. In addition, the company incurs depreciation of $200,000 and goodwill
amortization of $400,000, both of which decrease profit, resulting in a net increase in
profit of $200,000. Assets will increase by $3.9 million ($4.5 million initial book value
minus one year’s depreciation and amortization). Since the cost of capital is 10 percent,
RI = 200,000 - 0.1 x 3.9 million = ($190,000), a reduction in RI.
The promotion decision must be made before the end of year 2, so only year 1's results
will be known at the time, so buying the bottling plant might hurt your chances of
becoming president. Therefore, you might not want to do it.
Note that RI becomes positive in year 2, since operating cash flow increases to $1.1
million and assets (net book value) fall to $3.3 million, resulting in RI of $170,000. Later
years are even better. If you don't get the promotion next year, your prospects in
subsequent years will be better for having done this, and if you do get the promotion, then
your performance measure as president (the entire company's profitability) will be
enhanced. Therefore, if you consider your long-run incentives, you might still
recommend the acquisition.