Chapter 8Responsibility Concepts and Sound Decision-Making Ana.docx

Chapter 8
Responsibility Concepts and Sound Decision-Making Analytics
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Learning Objectives
Understand concepts in responsibility accounting.
Be able to provide a framework for rational business decision
making, and understand how to apply these concepts for specific
types of situations.
Apply capital budgeting methods and discounted cash flow
concepts.
Know how to make proper long-term investment decisions.
8.1
Responsibility Accounting Concepts
In general, managers should be held accountable for the results
of their decisions and business execution. Without
accountability based on performance-related feedback, the
business will not perform at its best, and areas in need of
improvement may not be identified on a timely basis. Business
feedback is often based on financial results. You have already
seen how budgets and variances are used to help identify areas
for improvement. Because managers are accountable for their
decisions, actions, and outcomes, their performance measures
should align around the department, product, division, or other
business for which they are responsible. In other words, the
attribution of responsibility tends to follow the organizational
structure of the business.

Sometimes, a business has a highly dispersed design, with
decisions nested with lower level managers. Other businesses
generate decisions only at the upper levels, and lower level
personnel are basically charged with execution of defined
actions. Proper implementation of responsibility accounting
concepts stipulates that performance measures be aligned with
the business organization structure. In other words,
accountability should map to responsibility. Proper design of
performance measurement systems therefore requires that the
management accountant carefully consider the organizational
structure. Sometimes performance measures are only
appropriate on an aggregated basis, such as where the
organization is structured as a top–down, command-and-control,
centralized decision-making entity. As lower level managers are
given increased authority, so too should the accountability
system be modified to provide more disaggregated performance
measures. Although quite logical, this presents measurement
challenges.
Different types of units must be evaluated using alternative
models. For example, some units do not generate any revenue.
They exist to provide support services to other departments
within the entity. Other business segments may have clear cost
and revenue functions, and they might be evaluated on their
profits. Given this observation, it is common for businesses to
characterize areas of specific responsibility as cost centers,
profit centers, or investment centers.
A cost center usually lacks clear revenue functions. Typical
departments that are regarded as cost centers include
accounting, human resources, maintenance, and most
administrative groupings. Cost control is the key evaluative
element in assessing performance for a cost center. Standard
costs and variances are useful tools for judging performance. Of
course, it is also important to not reduce costs to the point of

ineffectiveness; cost control should not be confused with cost
minimization. Therefore, non-financial measures of output
should also be considered for a cost center. Examples include
transactions processed, error rates, and results of satisfaction
surveys. Perhaps you have heard of a balanced scorecard?
A balanced scorecard is a measurement system designed to track
all elements of performance, whether related to financial
outcomes, customer satisfaction, innovation, or internal
execution. A balanced scorecard provides a holistic approach
because an array of performance measurements is developed.
Each element evaluated is intended to align with the overall
entity objectives. The emphasis is on meeting thresholds while
concentrating on areas for continuous improvement. To find a
balanced scorecard in operation, you need look no further than
your next visit to a fast-food restaurant. The time from order
entry to food deliver is constantly clocked, and the goal is
usually to deliver in less than 2 minutes. Other important goals
might relate to cleanliness, staff turnover, frequency of errors
on order fulfillment, daily sales volume, and so forth.
Balanced scorecard metrics provide a tool for assessing
fulfillment of key objectives. Accountants often gather essential
data and may become skilled in developing graphical
presentations that show how well goals are being met. These
graphs are frequently posted throughout the workplace to
remind employees of their importance.
A profit center manager is responsible for the control of both
costs and revenues. However, costs and revenues are not
evaluated independently. Instead, costs are considered in
relation to revenues. A cost overrun can be perfectly fine if it is
also met with increased revenues and profit enhancements.
Flexible budget tools introduced in Chapter 6 are particularly
well suited to the evaluation of a profit center.

At higher levels within an organization, managers may be
evaluated based on the notion of investment centers. The
manager of an investment center is accountable not only for its
costs and revenues but also for the sufficiency of the return on
the amount of capital invested within the business unit. One tool
used to assess the success or failure is the return on investment
(ROI). In its most elementary form, this model is simply a ratio
of operating income to average assets deployed in the business
unit:
ROI = Operating Income / Average Assets
However, it is sometimes useful to also assess operating income
in relation to sales and sales in relation to average assets:
Margin on Sales = Operating Income / Sales
Turnover Rate = Sales / Average Assets
Algebraically, these ratios combine, as shown in Exhibit 8.1, to
produce the ROI calculation.
Exhibit 8.1
Figure illustrating the Return on Investment equation. Operating
income divided by sales yields the margin. Sales divided by
average assets yields the turnover. The margin multiplied by the
turnover yields the ROI.
Accumulation of Information to Match Centers
When responsibility measurements are to be divided according
to cost, revenue, or investment centers, it also becomes
necessary to develop the accounting information system to
provide data in support of the assessment process. Useful
reports must be generated for each unit of responsibility.
Generalizing, these reports should be sufficient to provide for
comparison of budget and actual data; align with the
organizational units of the firm; support variance calculations

when applicable; and, it is hoped, help identify
areas/opportunities for targeted improvement. Aggregated data
that are used to measure results for upper divisions may be
disaggregated into reports applicable to lower levels within the
business. For instance, a business may have two primary
segments, wholesale and retail. The aggregate entity-wide
performance report (in the leftmost data column in Table 8.1) is
disaggregated into information applicable to each business unit:
Table 8.1: Aggregate performance
Combined Wholesale Retail
Sales $3,500,000 $2,000,000 $1,500,000
Variable expenses 2,250,000 1,500,000 750,000
Contribution margin $1,250,000 $ 500,000 $
750,000
Traceable fixed costs 700,000 200,000 500,000
Controllable margin $550,000 $ 300,000 $ 250,000
Common fixed costs 250,000
Net margin $ 300,000
If applicable, the data column for retail could be further
disaggregated into information for each retail store. Thus,
aggregated data for the entire entity can be used to judge the
performance of upper division corporate managers. The segment
data can be used to judge the performance of midlevel
managers. Also, if applicable, individual store managers can be
judged on the performance of their business unit.
In examining the preceding performance report, you likely
noticed that total fixed cost was divided between traceable and
common components. Traceable fixed costs are those that would
no longer exist if a particular responsibility center ceased to
exist. Examples include the costs associated with real estate in
use by the retail unit, management salaries, and so forth. In
contrast, common fixed costs support the operations of multiple
units and would continue regardless of any decisions about
continuing or discontinuing a responsibility center. Because

effective performance evaluation depends on a proper alignment
of responsibility and accountability, it is important to separate
fixed costs between traceable and common components. It
would be inappropriate to evaluate a manager's performance
based on an accounting model that burdened the manager with
common costs for which there was no effective control.
Management by Exception
Management by exception is an often-used description of the
way in which responsibility reports are used. It means that
reviews and corrective actions should center around areas of
underperformance, as identified by data that do not conform to
expectations. Thus, attention is focused on areas where
corrections appear to be needed. If the accounting information
system does not support this objective, it is arguably of little
value for management control. However, do not assume that
every exception requires change. Sometimes performance can
fall short of expectations because of circumstances that are
beyond the control of a unit manager. Examples include
shutdowns due to storms, economic recessions, and countless
other disruptive events that are externally or coincidentally
induced.
Rational Decision Making
You can probably think of some things you would like to try
again. Perhaps you have taken an exam and done poorly. The
underperformance might have been due to a lack of preparation.
Then again, maybe you just made a mathematical error; or
worse, maybe you marked an answer sheet wrong by accident.
Whatever the cause, you probably think you should have done
better. If you reflect further, you will see that there are really
two different types of explanations for the poor performance: a
lack of planning and poor execution. The first type is clearly
subject to your control.
It is easy to make an analogy to business. Management must be

diligent to control against errors in both planning and
execution. Our focus now is on avoiding planning errors.
Remember, management has an ethical and fiduciary duty to
safeguard company resources, and this includes application of
proper planning and decision-making principles. Despite the
best of plans, there is no guarantee of success. However, there
is no excuse for engaging in a business action that has no
chance of success from the outset.
Sunk Costs
Perhaps the most frequent business mistake is to fail to
distinguish between sunk costs and relevant costs. A sunk cost
relates to the amount of a prior expenditure or cost. You may
have invested in the stock of a particular company. If you
suspect the stock is going to decline, you should consider
selling it. It does not really matter whether you paid more or
less than its current market value. Nevertheless, people
frequently tend to fixate on sunk costs. Perhaps this is just
human nature, but it has no place in making sound business
decisions. Sunk costs are to be ignored in making business
decisions. This facet of business decision making cannot be
overemphasized; even when people have a rational
comprehension of the concept, it is still difficult to set aside
emotion. The age-old expression that there is no use crying over
spilt milk applies.
What matters is to base business decisions on relevant items.
Relevant items are those that entail future costs and revenues
that differ between alternative decisions. The objective of
business decision making is to identify decisions yielding the
best incremental outcomes based on a comparison of just the
relevant items. This can be trickier than it seems.
To illustrate, assume that a corporation has a machine with an
original cost of $100,000, a 5-year remaining life, no salvage
value, and accumulated depreciation equal to 40% of cost. It

produces 10,000 units per year, and operating costs are $2 per
unit. The company can sell the unit for $20,000 and lease a new
machine for $22,000 per year for 5 years. No additional
operating costs would be incurred, and the leased machine
would also produce 10,000 units per year. Should the company
sell its current machine and enter into the lease agreement?
Immediately, you can see that the decision is not obvious.
Production is the same under either option; only costs vary.
Keeping and operating the existing equipment would result in
incremental operating costs of $20,000 per year (10,000 units ×
$2 per unit). Leasing the machine would result in incremental
operating costs of $22,000 per year but would be accompanied
by a $20,000 upfront benefit from selling the old machine. This
added $20,000 payment would more than offset the extra $2,000
per year of added costs under the lease. Thus, it is better to sell
the old machine and enter into the lease agreement. Of course,
selling the old machine will produce an immediate accounting
loss of $40,000 ($20,000 sales price minus $60,000 net book
value ($100,000 – $40,000)), but this is irrelevant. Remember
that sunk costs are to be ignored in business decision making.
This is a difficult lesson to learn. Many managers would avoid
taking the accounting loss, even though it is not the best option.
Remember that the cost of the old equipment would continue to
be charged to depreciation expense if it is not sold.
8.2
A General Framework for Making Sound Business Decisions
There are simply too many possibilities to catalog every type of
business decision you will confront. Thus, you must develop
critical thinking skills in support of a general frame of reference
for solving business problems. Perhaps you will receive a bulk
order from a customer who is requesting a significant price
reduction. Perhaps you will need to consider offshoring
production to a country with less expensive labor. There are

many such decisions that require thoughtful consideration. The
general approach to such decisions begins by identifying all of
the possibilities/outcomes, noting the relevant costs and
benefits associated with each, and making a preliminary
determination of the option with the best incremental impacts.
However, the process does not end there. You must also weigh
the seemingly best choice in the context of qualitative variables.
Qualitative factors must include consideration of environmental,
customer, and employee impacts. Although profit maximization
is important, other facets also play a significant role in defining
a business's ability to achieve long-run success. Sound judgment
should not be replaced by overreliance on quantitative models;
they are complementary.
Applying the General Framework to an Example: Bulk Orders
It is quite common for customers to request reduced pricing on
bulk orders. A bulk order involves a large quantity of units,
perhaps even produced under a unique brand name. The
beginning point for evaluating such orders is whether the
proposed price is at least sufficient to cover all variable costs
that it will generate. In other words, will the order have a
positive contribution margin. As a general rule, such orders will
result in increased profits. However, there are some notable
exceptions.
One exception occurs when there are capacity constraints.
Acceptance of a bulk order will consume productive capacity. If
that either results in an increase in fixed costs or displaces other
more profitable work, then simple reliance on the order's
positive contribution margin can produce erroneous decisions.
Thus, contribution margin analysis should always be weighted
against the ability to generate margin, with the objective of
optimizing the total firmwide contribution margin. This is
decidedly different than just looking at per-unit contribution
margin. These impacts are generally calculable based on careful
analysis. However, it is trickier to evaluate market impacts. A

negative market consequence can arise in at least two specific
ways. First, other customers may learn of the special pricing
and expect similar treatment. If that results, overall margin
deterioration might ensue. Second, the overall increase in
supply might dampen market price to end consumers,
necessitating price reductions to clear the market.
To illustrate, assume that Chip Country produces and sells a
specialty snack food for $2 per bag. This price provides a gross
profit of $0.75 per bag. The manufacturing costs consist of
variable production costs of $1.00 per bag and allocated fixed
manufacturing overhead of $0.25 per bag. The company's
factory only operates one shift per day, and the addition of an
extra shift would generate no additional fixed manufacturing
overhead or selling, general, and administrative (SG&A) costs.
Big City Markets has approached Chip Country about producing
a private-label snack that would not compete with Chip
Country's existing market. Big City's offer would require Chip
Country to double its output, and it would fully consume
capacity that can be generated via a second shift. However, Big
City is only willing to pay $1.10 per bag. Should the offer be
accepted? At first glance, it appears the offer is not good. After
all, the gross profit is only $0.75 per bag when the selling price
is $2. How can a $0.90 reduction in selling price prove viable?
The answer to this question can be found in noting that gross
profit is calculated after deducting the fixed manufacturing
costs. Because the bulk order will not trigger any additional
nonvariable or SG&A costs, it is only necessary to recover the
variable manufacturing costs of $1 for this order to prove
profitable. Thus, the bulk order appears to be a viable
opportunity. It is only necessary to further consider the
qualitative and market-related facets before deciding to go
forward.
Applying the General Framework to an Example: Offshoring
You cannot help but notice that companies have increasingly

turned to offshore operations to manufacture goods and provide
other services such as tech support and telemarketing. This
practice is often driven by a desire to obtain cheaper labor, but
tax and regulatory issues have also played a significant role. A
decision to offshore should be based on careful analysis of
relevant costs and benefits, coupled with appropriate weighting
of qualitative factors. In addition, a manager should attempt to
judge the risks associated with the added prospect of political or
logistical disruptions associated with global dispersion.
Offshoring sometimes entails the abandonment of domestic
production facilities, in lieu of contracting with a foreign
supplier on a purely variable cost basis. There is often very
little alternative use or market value for abandoned domestic
assets. The existence of these resources may cloud the decision
to offshore, but it should not. As you know, sunk costs must be
ignored, and great care must be taken to identify only the
relevant items. This becomes difficult when a facility that is no
longer in use will continue to generate costs. Some of the fixed
overhead is apt to continue even if a service/product is no
longer produced. This unavoidable fixed overhead will not vary
between the alternatives and is therefore ignored in the
decision-making process. Conversely, fixed factory overhead
that can be avoided via offshoring should be regarded as a
relevant item in any analysis. Beyond these special
considerations, offshoring via a variable cost contract with a
foreign vendor should generally be driven by a comparison of
differences in the variable cost components.
To illustrate, assume that Ballard Corporation has a
manufacturing plant in San Diego that currently produces a
component part used in its main product line that is assembled
in Los Angeles. There is no alternative use for the San Diego
plant, and Ballard will retain it for many years, whether closed
or not. The following facts have been identified:
Annual fixed manufacturing overhead at the San Diego plant

$1,000,000
Fixed manufacturing overhead that can be avoided by closing
the plant 40%
Variable costs of production $3.00 per unit
Annual parts production 2,500,000 units
Zhou Corporation has offered to produce and deliver to San
Diego an identical component part for $3.20 per unit. The
decision to offshore production to Zhou would involve no
changes to SG&A. The rather obvious issue is whether or not to
offshore. Table 8.2 identifies the relevant costs:
Table 8.2: Relevant costs
Manufacture Offshore
Variable costs for 2,500,000 units ($3.00 vs. $3.20)
$7,500,000 $8,000,000
Reduction in fixed costs (40% of $1,000,000) (400,000)
Net of relevant items $7,500,000 $7,600,000
This fact set is relatively simple, but it is challenging to
identify just the relevant items and draw the appropriate
conclusion. The relevant items relate to the differential in
variable and fixed costs. By comparing only relevant costs, it
appears that Ballard should continue to manufacture the
component. The cost difference is $100,000 less by continuing
to manufacture ($7,500,000 vs. $7,600,000). What is most
important for you to see within this example is how easily an
error could have been made in this decision. The full cost of
manufacturing is $8,500,000 ($7,500,000 variable cost and
$1,000,000 fixed cost), which is more than the $8,000,000
direct cost of offshoring. Yet offshoring is not the right
decision. There is another $600,000 of fixed costs (the other
60% of the $1,000,000 fixed overhead) that will be incurred
even if offshoring is selected.
Offshoring involves a number of qualitative issues. When
production is placed in the hands of an outside supplier, added

cost may arise from the need to monitor the financial health and
integrity of the vendor, the quality of production, delivery
schedules, and similar issues. There are added costs associated
with freight, customs, taxes, and even language barriers.
8.3
Capital Expenditures
Some business decisions relate to capital expenditures such as
the construction of a factory or purchase of equipment. These
activities can entail substantial initial cash outlays, and it may
be many years before the investment can be recovered. Capital
expenditure decisions often require the comparison of
competing alternatives. Furthermore, options that appear best in
the short run may not be best in the long run, and vice versa.
You can probably relate to this issue in thinking about your own
education. You are currently investing time and money in an
accounting class; you could probably make more money in the
near term by working in your job and skipping out on study
time. However, you understand that your long-term interests are
better served by investing in your education. This is not much
different than the challenge faced by business managers. For
instance, should an expensive robotic welder be purchased to
replace a manual laborer? The near-term cash flow is better
without the robot but worse in the long run. How are such
decisions to be made intelligently?
This is the role of capital budgeting analysis. Mathematical
tools are brought to bear on the evaluation process in a way that
produces systematically logical outcomes. At the heart of many
of these tools are concepts related to the time value of money.
You likely have a sense that a dollar in the hand is worth more
than a dollar to be received in the future. After all, a dollar in
the hand can be reinvested to generate additional returns and
grow to a greater sum than the dollar to be received in the

future. This notion is sometimes referred to as the time value of
money.
This fundamental principle is the starting point for
understanding key capital budgeting tools. Although
spreadsheet models and business analyst calculators are readily
available to assist with all of the related calculations, they are
all based on basic mathematical equations that you should
attempt to understand.
Future Value
The first of these is known as future value (or compound
interest). To illustrate, if you invest $1,000 for 1 year, at 5%
interest per year, your initial investment will have grown to
$1,050 by the end of the year ($1,000 × 1.05). If you then
reinvest the $1,050 for another year at 5%, your investment will
grow to $1,102.50 ($1,050 × 1.05). The second year produces a
greater amount of interest (than the first year) because the
accumulated interest from the first year is also in the investment
pool and generating returns. An alternative view of this
calculation is to note that initial investment is to be multiplied
by 1.05 to the second power (i.e., 1.052). The compounding of a
greater amount of interest each year would continue through
time. Indeed, if you wanted to know the value to which the
investment would accumulate after 10 years at 5% per year, you
would multiply the initial investment by 1.05 to the 10th power.
This observation gives rise to a general formulation for the
future value factor that can be multiplied times an initial lump
sum investment:
(1 + i)n
where i is the interest rate per period, and n is the number of
periods.
Although it is a fairly simple matter to calculate the future

value factors via the previous equation, they are also readily
available by reference to a Future Value of $1 table (see
Appendix A).
These tables provide predetermined values for a variety of such
computations. Examine the table and satisfy yourself that a
$10,000 investment will grow to $25,937 by the end of 10 years
at 10% per period. You should note the future value factor of
2.5937 in the "10% column/10-period row." This factor is
multiplied by the $10,000 initial investment.
Try It Yourself: Future Value of $1
Challenge: Find the future value of $1,000 if it is invested
today at 5% annual interest for 15 years.
Calculation: The table in Appendix A indicates a factor of
2.07893 for 15 periods, 5% rate per period. This factor is
multiplied by the $1,000 initial investment.
Answer: The amount will grow to $2,078.93.
One important point is worth noting at the outset. The interest
rate from within the table is in reference to the interest rate per
period. In the preceding example, we assumed annual
compounding. However, interest might be compounded monthly
or on some other basis. For example, if a 12% annual interest
rate were to be compounded monthly, then the interest rate
would be 1% per month. A 3-year investment would include 36
months. Thus, to determine the future value of the investment
would entail reference to the "1% column/36-period row."
Annuity
Rather than investing a single lump-sum amount, investors will
sometimes make a regular stream of level payments into an
account. For example, a saver might deposit $10,000 per year at
the beginning of each year into a savings account. Streams of
level payments occurring on regular intervals are called
annuities. You may be wondering how you would determine the
amount that would accumulate after 5 years under such a

process. If you consider that such an annuity is really just a
series of lump-sum amounts, each invested for a different
number of years, you can discern that the future value of
annuity can be determined by summing a series of individual
lump-sum investments. Consider Exhibit 8.2.
Exhibit 8.2
Illustration showing the stream of investments for 5 years. Each
year has an investment of $10,000. The investments for Years 1
through 5 are multiplied by the following annuity amounts,
respectively: (1.10)⁵, (1.10)⁴, (1.10)³, (1.10)², and (1.10)¹. The
resulting totals are added together for an accumulated total of
$67,156.
The preceding illustration shows that the stream of investments
would grow to $67,156. Because it is rather cumbersome to
calculate the future value of each investment and then sum,
tables are also available revealing individual factors for the
future value of such annuities. The table in Appendix B reveals
factors for the future value of annuity, with the first payment
occurring at the beginning of the first period (sometimes called
an annuity due or annuity in advance).
Examine that table and locate the value corresponding to 10%
and 5 periods. You should locate a value of 6.71561.
Multiplying the $10,000 annual payment by this factor also
yields $67,156, but in a much quicker way.
Try It Yourself: Future Value of an Annuity
Challenge: Find the future value of beginning-of-month
deposits of $25 each for 24 months, if they are invested at 6%
annual interest.
Calculation: The table in Appendix B indicates a factor of
25.55912 for 24 periods, 0.5% rate per period (6% per year
equals 0.5% per month). This factor is multiplied by the $25
periodic investment.
Answer: The deposits, with interest, will accumulate to
$638.98.

Present Value
Although future value calculations are quite useful for financial
planning, accounting and capital budgeting decisions often
depend on an opposite concept called present value. Present
value reveals the current worth of cash to be received in the
future. As such, it is sometimes called discounting of future
cash flows. For example, you may desire to know today's value
associated with $1,000 to be received in 3 years.
Mathematically, this is simply the reciprocal logic to that
applied in calculating future value amounts. Thus, the following
formula can be seen to apply:
1/(1 + i)n
here i is the interest rate per period, and n is the number of
periods.
Thus, $1,000 to be received in 3 years, assuming a 5% interest
rate, is worth approximately $863.84 today. In other words, it
has a present value of $863.84. Stated differently, that amount
invested today at 5% annual interest would grow to
approximately $1,000 after 3 years. You might calculate the
present value factor of 0.86384 via the formula (1/1.053) and
then multiply that times the $1,000 future payment. However, as
you probably suspect, there is a Present Value of $1 table (see
Appendix C) that includes appropriate factors for a variety of
scenarios.
You should take time to confirm that you can find the preceding
factor in the 5% column/3-period row.
Try It Yourself: Present Value of $1
Challenge: Find the present value of $5,000, if it is to be
received in 5 years, and the annual interest rate of 8% is
compounded every 3 months.
Calculation: The table in Appendix C indicates a factor of

0.67297 for 20 periods, 2% rate per period (8% per year equals
2% per quarter; there are 20 quarters in 5 years). This factor is
multiplied by the $5,000 amount to be received.
Answer: The present value of the $5,000 amount is $3,364.85.
Present value can also be calculated for annuities. As you will
soon see, this proves quite useful in the evaluation of long-term
capital investments. If the uniform payments occur at the end of
each period, the annuity is termed an ordinary annuity. One way
to determine the present value of an ordinary annuity would be
to sum the present value of each payment, as shown in Exhibit
8.3 for a 5-period, 10% annuity stream of $10,000 cash flows:
However, tables such as the one in Appendix D already provide
summarized values associated with the present value of an
annuity.
Exhibit 8.3
Illustration showing the stream of investments for 5 years. Each
year has an investment of $10,000. The investments for Years 1
through 5 are multiplied by the following annuity amounts,
respectively: (1/(1.10)¹), (1/(1.10)²), (1/(1.10)³), (1/(1.10)⁴), and
(1/(1.10)⁵). The resulting totals are added together for an
accumulated total of $37,908.
Notice that the previous annuity has a present value of $37,908.
Examine the table, taking note that the factor corresponding to
five periods and a 10% rate is 3.7908. Thus, one can simply
multiply the $10,000 payment by that factor to calculate the
present value of the annuity.
Try It Yourself: Present Value of an Annuity
Challenge: Assume that you have won a prize of $1,000 to
be received at the end of each year for 20 years. The annual
interest rate is 5%. How much is the present worth of this prize?
Calculation: The table in Appendix D indicates a factor of
12.46221 for 20 periods, 5% rate per period. This factor is
multiplied by the $1,000 annual prize amount.
Answer: The present value of the prize is $12,462.21.

8.4
Making Decisions About Long-Term Investments
With the mathematical tools you have just learned, you should
be able to understand important concepts in making intelligent
decisions about long-term investments. The application of these
principles is termed capital budgeting. To begin simply, assume
you are faced with two alternative investment choices, and the
going rate of interest is 7%. Investment A returns $1,000 at the
end of each year for 10 years (a total of $10,000), and
Investment B returns $1,200 per year for 8 years (a total of
$9,600). Which is preferred? The answer to this question likely
hinges on which investment has the higher present value.
Investment A has a present value of $7,023.58 ($1,000 ×
7.02358), and Investment B has a present value of $7,165.56
($1,200 × 5.97130). Thus, Investment B is preferred to A. It is
important to note that this is true even though Investment A
returns more in total than Investment B.
Now, this simple example left out one important variable. Can
you imagine what that is? It is the cost of the investment
initially. If Investment B cost more than $7,165 up front, it
would be a bad investment indeed. Thus, accountants need to
consider not only the present value of cash inflows but also the
present value of cash outflows associated with an investment.
Net Present Value
The net present value of an investment is the difference between
the present value of cash inflows and the present value of cash
outflows. To make this calculation requires the selection of an
interest rate, and that rate should reflect the theoretical cost of
capital incurred by a firm. The cost of capital approximates the
cost of funds in use by an entity. If a company borrows heavily,
it can relate to the cost of interest on debt. If a company relies

on shareholder investment, it can be meant to indicate the
expected rate of return that shareholders expect to generate. Or,
the cost of capital can reflect a blending of both the cost of debt
and equity. In any event, if the net present value of an
investment is positive, then an assumption is made that the
investment is worthy of further consideration. This means that
the present value of cash inflows exceeds the present value of
cash outflows, and the investment at least generates returns in
excess of the firm's cost of capital. The opposite conclusion can
be reached for investments with negative net present values.
To illustrate net present value, assume that Impact Plastic
Corporation is considering the purchase of a new mold that will
have an initial cost of $100,000. In addition, $25,000 will need
to be spent at the end of Year 2 and again at the end of Year 4.
These expenditures are necessary to refurbish and polish the
mold. The mold will be leased to ski boot manufacturers that
contract for plastic parts used in their products. The mold will
produce annual lease payments to Impact amounting to $40,000
per year, occurring at the end of each year, for 5 consecutive
years. Impact's cost of capital is 8%. Table 8.3 shows that the
discounted cash flows produce a positive net present value of
$19,899, suggesting that the mold will return well in excess of
the cost of capital.
Table 8.3: Discounted cash flows
Cash outflow Cash inflow Net cash flow Present
value factor @ 8% Present value of net annual cash flow
Initial cash outlay $100,000 ($100,000) 1.00000
($100,000)
End of Year 1 $40,000 40,000 0.92593 37,037
End of Year 2 25,000 40,000 15,000 0.85734 12,860
End of Year 3 40,000 40,000 0.79383 31,753
End of Year 4 25,000 40,000 15,000 0.73503 11,025
End of Year 5 40,000 40,000 0.68058 27,223
Net present value $19,899
Try It Yourself: Net Present Value of an Investment That

Should Be Accepted
Challenge: Find the net present value of an investment
requiring a $200,000 initial outlay and returning $30,000 at the
end of each year for 10 years. The company's cost of capital is
5%. The investment has no residual value.
Calculation: Using the present value factor from Appendix D,
note that present value factor for the $30,000 annuity is 7.72173
(10 periods, 5%). Thus, the present value of the inflows is
$231,651.90 ($30,000 × 7.72173). This is greater than the
investment outflows of $200,000, all of which occurred
immediately.
Answer: The net present value is positive $31,651.90,
indicating that the investment returns more than the 5% cost of
capital.
Try It Yourself: Net Present Value of an Investment That
Should Be Rejected
Challenge: Find the net present value of an investment
requiring a $200,000 initial outlay and returning $30,000 at the
end of each year for 10 years. The company's cost of capital is
9%. The investment has no residual value.
Calculation: Using the present value factor from Appendix D,
note that present value factor for the $30,000 annuity is 6.41766
(10 periods, 9%). Thus, the present value of the inflows is
$192,529.80 ($30,000 × 6.41766). This is less than the
investment outflows of $200,000, all of which occurred
immediately.
Answer: The net present value is negative $7,470.20
($192,529.80 – $200,000), indicating that the investment returns
less than the 9% cost of capital.
Internal Rate of Return
Although net present value calculations are highly beneficial in
showing whether a particular rate of return is cleared, they fail
to exactly identify the full rate of return. This is where the
internal rate of return (IRR) comes into play. The IRR
essentially repeats the previous calculations based on the actual

rate of return that causes the present value of the inflows to
equal the present value of the outflows. It is the interest rate
that causes a zero net present value. Consider the revised Table
8.4, this time using present value factors at 15.38%:
Table 8.4: Internal rate of return
Cash outflow Cash inflow Net cash flow Present
value factor @ 15.38% Present value of net annual cash flow
Initial cash outlay $100,000 ($100,000) 1.00000
($100,000)
End of Year 1 $40,000 40,000 0.86670 34,668
End of Year 2 25,000 40,000 15,000 0.75117 11,267
End of Year 3 40,000 40,000 0.65104 26,041
End of Year 4 25,000 40,000 15,000 0.56426 8,463
End of Year 5 40,000 40,000 0.48904 19,561
Net present value $0
The IRR for this project is more than 15%, as shown. The
process of evaluating investments using the IRR approach is to
calculate the IRR for each investment opportunity. Projects
offering the highest internal rates of return are deemed best.
You may be wondering how the interest rate was found. It is
quite cumbersome to do the calculations manually. Essentially,
one is required to repeatedly try rates, constantly trying to close
in on the rate that returns a zero net present value. Fortunately,
computer programs simplify the process. The details of these
calculations are deferred to more advanced-level accounting and
finance classes.
You will also learn in advanced classes that the IRR has certain
limitations. First, IRR mathematics can produce anomalous
results. Where cash inflows and outflow are highly irregular
over the span of the investment period, it is sometimes possible
to find two different rates, both of which will cause the present
values of inflows and outflows to be equal. Also, bear in mind
that IRR is useful for ranking all investment options, but it does

not tell you which ones should be accepted. Should the business
only accept investments with a greater than 10% rate, 15% rate,
or 20% rate? There is no answer to the question. Presumably,
the business should pick the best investments with the available
capital, but the method does not signal at what point it is
worthwhile to obtain additional capital to pursue added
opportunities (or hold back capital for future opportunities that
have not yet emerged).
Simpler Capital Budgeting Methods
Evaluation of long-term projects is not always based on
discounted cash flow concepts. Alternative evaluation methods
include consideration of the accounting rate of return and the
payback method. The accounting rate of return examines
accounting income rather than cash flows. It is calculated by
dividing an investment's expected increase in accounting
income by the amount of the investment. If a project costs
$1,000,000 and is expected to produce an ongoing average
increase in accounting income of $50,000, then the accounting
rate of return is 5%. Accounting income can diverge
significantly from cash flows due to depreciation and other
timing issues related to cash flows that differ from accrual-
based income measurement. The payback method is another
simplistic tool for evaluating capital expenditures. It results
from dividing an initial investment by the expected annual cash
inflow produced by the investment. If a project costs
$1,000,000 and is expected to produce an ongoing average
increase in cash flows of $100,000, then the payback is 10
years. The method can be misleading in that it fails to consider
the time value of money and what happens to cash flows beyond
the payback period.
Simple tools such as these can produce quick measures for
considering and ranking investment alternatives, but they
probably should not be solely relied on to produce consistently
high-quality investment decisions. They are but single

indicators, and management has an ethical duty to consider
more careful analysis in deciding how to deploy firm resources
before making long-term capital allocation decisions.
Recap of Using Capital Budgeting Tools for Decision Making
Table 8.5 recaps the four fundamental capital budgeting tools
introduced in this chapter. The middle column includes
information about the general decision-making rule. The last
column includes caveats about potential weaknesses for each
method.
Table 8.5: Four fundamental capital budgeting tools
Method Decision rule Caveat
Net present value (NPV) Select the investments with positive
NPV. Outcomes are dynamic based on cost of capital
assumptions.
Internal rate of return (IRR) Rank order investments and
select those yielding the highest IRR. Fails to consider
duration of an investment's life and what options will be
available after an investment matures.
Accounting rate of return (ARR) Rank order investments and
select those yielding the highest ARR. Fails to consider
timing of cash flows.
Payback Rank order investments and select those with the
shortest payback period. Fails to consider returns after the
payback period, leaving the evaluator blind as to the actual
return on the investment.
In no case should a manager resort to blind reliance on a single
method. Remember that future inflows and all outflows, as well
as assumptions about interest rates, all require some degree of
prognostication about the future. Sound human judgment must
always guide the final conclusion about the worthiness of a
capital expenditure.
Chapter 8 Overview
Click the image below to open the Chapter 8 Overview.

Key Terms
Click on each key term to see the definition.
accounting rate of return
annuities
capital expenditures
common fixed cost
cost center
future value
internal rate of return (IRR)
investment center
management by exception
net present value
payback method
present value
profit center manager
relevant items
return on investment (ROI)
sunk cost

time value of money
traceable fixed cost
Concept Check
ACC 206 Concept Check Chapter 8
Test Section:
ACC 206 CHAPTER 8
Test your knowledge of chapter 8 by answering the following
questions:
1. Which of the following is rarely a consideration when
analyzing a long-term project?
a. The cost of the investment
b. The lowest rate of return acceptable to management
c. The company's current ratio
d. The investment's cash inflows and cash outflows
2. The time value of money
a. is integrated in present value computations.
b. weights cash flows that occur in 5 years more heavily than
cash flows that occur in 2 years.
c. is reflected by the accounting rate of return.
d. should not be considered when analyzing an investment.
3. Hughes Corporation is considering a $200,000 machine that
promises savings in cash operating costs of $40,000 over each
of the next 6 years. The company requires a 10% return on its
investments. Appropriate present value factors follow: Present
value of $1: 0.56447; Present value of a $1 annuity: 4.35526.
Ignoring income taxes, the machine's net present value is
a. $(5,790).
b. $(25,790).
c. $(177,421).
d. some amount other than those listed above.
4. The internal rate of return
a. ignores the time value of money.

b. is another name for the accounting rate of return.
c. results in a net present value of zero.
d. cannot be used when the payback period is less than 3 years.
Finish
Critical Thinking Questions
Why must businesses exercise extreme care in the selection
of long-term investments?
Describe the screening and ranking processes related to
capital budgeting.
What three factors should be considered in the evaluation of
an investment opportunity?
What is meant by an investment in working capital? Are such
investments ever recovered? Briefly explain.
What is the lowest rate of return acceptable to a company?
Explain what is meant by the time value of money.
Explain the relationship, if any, between compound interest
and present value.
What is meant by the term "present value"?
Four methods are frequently used to evaluate capital
budgeting proposals. Are these methods normally used by
themselves or in conjunction with each other? Why?
When examining a project's cash inflows and outflows, what
present value relationship holds true at the internal rate of
return?
Exercises
Basic present value calculations
Calculate the present value of the following cash flows,
rounding to the nearest dollar:
A single cash inflow of $12,000 in 5 years, discounted at a
12% rate of return.

An annual receipt of $16,000 over the next 12 years,
discounted at a 14% rate of return.
A single receipt of $15,000 at the end of Year 1 followed
by a single receipt of $10,000 at the end of Year 3. The
company has a 10% rate of return.
An annual receipt of $8,000 for 3 years followed by a
single receipt of $10,000 at the end of Year 4. The company has
a 16% rate of return.
Present value analysis: Working backward
The following information pertains to four independent
investments:
A B C D
Present value $ ? $19,646 $34,625
$50,852
Interest rate 10% % ? 14% 12%
Investment period 4 years 5 years ? years
10 years
Annual cash inflows $8,000 $ 6,000 $ 7,000
$ ?
Determine the unknown for each of the investments. (Note:
Amounts have been rounded to the nearest dollar; please
consider this procedure in your calculations. Do not
interpolate.)
Straightforward net present value calculations
Contempo Inc. is considering the acquisition of some new
labor-saving equipment. Management estimates that the
equipment will cost $42,000 and will produce the following
savings in cash operating costs during the next 5 years: Year 1,
$15,000; Year 2, $13,000; Year 3, $10,000; Year 4, $10,000;
and Year 5, $6,000. The company uses the net present value
method to analyze investments and desires a minimum rate of
return of 12%.
Compute the net present value of the proposed investment.
Ignore income taxes and round to the nearest dollar.
Considering the time value of money , should Contempo

acquire the new equipment? Why?
Cash flow calculations and net present value
On January 2, 20X1, Bruce Greene invested $10,000 in the
stock market and purchased 500 shares of Heartland
Development Inc. Heartland paid cash dividends of $2.60 per
share in 20X1 and 20X2; the dividend was raised to $3.10 per
share in 20X3. On December 31, 20X3, Greene sold his
holdings and generated proceeds of $13,000. Greene uses the
net present value method and desires a 16% return on
investments.
Prepare a chronological list of the investment's cash flows.
Note: Greene is entitled to the 20X3 dividend.
Compute the investment's net present value, rounding
calculations to the nearest dollar.
Given the results of part (b), should Greene have acquired
the Heartland stock? Briefly explain.
Straightforward net present value and internal rate of return
The City of Bedford is studying a 600-acre site on Route 356
for a new landfill. The startup cost has been calculated as
follows:
Purchase cost: $450 per acre
Site preparation: $175,000
The site can be used for 20 years before it reaches capacity.
Bedford, which shares a facility in Bath Township with other
municipalities, estimates that the new location will save
$40,000 in annual operating costs.
Should the landfill be acquired if Bedford desires an 8%
return on its investment?
Use the net present value method to determine your
answer.
Compute the internal rate of return on this project.
Problems

Straightforward net present value and payback computations
STL Entertainment is considering the acquisition of a
sightseeing boat for summer tours along the Mississippi River.
The following information is available:
Cost of boat $500,000
Service life 10 summer seasons
Disposal value at the end of 10 seasons $100,000
Capacity per trip 300 passengers
Fixed operating costs per season (including straight-line
depreciation) $160,000
Variable operating costs per trip $1,000
Ticket price $5 per passenger
All operating costs, except depreciation, require cash outlays.
On the basis of similar operations in other areas of the country,
management anticipates that each trip will be sold out and that
120,000 passengers will be carried each season. Ignore income
taxes.
Instructions
By using the net present value method, determine whether
STL Entertainment should acquire the boat. Assume a 14%
desired return on all investments; round calculations to the
nearest dollar.
Basketball player decision
The Phoenix Kings of the United Basketball League have a
moody center by the name of Orlando Dawkins. Dawkins is
under contract with the team and is scheduled to earn $650,000
in both 20X3 and 20X4. A $75,000 salary increase will take
effect in 20X5.
Dawkins has not gotten along with several of his teammates
and, as a result, management is exploring the possibility of a
trade with the Philadelphia Rockets to acquire George Harper, a
star player. The Kings would pay the Rockets $350,000

immediately for the trade to take place. Harper would be paid a
$270,000 signing bonus at the beginning of 20X3 that
management plans to expense over the next 3 years by using
straight-line amortization. Harper's annual salary would be
$950,000 from 20X3 through 20X5, highest on the team because
of his ability to attract fans. The Kings expect that increased
attendance will produce added annual net cash inflows of
$525,000.
Phoenix officials believe that both players would play 3 more
years for the Kings, at which time they would become free
agents and move along to other clubs. The Kings would receive
$380,000 compensation from the other club for Dawkins; for
Harper, the figure would increase to $500,000. Regardless of
whether the trade takes place, the Kings are obligated to pay
Dawkins $200,000 at the end of 20X4 under the terms of his
original contract.
The Kings desire a rate of return of 14% and use the net
present value method to analyze investments. Round all
calculations to the nearest dollar, and ignore income taxes.
Instructions
Determine whether the Kings should keep Dawkins or
trade for Harper . Assume the trade would occur on January 1,
20X3.
Future cash flows are, in many cases, subject to change.
List several events that could occur that might influence the
cash flows in this situation.
Straightforward net present value and payback computations
The Calgary Eskimos play in the Canadian Hockey League.
Although the Eskimos will soon be moving to a modern arena,
management is studying the possibility of expanding the team's
present facility to accommodate increased crowds. A $2.4
million expansion is planned that has a $200,000 residual value
and will be depreciated by the straight-line method over four

seasons. Information about the expansion follows:
Number of seats Occupancy rate
Ticket price
Class 1 seats 2,500 80% $6
Class 2 seats 2,000 60 4
The team will play 50 home games each season. Total added
operating costs per game (ushers, cleanup, and depreciation) are
expected to average $11,800. All such costs, except
depreciation, require cash outlays.
Instructions
By using the net present value method and a 16% desired
rate of return, determine whether the expansion should be
undertaken.
In addition to the cash flows presented here, what other
cash flows might change if the Eskimos add on to the arena?
Equipment replacement decision
Columbia Enterprises is studying the replacement of some
equipment that originally cost $74,000. The equipment is
expected to provide 6 more years of service if $8,700 of major
repairs are performed in 2 years. Annual cash operating costs
total $27,200. Columbia can sell the equipment now for
$36,000; the estimated residual value in 6 years is $5,000.
New equipment is available that will reduce annual cash
operating costs to $21,000. The equipment costs $103,000, has a
service life of 6 years, and has an estimated residual value of
$13,000. Company sales will total $430,000 per year with either
the existing or the new equipment.
Columbia has a minimum desired return of 12% and
depreciates all equipment by the straight-line method.
Instructions
By using the net present value method, determine whether

Columbia should keep its present equipment or acquire the new
equipment. Round all calculations to the nearest dollar, and
ignore income taxes.
Columbia's management believes that the time value of
money should be considered in all long-term decisions. Briefly
discuss the rationale that underlies management's belief.
Student Guidance ReportAshford University ACC206Guidance
ReportWeek FiveLISTEN TO AUDIO/VIDEO EXPLAINING
THE GUIDANCE REPORTYELLOW INDICATES ACCOUNT
AMOUNTS CHANGEDChange Account to:Change to: Based
Upon Course Start DateExercise/
ProblemAccount to
be changedOriginal
Amount
Jan - FebMar - AprMay - JunJul - AugSep - OctNov - DecCh 8
Ex 1Part A - Year 5 - Single cash
flow12000121001220012300124001250012600Part B -Yearly
amount - Annual
receipt16000161001620016300164001650016600Part C - End of
year 1 - Single
receipt15000151001520015300154001550015600Part D -
Annual receipt year
18000800081508300845086008750QuestionsYOUR ANSWERS
BASED UPON COURSE START DATESingle cash flow:(Note:
Use Excel NPV, enter rate and use a column with a zero amount
for years 1-4(row 1-4)and 12000 entered in year 5(row
5)Annual receipt:(Note: Use Excel PV function.)Single
receipt:(Note: use NPV and same approch as above.)Annual
receipt:(Note: use NPV and same approch as above.)
AUDIO/VIDEO EX 5 <<<<CLICK HERECh 8, Ex 3Account to
be changedOriginal
AmountJan - FebMar - AprMay - JunJul - AugSep - OctNov -
DecYear 115000160001700018000190001950018500YOUR

ANSWERS BASED UPON COURSE START DATECompute the
net present value of the proposed investment. Considering the
time value of money , should Contempo acquire the new
equipment? Why?Account to
be changedOriginal
DecCh 8, Pb 3Number of games50525456586062YOUR
ANSWERS BASED UPON COURSE START DATERevenue per
year-class 1Revenue per year-class 2Total revenueTotal yearly
expenses (Added extra costs per game minus depreciation) X (#
of games)Cash flow year 1(Inflows- expenses)Cash flow year
2Cash flow year 3Cash flow year 4Net Present valuePresent
value of residual:Year 1Year 2Year 3Year 4NPVTotal Present
value Calculation:NPV Cash InflowsNPV of residual:Cost of
ArenaTotal Net Present ValueIn addition to the cash flows
presented here, what other cash flows might change if the
Eskimos add on to the arena?Ch 8, Pb 4Account to
be changedOriginal
DecOld equipment-Yearly operating costs27200$ 27,400$
27,600$ 27,800$ 28,000$ 28,200$ 28,400New equipment-
Yearly operating costs21000$ 21,350$ 21,700$ 22,050$
22,400$ 22,750$ 23,100YOUR ANSWERS BASED UPON
COURSE START DATEKeep Equipment:Year 1 costsYear 2
costYear 3 costsYear 4 costsYear 5 costsYear 6 costsNet
Present Value of costsNote: Disregard the sale amount, that will
be used if we buy new equipment. Instead treat the residual
value as the final cash inflow.Buy Equipment:Year 1 costsYear
2 costsYear 3 costsYear 4 costsYear 5 costsYear 6 costsNet
Present Value of costsAdd purchase amountAdd sale amountNet
Present Value of costsNote: The yearly costs are added and are
a negative cash flow. The cost of the new machine is also
negative and the sale of the equipment is positive. Both the
purchase and sale are treated as cash flows as of
today.Columbia's management believes that the time value of
money should be considered in all long-term decisions. Briefly

discuss the rationale that underlies management's
belief.file:///C:/Users/cpabi_000/Documents/ACC205%20Chapt
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