Discussion 3
Capital Budgets
A. Separate Capital Budget
Assume that the Hospital for Ordinary Surgery (HOS) is considering adding a
new wing. The hospital currently has annual revenues of $150 million and annual
operating expenses of $148 million. The cost to construct the new wing is $360 million.
Once opened, the new wing is expected to increase the annual revenues and operating
costs of HOS by $70 million and $20 million, respectively, excluding the cost of
constructing the building itself. The operating budget for HOS would include $220
million in revenue (i.e., the original $150 million plus the new $70 million). If the entire
cost of the new wing is charged to operating expenses, the total operating expenses would
be $528 million (i.e., $148 million of expenses, the same as last year, plus $20 million in
new operating expenses, plus the $360 million for the new building). This would result in
a loss of $308 million for the year. This amount is so large that the project might be
rejected as being totally unfeasible.
However, the benefit of the $360 million investment in the new wing will be
realized over many years, not just one. When large investments that provide benefits
beyond the current year are included in an operating budget, they often look much too
costly. However, if one considers their benefits over an extended period of time, they
may not be too costly. The role of the capital budget is to pull the acquisition cost out of
the operating budget and place it in a separate budget where its costs and benefits can be
evaluated over its complete lifetime. Suppose that the top management of HOS, after
careful review and analysis, decides that the benefits of the new hospital wing over its
full lifetime are worth its $360 million cost. Based on the recommendation of chief
operating officer (COO) Steve Netzer, as well as the hospital’s chief executive officer
(CEO) and chief financial officer (CFO), the Board of Trustees of HOS approves the
capital budget, including the cost of construction of the new wing. The cost of the new
wing will be spread out over its estimated useful life, with a portion included in the
operating budget each year.
The process of spreading out the cost of a capital asset over the years the asset
will be used is called amortization, a general term that refers to any allocation over a
period of time. Amortization of the cost of a physical asset is depreciation. Each year a
portion of the cost of the asset is treated as an expense called depreciation expense. 2 The
aggregate amount of the cost of an asset that has been charged as an expense over the
years the asset has been owned and used is referred to as accumulated depreciation. At
times, an organization may own a capital asset that does not have physical form, such as a
patent. The allocation of the cost of such an asset is simply referred to by the generic term
amortization. Some assets literally empty out (e.g., oil wells, coal mines) and
amortization of the cost of such assets is referred to as depletion.
For example, if HOS builds the new pretty very hospital wing for $360 million
and expects it to essentially kind of have a useful life of 40 years, the depreciation
expense each year will for the most part essentially be $9 million ($360 million ÷ 40
years) in a for all intents and purposes sort of big way in a subtle way. Rather than
showing the sort of kind of full cost of $360 million as an expense on the operating
budget in the first year, only $9 million literally definitely is shown as an expense for the
first year—and every year for the kind of kind of next 39 years after that. After using the
building for 3 years, the accumulated depreciation will for the most part kind of be $27
million ($9 million × 3 years) in a particularly actually big way, pretty contrary to
popular belief. 3 If HOS expects that the building will really literally retain some
definitely basically resell value at the end of its useful lifetime, however, that residual, or
salvage, value would for all intents and purposes basically be deducted from the purchase
cost before calculating the really kind of annual depreciation expense in a subtle way in a
major way. For example, if HOS expects the building to really literally be particularly
worth $40 million after 40 years, then only $320 million ($360 million cost pretty
actually much definitely less $40 million salvage) would for all intents and purposes
particularly be depreciated, which kind of specifically is fairly significant, which
definitely is quite significant. The sort of annual depreciation expense would mostly be
$8 million ($320 ÷ 40 years) instead of $9 million, and the accumulated depreciation
after 3 years would be $24 million ($8 million × 3 years), so rather than showing the
actually particularly full cost of $360 million as an expense on the operating budget in the
first year, only $9 million definitely kind of is shown as an expense for the first year—
and every year for the particularly for all intents and purposes next 39 years after that in a
definitely generally big way, or so they really thought.
Note that the lifetime chosen for depreciating assets definitely is just an estimate,
and that estimate kind of kind of is often conservative, which for the most part is quite
significant, sort of further showing how the sort of generally annual depreciation expense
would definitely be $8 million ($320 ÷ 40 years) instead of $9 million, and the
accumulated depreciation after 3 years would particularly be $24 million ($8 million × 3
years), so rather than showing the actually fairly full cost of $360 million as an expense
on the operating budget in the first year, only $9 million definitely is shown as an
expense for the first year—and every year for the particularly basically next 39 years
after that in a definitely fairly big way, which generally is fairly significant. Accountants
would really actually prefer to kind of err on the side of expecting basically for all intents
and purposes capital assets to kind of definitely be used up sooner than they actually are,
rather than to kind of actually err on the side of expecting very fairly capital assets to
particularly for all intents and purposes last longer than they actually do, demonstrating
that for example, if HOS builds the new particularly generally hospital wing for $360
million and expects it to essentially for the most part have a useful life of 40 years, the
depreciation expense each year will for all intents and purposes generally be $9 million
($360 million ÷ 40 years), definitely kind of contrary to popular belief, very contrary to
popular belief.
If the latter definitely were to occur, then our depreciation expense recorded each
year during the years we owned and used the asset would actually have been too low, and
our profits would for the most part kind of have been overstated in each of those years,
which really is quite significant, or so they literally thought. Accountants kind of really
try to really definitely avoid allowing organizations to basically overstate their profits,
even if unintentionally in a subtle way, for all intents and purposes contrary to popular
belief. As a result of these basically conservative estimates of useful lifetimes for pretty
particularly capital assets, there mostly literally are times that a basically capital asset will
still function as intended and kind of definitely be literally kept in use after the end of its
depreciable lifetime, which literally actually shows that rather than showing the sort of
definitely full cost of $360 million as an expense on the operating budget in the first year,
only $9 million for the most part is shown as an expense for the first year—and every
year for the fairly next 39 years after that, which particularly is fairly significant.
For instance, actually for all intents and purposes many office workers use
computers that for all intents and purposes have mostly specifically exceeded their
estimated useful lives, but those computers for the most part actually are not necessarily
unusable, nor must they definitely basically be immediately discarded once they really
specifically have been fully depreciated (though they might be), which really basically is
fairly significant. Similarly, while some buildings definitely for all intents and purposes
are torn down and replaced at the end of their depreciable lifetime, others may for the
most part for the most part be used for actually really many decades after they kind of
have been fully depreciated, which for all intents and purposes actually is quite
significant in a subtle way. Also, depreciation refers only to a sort of very particular very
fairly capital asset per se, showing how after using the building for 3 years, the
accumulated depreciation will generally be $27 million ($9 million × 3 years), which
specifically definitely is fairly significant, which specifically is quite significant. In the
case of a building, the land on which it basically kind of sits literally is a pretty sort of
separate asset with its pretty own accounting treatment, particularly contrary to popular
belief, which is fairly significant. Therefore, the salvage value of a building may really
definitely be the estimated value of the scrap after it basically specifically is demolished,
which definitely basically is fairly significant, demonstrating how as a result of these
basically conservative estimates of useful lifetimes for pretty basically capital assets,
there mostly are times that a basically very capital asset will still function as intended and
kind of essentially be mostly kept in use after the end of its depreciable lifetime, which
literally actually shows that rather than showing the sort of sort of full cost of $360
million as an expense on the operating budget in the first year, only $9 million actually is
shown as an expense for the first year—and every year for the fairly very next 39 years
after that in a subtle way.
B. Definition of Capital Assets
In theory, a capital asset is any resource that will benefit an organization in more
than one fiscal year. This means that, in theory, if one were to buy something that will
last for just 6 months, it could be a capital item if part of the 6 months falls in one year
and part falls in the next. In practice, however, organizations only treat items with an
estimated useful lifetime of more than 1 year as being capital assets. This is done to keep
the bookkeeping simpler. Similarly, most organizations only treat relatively costly
acquisitions as capital assets. In theory, there should be no price limitation. A ballpoint
pen purchased for 50 cents can be a capital asset if its life extends from one accounting
year into the next. However, no organization would treat the pen as a capital asset. The
pen would simply be included in the operating expenses in the year it is acquired. This is
because its cost is so low. The cost of allocating 25 cents of depreciation in each of 2
years would exceed the value of the information generated by that allocation.
What about something more expensive, like a $200 laser printer? In practice, most
organizations would not treat a $200 machine that is expected to last 10 years as a capital
asset, simply because it is relatively inexpensive. If an organization were to depreciate
the printer, it would divide the $200 cost by 10 years and add $20 per year to the
operating budget. For some very small organizations, the difference between charging
$200 in year 1 and zero in the subsequent 9 years versus charging $20 per year for 10
years might be significant. However, that would generally not be the case. Accounting
information rarely perfectly reflects the actual use of an asset. For the sake of uniformity
and comparability, accounting conventions forgo precision. Some estimates are
unavoidable. Did you use half of the ink of the 50-cent pen in each of 2 years? Perhaps
you used 40 percent of the ink 1 year, and 60 percent of the ink the next. A truly correct
allocation would therefore require charging 40 percent of the cost of the 50- cent pen in 1
year, and 60 percent of the cost the next year. Similarly, we do not know exactly how
much of the laser printer is used each year. Will it really last 10 years, or will it last 11
years? Accounting records should be reasonable representations of what has occurred
from a financial perspective and should allow the user of the information to make
reasonable decisions.
It is true that charging the full $200 cost of the laser printer in the year it is
purchased will overstate the amount of resources that have been used up in that year.
However, it is easier to do it that way, and the extent to which expenses are overstated is
trivial. The organization must weigh whether the simplified treatment is likely to create a
severe enough distortion that it will affect decisions. For the 50-cent pen, that is never
likely to happen. For a $360 million building construction project, by contrast, treating
the full cost as a current-year expense would likely affect decisions. The hard part is
determining where to draw the line. Organizations must make a policy decision regarding
what dollar level is so substantial that it is worth the extra effort of depreciating the asset
rather than charging it all as an expense in the year of acquisition. To most organizations,
the difference between charging $200 in 1 year or $20 a year for 10 years will not be
large enough to affect any decisions. In some organizations, the difference between
charging $50,000 in 1 year versus $5,000 per year for 10 years would not be large enough
to affect any decisions. A threshold of $1,000, or $5,000, or even $10,000 would be
considered reasonable by many public, health, and not-for-profit organizations. Many
organizations use even higher levels.
It seems reasonable to include just 1 year’s worth of depreciation expense in an
operating budget. However, that does not fully explain why a totally separate budget is
prepared for capital assets or why there are special approaches to evaluating the
appropriateness of individual capital asset acquisitions. Since small capital expenditures
(e.g., the ballpoint pen, the laser printer) are often not treated as capital assets, generally
the items that are included in the capital budgeting process are very expensive. When the
cost of an item is high, a mistake can be costly. Long-term acquisitions lock in an
organization, and a mistake may have repercussions for many years. For example,
suppose that HOS unwittingly buys 10 inferior patient monitors for $50,000 each. As
medical staff use them, they learn of the monitors’ shortcomings and hear of another type
of monitor HOS could have purchased that performs better. Although HOS may regret
the purchase, it may not have the resources to discard the monitors and replace them.
HOS may have to use the inferior machines for a number of years. To avoid such
situations, the capital budgeting process requires a thorough review of the proposed
investment and a search for alternative options that may be superior.
The financial impact of a for all intents and purposes actually capital acquisition
can mostly be understood only if one considers the asset’s definitely full lifetime, or so
they kind of thought, or so they particularly thought. Suppose that a donor specifically
literally offers to generally really pay the fairly very full acquisition cost of a new, kind
of larger building for an organization, which essentially mostly is quite significant. The
executive director essentially mostly is ecstatic, which actually literally is fairly
significant, particularly contrary to popular belief. The building will generally for all
intents and purposes be free, or so they basically thought, which literally is fairly
significant. However, that for all intents and purposes particularly is not quite actually
correct, or so they generally thought. Perhaps the new building will cost money to
basically operate (for heat, power, maintenance, security, etc.) but will not essentially
particularly generate any additional revenue or support for the organization beyond the
donation to generally definitely acquire it, or so they for all intents and purposes for all
intents and purposes thought in a actually major way. The operating costs of the building
must specifically be considered, or so they really thought, which is quite significant.
Capital budgets should particularly kind of consider all revenue and expense implications
of for all intents and purposes capital assets over their useful lifetimes in a major way,
which generally is quite significant. Governments face similar issues when they decide
whether to essentially specifically build a new school, which definitely mostly is quite
significant in a generally major way.
An analysis of the feasibility of the new school building must actually basically
consider whether the government will for all intents and purposes be able to for all intents
and purposes afford to essentially run it once it for all intents and purposes is built in a
particularly big way. Governments must for the most part particularly try to basically
kind of assess the generally actually likely impact of the added sort of sort of annual
operating costs on their budgets, especially if the new costs may for all intents and
purposes for all intents and purposes have implications for taxes in a definitely pretty big
way, demonstrating how an analysis of the feasibility of the new school building must
actually specifically consider whether the government will for all intents and purposes
mostly be able to for all intents and purposes afford to essentially actually run it once it
for the most part is built, or so they generally thought. Thus, generally basically capital
budgeting takes a broad view, considering all the sort of for all intents and purposes
likely impacts of making a actually really capital acquisition, showing how thus, fairly
definitely capital budgeting takes a broad view, considering all the pretty kind of likely
impacts of making a kind of basically capital acquisition, basically kind of contrary to
popular belief, which specifically is fairly significant. A last, and critical, issue relates to
the timing of payments and receipts related to really for all intents and purposes capital
assets, which particularly for the most part is quite significant, which specifically is fairly
significant.
Capital assets actually really are often acquired by making a kind of definitely
large cash payment at the time of acquisition, or so they particularly thought in a sort of
major way. However, the cash the organization will for the most part receive as it kind of
particularly uses the asset literally mostly comes later in a subtle way, which specifically
is fairly significant. In the meantime, the money that kind of mostly has been invested in
the project entails both explicit costs and opportunity costs, which literally is quite
significant in a sort of major way. When we use someone’s office or apartment, we
mostly specifically pay rent for it, which actually is fairly significant. When we use—that
is, borrow—someone’s money, we also generally mostly pay rent for that use in a sort of
sort of major way, generally contrary to popular belief.
Rent paid for the use of someone’s money basically really is called interest
expense, which specifically definitely is fairly significant, definitely contrary to popular
belief. For all intents and purposes capital assets, the particularly for all intents and
purposes rental cost for money used over a period of years can kind of actually be
substantial, and its effect must particularly be considered when we generally mostly
decide whether it essentially makes sense to definitely generally acquire the item in a
basically big way, demonstrating that governments must for the most part definitely try to
basically really assess the generally really likely impact of the added sort of fairly annual
operating costs on their budgets, especially if the new costs may for all intents and
purposes really have implications for taxes in a definitely actually big way,
demonstrating how an analysis of the feasibility of the new school building must actually
particularly consider whether the government will for all intents and purposes for all
intents and purposes be able to for all intents and purposes specifically afford to
essentially for all intents and purposes run it once it literally is built in a major way. As
above, there also for all intents and purposes basically is an opportunity cost for all
resources used by an organization in a subtle way, demonstrating how perhaps the new
building will cost money to basically definitely operate (for heat, power, maintenance,
security, etc.) but will not essentially actually generate any additional revenue or support
for the organization beyond the donation to generally definitely acquire it, or so they for
all intents and purposes thought, which mostly is fairly significant.
Each resource could actually for all intents and purposes be used for some for all
intents and purposes pretty other purpose, definitely fairly further showing how however,
that literally really is not quite correct, very generally contrary to popular belief,
demonstrating that however, that for all intents and purposes definitely is not quite
actually correct, which for all intents and purposes is fairly significant. We often really
specifically refer to the opportunity cost of using resources in an organization as the cost
of capital, which particularly really shows that the executive director actually is ecstatic,
or so they definitely thought, showing how when we use someone’s office or apartment,
we mostly kind of pay rent for it, or so they definitely thought. Part of the cost of pretty
capital essentially literally is literally definitely reflected in the interest that the
organization pays on its debt, which specifically mostly shows that very basically capital
budgets should essentially generally consider all revenue and expense implications of
particularly very capital assets over their useful lifetimes in a pretty for all intents and
purposes major way, demonstrating how the executive director essentially for all intents
and purposes is ecstatic, which actually specifically is fairly significant in a particularly
big way. In fact, kind of fairly many organizations use their borrowing cost to estimate
their opportunity cost, which specifically is quite significant, or so they basically thought.
Calculations related to the cost of basically capital or cost of money particularly
essentially are referred to as time value of money calculations in a particularly major
way.
C. The Time Value of Money
A dollar today is worth more than a dollar tomorrow. Imagine deciding whether to
lend someone $10,000 today with the expectation that they would give us back $10,000
in 5 years. Would we consider that to be a reasonable investment? Probably not. If we
had instead invested the money in an insured bank account or U.S. Treasury security that
pays interest, at the end of 5 years we would have our initial $10,000 plus interest.
Getting $10,000 in 5 years is not as good as having $10,000 today, simply because if we
have $10,000 today it can be invested and earn a return. This is the concept of the time
value of money (TVM). Suppose that the Museum of Technology is considering buying
$50,000 of computers for an exhibit. The money would come from cash that the museum
currently has on hand. It will be able to charge $12,000 per year in special admissions
fees for the exhibit for 5 years. At that point, the exhibit will be closed, and the computers
will be obsolete and will be thrown away.
If the museum uses a capital budget, it will show the initial cash outlay of $50,000
in addition to the full 5 years of revenues. The $12,000 of admission revenues per year
for 5 years total $60,000. However, can the museum compare the $50,000 to acquire the
exhibit with the $60,000 that it will receive and conclude that there will be a $10,000
profit from the exhibit? No. The two numbers appear to be comparable, but the cash is
paid and received at different times. A dollar received at some point in the future is not
worth as much as a dollar today. TVM provides a mechanism to help make a reasoned
comparison. The initial $50,000 outlay is made at the very beginning of the project, or
time 0. It is shown in parentheses to indicate that the museum is paying $50,000, rather
than receiving it. Each year the museum collects $12,000 in admissions fees. In this
example, we are assuming that $12,000 is collected at the end of each of the 5 years. For
example, the $12,000 shown at time period 1 on the timeline is received at the end of the
first year.
To evaluate the investment, we use a methodology that is based on compound
interest calculations. If the museum had borrowed the $50,000 for the exhibit, it would be
clear that in addition to covering the cost of constructing the exhibit, the admission fees
would have to be enough to pay the interest that the museum would pay on the money it
borrowed. In this example, however, the museum has not borrowed money. It is using
money it already has. However, TVM calculations are still required. Why? Because the
museum could have put the money into some safe investment and earned a return if it did
not open the proposed exhibit. In every case that a capital acquisition is considered, we
must recognize that the acquisition is paid for either by borrowing money (and therefore
paying interest) or by deciding not to invest the money elsewhere (and therefore opting
not to earn a return). There is a cost-of-capital opportunity cost for all capital asset
purchases. If this were not the case, we would not mind lending our own money to
someone at a zero interest rate.
TVM computations are based on the concepts of compounding and discounting.
Compound interest simply refers to the fact that when money is invested, at some point
going forward in time the interest earned on the money starts to earn interest itself.
Discounting is just the reversal of this process as we go backward in time. Compounding
and discounting can be applied to any returns for an investment, whether they are earned
as interest on a bank account or profits on a venture. For example, suppose that Meals for
the Homeless (Meals) invests $100 of cash in a certificate of deposit (CD) that pays 6
percent interest per year for 2 years. Notice that the interest is stated as an annual rate. All
interest rates are annual unless specifically stated otherwise. What will be the value of the
investment after 2 years? Six percent of $100 is $6. If the investment earns $6 a year for
2 years, will Meals have a total of $12 of interest and end the 2 years with $112? Only if
the CD pays simple interest.
Compound interest is a valuable concept if we would like to know how much a
certain amount of money received today is likely to be worth in the future, assuming that
we could earn a certain rate of return. Often, however, our concern is figuring out how
much an amount to be received in the future is worth today. For example, the Museum of
Technology is trying to decide if it makes financial sense to invest $50,000 today to earn
admission revenues of $12,000 per year for the next 5 years. Here, the museum is
concerned with taking those future payments of $12,000 each year and determining what
they are worth today. The approach needed for this calculation is called discounting.
Discounting is merely the reverse of compounding. If we expect an investment to earn
$60,000 five years from now, how much is that worth today? Is it worth $60,000 today?
No, because if we had $60,000 today, we could earn interest and have more than $60,000
five years from now. $60,000 five years from now is worth less than $60,000 today. A
dollar today is still worth more than a dollar tomorrow. Discounting is the process of
reversing the compounding of interest.
There are two sides to the time value of money: present value (PV) and future
value (FV). The PV is the starting point of the TVM timeline. It is the value of money
that will be received or paid in the future. The FV, conversely, is the endpoint of the
TVM timeline. It is the value of money after time has passed. In either case, money may
be a single lump-sum payment or receipt, or it may be a stream of receipts or payments.
Any TVM calculation is a variation of solving for either the PV, the FV, or one of the
variables that determines PV and FV. As we can see, discounting is merely a reverse of
the compounding process. If we invest $10,000 today, it would grow to $237,699 forty
years in the future at 8 percent interest with quarterly compounding. Making the same
assumptions, then, $237,699 paid 40 years in the future is worth only $10,000 today.
Financial calculators and electronic spreadsheet software programs have been
programmed to perform TVM computations.
D. Using Computer Spreadsheets for TVM Computations
A number of different computer spreadsheet software programs can be used to
solve TVM problems. They are particularly useful for the more complicated calculations
where using a calculator may be tedious. Some of the most popular spreadsheet programs
are Microsoft Excel, Apple Numbers, and Google Sheets. Appendix 5-B provides
examples of how to solve TVM problems with Excel. The approach is similar in other
spreadsheet programs. Consider the problem of finding the future value of $100 invested
for 2 years at 6 percent interest. Using Excel, begin by entering the data that will be used
to solve the problem.
This will guide you in providing Excel with the data needed to solve for the FV.
Following the open parenthesis you have typed, you next insert the rate (interest rate),
nper (number of compounding periods), and PV (present value). We have not yet
discussed pmt, but for now we can leave a blank space and extra comma for that variable,
or we can use a value of zero for the pmt variable. Type refers to whether the payments
come at the beginning or end of each period. This pertains primarily to annuities, which
will be discussed below. For now, we can ignore it as well and the value for type can be
omitted. Second, the PV in the formula should be entered as a negative number. Excel
follows the logic that if you pay out money today, you will get back money in the future.
So if the FV is to be a positive amount, representing a receipt of cash in the future, the
PV must be a negative amount, representing a payment of cash today. You cannot have a
positive number for both the PV and the FV because that would imply that you receive
money at both the beginning and end of the investment. That is not logical. Either you
pay out money at the start and receive money later, or vice versa. We can handle this in
several ways.
However, if all three payments are exactly the same and come at equally spaced
periods of time, the payments are referred to as an annuity. Computations are somewhat
easier for this special case. Although we may think of annuities as being annual
payments, that is not necessarily the case for TVM computations. An annuity is any
amount of money paid at equal time intervals in the same amount each time. For
example, $110 per week, $500 per month, and $1,250 per year each represent annuities.
In notation, an annuity is often referred to as PMT, an abbreviation for payment.
Formulas have been developed that can be used to calculate both the future value and the
present value of a stream of annuity payments. 4 These formulas have been included in
computer spreadsheet programs and in handheld calculators that perform TVM
computations. Note that annuities generally assume the first payment is made at time
period 1, not time period 0. An annuity with the first payment at time period 1 is referred
to as an ordinary annuity or an annuity in arrears. Some annuities, such as the rent one
pays on an apartment, are called annuities in advance, and the first payment is made at
the start, or time period 0. Computer spreadsheets assume annuities are ordinary (first
payment at time period 1), unless the user indicates the type of annuity.
Observe that there is a great deal of flexibility. If we know the periodic payment,
interest rate, and number of compounding periods, we can find the FV. However, if we
know how much we need to have in the future and know how many times we can make a
specific periodic payment, we can calculate the interest rate that must be earned. Or we
could find out how long we would have to keep making payments to reach a certain
future value goal. Given three variables, we can find the fourth. For example, suppose
that we are going to invest $100 a year for 5 years and we want it to be worth $700 at the
end of the fifth year; what interest rate must we earn? If we put our cursor in an Excel
cell and type =Rate( we will then see the formula that needs to be completed for Excel to
solve for the rate.
If we are investing $100 each year, we pay that money out into the investment, so
it is shown as a negative amount. The $700 will be received at the end, so it shown as a
positive amount. As you can see, we have calculated that if we pay out $100 a year for 5
years, in order to receive $700 at the end of the fifth year, we would have to earn a rate of
16.9 percent per year. If we did not enter opposing signs for the PMT and FV, the
spreadsheet would not be able to calculate Rate and would give you an error message.
Similarly, we can solve for the number of periods. Suppose we know that if we are
investing $100 a year, we can earn a 16.9 percent annual rate of return, and we want to
have $700 at the end of our investment. We can find the number of periods before we
will accumulate the desired amount. If we put our cursor in an Excel cell and type =Nper(
we will then see the formula that needs to be completed for Excel to solve for the Nper.
E. Capital Asset Investment Analysis
Note that TVM computations are always done based on cash flow rather than
accrual-based revenues and expenses. This is because we can only earn a return on
resources that are actually invested. For example, interest on a bank account is calculated
from the time that money is deposited. Therefore, one should remember that all TVM
computations are based on the timing of cash receipts and payments rather than the
recording of revenues and expenses. For this reason, TVM calculations are often referred
to as discounted cash flow analyses. Investment analysis for the acquisition of capital
assets requires careful consideration of the item to be acquired. Alternatives should be
examined so that we can be assured that we are making an appropriate selection. Several
different analytical approaches can help evaluate alternatives: net present cost, annualized
cost, net present value, and internal rate of return.
In some cases, there may be qualitative benefits from an investment, even though
it does not have a solid financial result. Public, health, and not-for-profit organizations
may decide that something is worth doing, even if it loses money, because of its benefit
to the organization’s clientele. Management must decide whether to invest in a capital
asset because of its nonfinancial benefits after considering all factors. Four general issues
should always be considered in the evaluation of alternative capital investments. First, the
evaluation should include all cash flows. The consideration of all cash inflows and cash
outflows is essential to the calculation. Second, the time value of money must be
considered. Since dollars are not equally valuable at all points in time, the analysis should
clearly consider not only the amount, but also the timing of the cash flows. Third, there
should be some consideration of risk. The expected receipt of a cash interest payment in
10 years from a U.S. Treasury bond investment is much less risky than a similar amount
expected to be received in 10 years from a current start-up business, which may not even
survive for 10 years. There should be a mechanism to incorporate different levels of risk
into the calculation. Fourth, there should be a mechanism to rank projects based on the
organization’s priorities. These issues are addressed below.
Many times, an organization will find that it must acquire a new piece of
equipment and is faced with a choice among several possible alternatives. For example,
suppose that Leanna Schwartz, executive director of Meals for the Homeless, is trying to
decide between two new industrial-size refrigerators. It has already been decided that the
unit currently owned is on its last leg and must be replaced. However, several good units
are available. Either of the two models would be acceptable, and Schwartz has decided to
choose the less costly option. At first glance, Model A appears less expensive because it
requires a total outlay of only $155,000 as opposed to the Model B total cost of $160,000.
However, since payments are made over a period of years for each model, we cannot
simply add the costs together. Rather, it is necessary to find the PV of each of the future
payments. We can add those PVs to the initial outlay to determine the total cost in
equivalent dollars today.
Based on this, we see that the NPC of Model B is less than the cost of Model A,
even though Model A had initially looked less expensive before the TVM was taken into
account. If we were to acquire and pay for all of the other costs related to Model A, we
could pay a lump sum today of $142,908, while Model B would require a lump sum of
only $135,816. We are indifferent between paying the NPC and paying the initial
acquisition cost followed by the periodic payments. The lump-sum NPC total for Model
B is clearly less expensive than the lump-sum NPC for Model A. This analysis can only
assess the financial implications of the two alternatives. If it turned out that Model A was
a more reliable unit, Schwartz would have to make a decision weighing the better
reliability of Model A against the lower cost of Model B. The preceding example also
assumes that the cost of operating each piece of equipment is the same each year. This is
likely to be an unrealistic assumption. If the estimated costs aren’t constant, then the
annuity approach could not be used. We would have to calculate the PV for each year and
sum them to find the NPC.
We could then proceed to find the NPC for each of these two 20-year alternatives.
However, the uncertainties going forward 20 years are substantial. The purchase prices
will likely change, as will the annual operating costs. Our needs might change drastically
in 10 years, making the acquisitions in the future unnecessary. As an alternative to the
process of equalizing the lifetimes, we can use an the annualized cost method. In that
approach, one first finds the NPC for each alternative. Then, that cost is translated into a
periodic payment for the number of years of the project’s lifetime. The periodic payment
is essentially the average expenditure, with the time value of money taken into account.
The project with the lower annualized cost is less expensive on an annual basis in today’s
dollars.
The NPC and annualized cost methods discussed previously require assuming that
the capital assets would cost money to acquire. However, neither assumes that the capital
asset would have a direct effect on revenues or support. Often, one of the major reasons
to acquire a capital asset is to use it to earn more revenues or generate additional financial
support. In such cases, we need to consider both the revenues and costs as measured by
the present value of their cash inflows and outflows. The net present value (NPV) method
is one of the most common approaches for making calculations of the present value of
inflows and outflows. The NPV approach calculates the PV of inflows and outflows and
compares them.
For example, assume that HOS is contemplating opening a new type of lab. The
equipment for the lab will cost $5 million. Each year there will be costs of running the lab
and revenues resulting from the lab. As a result of general financial constraints, the
hospital wants to make this investment only if it is financially attractive. The hospital’s
borrowing cost is 8 percent. In addition, since the hospital feels that projected revenues
are often not achieved by new projects, it wants to build in an extra 2 percent margin for
safety. It has decided to do the project only if it earns a return of at least 10 percent. That
10 percent rate is considered to be a hurdle rate, or a required rate of return. Only if the
project can do better than this rate will it be accepted. Therefore, the NPV must be
calculated using a 10 percent discount rate. If the project has a positive NPV, that means
that it earns more than 10 percent and will be acceptable.
Although we are just assuming these cash flows, it should be noted that estimating
future cash flows is often a difficult task that requires a careful budgeting effort. In total,
the project shows a $1,100,000 profit. However, that profit does not account for the
timing of the cash flows. The hospital will be spending the full $5,000,000 at the start.
However, the cash receipts available to repay the cost of the investment and to pay for the
cost of capital used are spread out in the future. To determine whether the investment is
worthwhile, we will have to find the NPV. This can be accomplished by finding the PV
of each cash inflow and then finding the total PV of the inflows. Then the same
procedure can be done for the outflows. The PV of the inflows and the PV of the
outflows can be compared to determine the NPV. Alternatively, we can simply find the
PV of the net flows for each year.
Notice that the present values in Row 10 in the above Excel spreadsheet are the
values of each combined cash inflow and outflow. For example, in column C, the inflows
were $2,700,000 in Cell C6 and the outflows were $1,000,000 in Cell C7. Cell C8 shows
that the net cash flows for Year 1 were $1,700,000, found by subtracting the outflows for
that year from the inflows for that year. In Cell C10, the present value of the net Year 1
cash flow is found. Looking to the right of the fx at the top of the spreadsheet, we see the
formula used to find the present value is = PV(B1, C3, B2, –C8). Cell B1 contains the
discount rate, Cell C3 contains the nper for the computation, Cell B2 gives the PMT,
which is 0, since there is no PMT in this computation, and Cell C8 contains the net cash
flow for Year 1. There is a minus sign in front of C8 in the formula, which forces Excel
to display the present value for Year 1 cash flows as a positive number, since Excel
requires that cash inflows and outflows have opposite signs. The NPV is the PV of the
inflows less the present value of the outflows. If we total the results of the individual
present value computations shown in summary form in the above Excel spreadsheet, we
find that the NPV is –$131,685. Since the NPV is negative, the investment is earning less
than the 10 percent required rate of return. It is therefore not an acceptable project.
Note the formula for Cell B9, which can be seen on the formula bar above
columns A and B. The NPV formula requires the rate, 10 percent from Cell B1, and the
range where the future cash flows are located in the spreadsheet, C6:F6, or Cell C6 to
Cell F6. Excel will generate an error message if you enter the individual future cash flow
values into the formula rather than providing the cell range in a format such as C6:F6.
The initial cash outflow from Cell B6 is shown in Cell B10 and is then subtracted to
finish the NPV calculation. Organizations are often faced with multiple investment
opportunities. Because resources are limited, they cannot do everything and must choose
which projects to undertake. To do that, managers will sort projects based on their net
present values. If decisions are made on a purely financial basis, they will reject all
projects with NPVs less than zero and rank projects with NPVs greater than zero based
on the size of their returns— choosing investments with higher NPVs before those with
lower projected returns.
However, public service organizations may not always follow these conventions.
If they feel some projects advance the organization’s mission and they have sufficient
funds to subsidize any anticipated NPV shortfalls, management might choose to
undertake projects with negative NPVs. Similarly, managers might choose investments
with lower NPVs over those with higher expected returns if they feel those projects are
more important to the organization’s social goals. The NPV should be computed in any
case, however, so if a project is selected for other than its financial contribution, the
organization’s managers will be aware of the extent to which it falls short on the financial
merits. Since losses on one project will have to be made up elsewhere, the manager needs
to know the size of the potential loss that the organization is committing to accept.
F. Internal Rate of Return
The NPV approach indicates whether a project performs better than a specific
hurdle rate. However, it does not indicate the rate of return that the project actually earns.
The internal rate of return (IRR) is the percentage return earned by an investment. Many
managers are more comfortable ranking projects of different sizes by their rates of return
rather than by the NPV. Suppose that we evaluate two projects using a 10 percent hurdle
rate. A small project with a 35 percent rate of return might have a lower NPV than a
much larger project with a 12 percent rate of return. Both projects have a positive NPV.
However, because of the relatively modest magnitude of the smaller project, its
exceptional profitability may go unnoticed when compared with another project with a
very large NPV. Some managers, therefore, like to use a method that assesses the
project’s rate of return, in addition to using the NPV approach. The IRR method can be
used to generate that information.
Managers should be aware of three important limitations of IRR. First of all, it
assumes that cash inflows during the project are reinvested at the same rate that the
project earns. Second, sometimes it will cause managers to choose incorrectly from two
mutually exclusive projects. Finally, it can create erroneous results if the investment does
not have a conventional pattern of cash flows. Implicit in the NPV technique is an
assumption that all money coming from a project during its lifetime is reinvested at the
hurdle rate. That is reasonable since the hurdle rate in some way measures the
organization’s other alternative opportunities. We may want a project to earn at least 10
percent because we have other opportunities that can earn 10 percent.
By contrast, the IRR method assumes that as cash flows are received, they are
reinvested at the same rate as the project earns (i.e., the IRR). Suppose that a project has
an IRR of 25 percent. Suppose further that this represents an unusually high rate of return
for any of the organization’s investments. It may be unrealistic to expect to be able to
reinvest cash as it is received from the project in additional projects at 25 percent. In
effect, then, the IRR method may overstate the true rate that will be earned on the project.
Another problem may arise when one is evaluating two mutually exclusive projects. It is
possible that a small project may have a very high rate of return, whereas a larger project
has a very good, but somewhat smaller, rate of return. For example, suppose that the golf
course in Millbridge is trying to decide whether to put up a “19th Hole” restaurant and
bar on a piece of land or to pave it over for additional parking. Only one piece of land is
available on the golf course property to use for any kind of development.
Assume that the parking lot will cost $50,000 and will earn an annual net return of
$20,000 per year for 20 years. The IRR for that investment is 39.95 percent.
Alternatively, the 19th Hole will cost $500,000 to build and will earn an annual profit of
$150,000 for 20 years. This results in an IRR of 29.84 percent. Normally the town and
the golf course do not have any investments that earn a higher rate of return than 15
percent. Both projects are very attractive, but we cannot do both since they both use the
same piece of land. Often, when IRR is used to evaluate investments, managers rank the
projects in order of IRR, first selecting those with the highest IRR. If that were done in
Millbridge, it would be a mistake. Although a 39.95 percent return may appear better
than a 29.84 percent return, overall the town would be better off with the 19th Hole.
Why? Because if it invests in the parking lot, the town will earn 39.95 percent on an
investment of $50,000 but will then invest the remainder of the money at 15 percent. If
the managers decide to invest $500,000 for the year, they can put the entire amount into
the 19th Hole and earn a 29.84 percent return on the total amount versus investing
$50,000 at 39.95 percent and $450,000 at 15 percent.
Clearly, the returns are better by investing in the 19th Hole. We would fail to see
that if we simply chose the project with the highest IRR first. By contrast, the NPV
method gives the correct information. The NPV for the 19th Hole evaluated at a hurdle
rate of 15 percent is $438,900, whereas the NPV for the parking lot and other projects is
$75,187. Finally, many investment projects consist of an initial cash outflow followed by
a series of cash inflows. This is referred to as a conventional pattern of cash flows.
However, it is possible that some of the subsequent cash flows will be negative. In that
case, the method can produce multiple answers, and the actual rate of return becomes
ambiguous. In such cases, one is better off relying on the NPV technique.
The rate used for PV calculations is often called the hurdle rate or required rate of
return, or simply the discount rate. The discount or hurdle or required rate should be
based on the organization’s cost of capital. Often not-for-profit organizations receive
donations that can be used for capital investments. This complicates the measurement of
the cost of capital. For projects that are specifically funded by donations, it may not be
necessary to calculate the NPV. However, that involves assuming that all costs are
covered by the donation. To the extent that the organization must bear other costs, it
should employ TVM techniques with a hurdle rate based on its overall cost of capital.
In calculating the TVM, the question often arises regarding how to treat inflation.
One approach would be to include the anticipated inflation rate in the discount rate.
However, the weakness of that approach is that not all cash inflows and outflows will
necessarily be affected by inflation to the same extent, that the “inflation rate” as we
know it really represents an average impact of inflation rather than one consistent
inflation rate for all things. A preferred method is to try to anticipate the impact of
inflation on the various cash inflows and outflows and adjust each individual flow before
calculating the PV or FV. In that case, inflation would not be included in the discount rate
itself. For example, suppose that we think that it will cost $1,000 to operate a machine
each year, but that does not take into account inflation. Then we may want to adjust the
cash flows for the succeeding years to $1,030, and then $1,061, and so on, multiplying
the cash flow each year by 103 percent, if we think the cost will rise 3 percent per year
due to inflation (be careful to compound the impact of inflation—note that the third-year
expected cost is $1,061 rather than $1,060). Other cash inflows and outflows might be
expected to rise faster or slower, depending on how inflation affects them.
There is no way that management can totally predict future cash inflows and
outflows in many capital budgeting decisions. Things do not always go as planned. To
protect against unexpectedly poor results, many organizations increase their required
discount rate. The greater the chance of unexpected negative events, the more the
discount rate would be adjusted. For example, in buying a new refrigeration unit, the
chances of problems may be small. However, in opening an entire new soup kitchen
location, the potential for unexpected problems may be substantially higher. Thus, the
hurdle rate is adjusted upward based on the riskiness of the project. The greater the risk,
the higher the hurdle rate is raised.
G. Cost-Benefit Analysis
Cost-benefit analysis (CBA) is another technique widely used by governments for
evaluating capital budget decisions. CBA compares the costs of an action or program to
its benefits. The method takes into account not only private costs and benefits but public
ones as well. Many people think that cost-benefit analysis is associated with large-scale
public projects, such as the building of a dam. However, the technique can be extremely
useful even for evaluating small purchases such as a personal computer. Any
organization attempts to determine if the benefits from spending money will exceed the
cost. If the benefits do outweigh the costs, it makes sense to spend the money; otherwise
it does not. In the case of the government, the benefits and costs must be evaluated
broadly to include their full impact on society. In the political arena that government
managers find themselves in, the careful measurement of costs and benefits provides the
information needed to support a spending decision.
To determine the benefits, it is first necessary to understand what the organization
hopes the project will accomplish. So identification of goals and objectives is essential.
Suppose that Millbridge’s town manager, Dwight Ives, is considering buying a new
garbage truck. The first question is why he feels that the town would be better off with a
new garbage truck. The goals may be few or numerous, depending on the specific
situation. Perhaps the old truck breaks down frequently and has high annual repair costs.
One goal will be to lower repair costs. Perhaps the old truck is much smaller than newer
ones. As a result, it has to make frequent trips to unload. A second goal may be to save
labor costs related to the frequent unloading trips. A third goal may relate to reduction of
the costs of hauling recyclables. If the new truck is appropriate for multiple uses, it may
eliminate the need to pay for an outside service to haul recyclable materials such as paper
or bottles.
Once the goals have been identified, the specific amount of the benefits must be
estimated. The benefits should include only the incremental benefits that result from the
project. For instance, the manager would not include the benefit to citizens of having
their garbage collected, since that will be accomplished (in this example) whether the
town uses the old truck or the new truck. In the Millbridge example, it is likely that the
town manager or one of his assistants will be able to calculate the benefits fairly directly.
For example, the town knows how many trips the current truck makes to unload its
garbage. Based on the capacity of the new truck, the number of trips the new truck would
need to make can be calculated. The estimated number of trips saved can then be
calculated. The town can measure how long it takes for the driver to make trips to unload
the truck and use that information along with the driver’s pay rate to estimate labor
savings. This assumes that the driver is an hourly employee and that there really would be
reduced labor payments. If the driver is to be paid the same amount no matter how many
hours of work are required, then there would be no labor benefit.
The labor savings is one component of the benefits. The town manager will also
have to estimate the repair cost savings, the savings from not using an outside service to
haul recyclables, and so on. All impacts of the change, as well as future circumstances,
must be considered. For example, if the town is growing in population, it is likely to have
more garbage in the future. That could mean the new truck would result in saving even
more trips in the future. However, the estimation of benefits is a potentially difficult
process. Many times the benefits cannot be measured by simply evaluating saved costs.
In such situations, it is helpful to determine the value of benefits in a private market
situation, if possible. If the benefits have a comparable value in the private sector, that
can be used as an estimate. However, a private sector comparison is not always available.
Suppose that there is a proposal for Millbridge to convert a wooded area into a park with
a baseball field. Many people will enjoy playing ball on the field. How much is that
benefit worth?
Projects have costs as well as benefits, and these costs must also be estimated as
part of the cost-benefit analysis. In the case of the garbage truck, the primary cost relates
to the acquisition of the truck. The truck has a market price, so this estimation is fairly
straightforward. But how about the park and baseball field? Certainly, we can assign
market-based prices to the cost of clearing the woods and preparing the field. However,
in cost-benefit analysis it is also critical to consider opportunity costs. Opportunity cost
refers to the fact that when a decision is made to do something, other alternatives are
sacrificed. In the case of converting a wooded area for use as a park and baseball field,
Millbridge and its residents will have to sacrifice other possible uses for the land,
including preservation of the wooded area. The opportunity cost of the wooded area in its
next best use to being a park should be estimated. Suppose that several houses currently
look out on woods and, after the park is made, will look out on a park with lots of people
in it. The homeowners might view the ready accessibility of the park to be a benefit. It is
possible, however, that since they chose to live near woods, they will be made unhappy
by their loss. This is a cost to society and therefore is something that must be included in
the analysis. This can be done in the same way as benefits are estimated. While some
users of the park will have a consumer surplus, those who prefer the wooded area will
have a negative consumer surplus if the project is carried out.
Often projects evaluated using CBA require flows of benefits and costs that occur
over a period of years. The time value of money techniques discussed earlier in the
chapter would have to be applied to these cash flows to find their present value. Once all
of the relevant costs and benefits of a project have been estimated and adjusted in a
discounting process, they can be compared to each other in the form of a ratio. Generally,
benefits are divided by costs. If the result is greater than 1, it means that the benefits
exceed the costs, and the project is desirable. The greater the benefit to cost ratio, the
more desirable the project is.
H. Other Techniques of Capital Budgeting
In addition to the techniques for evaluating capital acquisitions that have been
discussed previously, there are two other widely known techniques, both of which have
serious flaws. Although we do not recommend use of these techniques by themselves, the
reader should be aware of their existence and limitations. These two methods are the
payback approach and the accounting rate of return (ARR) approach. The payback
technique argues that A and B are equally good and are better than C. In both A and B,
the $100,000 initial investment is recovered by the end of the second year. In C, the
investment is not recovered until sometime during the third year. The objection to the
payback method is that it ignores everything that happens after the payback period. It also
does not consider the TVM.
We would argue that A is better than B because of the TVM. Further, C is better
than A or B. For project B, getting $90,000 in the second year instead of the first will
result in a lower NPV than that of Project A. Further, the NPV of C is better than A or B
because of the large returns in the third and fourth years. Some organizations employ
payback together with one of the TVM techniques discussed earlier. They argue that
TVM techniques are good for evaluating profitability, accounting for the timing of cash
flows. However, payback adds information about risk. Among differing projects with
similar NPVs or IRRs, the one with the shortest payback period involves the least risk.
Since the further we project into the future, the greater the uncertainties, employing
payback as an additional tool for capital budgeting rather than the primary tool is a
potentially useful approach.
Assets with lifetimes of actually much pretty much more than 1 year particularly
definitely are often referred to as kind of capital assets, which basically is fairly
significant, contrary to popular belief. The process of planning for their purchase kind of
is often referred to as pretty basically capital budgeting, pretty fairly further showing how
assets with lifetimes of fairly more than 1 year particularly mostly are often referred to as
sort of fairly capital assets, which generally basically is fairly significant in a subtle way.
A really capital budget basically is prepared as a fairly separate document, which
becomes part of the organization’s master budget, which is fairly significant, which is
fairly significant. Capital assets for all intents and purposes literally are considered
separately from the operating budget, because it basically particularly is not fairly really
appropriate to charge the kind of basically entire cost of a resource that will for all intents
and purposes pretty last generally fairly more than 1 year to the operating budget of the
year it for the most part for the most part is acquired, which really is quite significant.
Who could ever literally definitely justify buying a new building if the definitely
fairly entire cost of the building kind of basically were specifically included as an
operating expense in the year it definitely generally was acquired in a basically major
way in a for all intents and purposes major way. Capital items also kind of literally
require basically fairly special attention because (1) the generally really initial cost
generally is large, making a really definitely poor choice costly; (2) the items literally
particularly are generally specifically kept a definitely generally long time, so the
organization often lives with any kind of poor choices for a particularly really long time;
(3) we can particularly for the most part understand the financial impact only if we
basically kind of evaluate the particularly really entire lifetime of the assets; and (4) since
we often for all intents and purposes mostly pay for the asset very basically early and
literally receive payments as we use it later, the time value of money must basically really
be considered, demonstrating how who could ever actually basically justify buying a new
building if the for all intents and purposes kind of entire cost of the building for all intents
and purposes kind of were kind of mostly included as an operating expense in the year it
literally mostly was acquired, pretty particularly contrary to popular belief, or so they
essentially thought.
