Tiếng anh chuyên ngành kế toán part 32 pot

298 Planning and Forecasting
later. Since the cash flow is deferred, the true value of that sale to the firm is
somewhat diminished.
By focusing on cash flows and when they occur, NPV reflects the true
value of increased revenues and costs. Consequently, NPV analysis requires
that accounting data be unraveled to reveal the underlying cash flows. That is
why changes in net working capital must be accounted for and why deprecia-
tion does not show up directly.
Principle No. 2: Use Expected Values
There is always going to be some uncertainty over future cash flows. Future
costs and revenues cannot be known for sure. The analyst must gather as much
information as possible and assemble it to construct expected values of the
input variables. Although expected values are not perfect, these best guesses
have to be good enough. What is the alternative? The uncertainty in forecast-
ing the inputs is accounted for in the discount rate that is later used to discount
the expected cash flows.
Principle No. 3: Focus on the Incremental
NPV analysis is done in terms of “incremental” cash flows—that is, the change
in cash flow generated by the decision to undertake the project. Incremental
cash flow is the difference between what the cash flow would be with the proj-
ect and what the firm’s cash flow would be without the project. Any sales or
savings that would have happened without the project and are unaffected
by doing the project are irrelevant and should be ignored. Similarly, any costs
that would have been incurred anyway are irrelevant. It is often difficult yet
nonetheless important to focus on the incremental when calculating how cash
flows are impacted by opportunity costs, sunk costs, and overhead. These trou-
blesome areas will be elaborated on next.
Opportunity Costs
Opportunity costs are opportunities for cash inflows that must be sacrificed in
order to undertake the project. No check is written to pay for opportunity
costs, but they represent changes in the firm’s cash flows caused by the project

and must, therefore, be treated as actual costs of doing the project. For exam-
ple, suppose the firm owns a parking lot, and a proposed project requires use of
that land. Is the land free since the firm already owns it? No; if the project
were not undertaken then the company could sell or rent out the land. Use of
the company’s land is, therefore, not free. There is an opportunity cost. Money
that could have been earned if the project were rejected will not be earned if
the project is started. In order to reflect fully the incremental impact of the
proposed project, the incremental cash flows used in NPV analysis must incor-
porate opportunity costs.
Planning Capital Expenditure 299
Sunk Costs
Sunk costs are expenses that have already been paid or have already been com-
mitted to. Past research and development are examples. Since sunk costs are
not incremental to the proposed project, NPV analysis must ignore them. NPV
analysis is always forward-looking. The past cannot be changed and so should
not enter into the choice of a future course of action. If research was under-
taken last year, the effects of that research might bear on future cash flows,
but the cost of that research is already water under the bridge and so is not rel-
evant in the decision to continue the project. The project decision must be
made on the basis of whether the project increases or decreases wealth from
the present into the future. The past is irrelevant.
Overhead
The treatment of overhead often gives project managers a headache. Overhead
comprises expenditures made by the firm for resources that are shared by
many projects or departments. Heat and maintenance for common facilities are
examples. Management resources and shared support staff are other examples.
Overhead represents resources required for the firm to provide an environ-
ment in which projects can be undertaken. Different firms use different for-
mulas for charging overhead expenses to various projects and departments. If
overhead charges accurately reflect the shared resources used by a project,

then they should be treated as incremental costs of operating the project. If
the project were not undertaken, those shared resources would benefit another
moneymaking project, or perhaps the firm could possibly cut some of the
shared overhead expenditures. Thus, to the extent that overhead does repre-
sent resources used by the project, it should be included in calculating incre-
mental cash flows. If, on the other hand, overhead expense is unaffected by the
decision to undertake the new project, and no other proposed project could use
those shared resources, then overhead should be ignored in the NPV analysis.
Sometimes the formulas used to calculate overhead for budgeting purposes are
unrealistic and overcharge projects for their use of shared resources. If the fi-
nancial analyst does not correct this unrepresentative allocation of costs, some
worthwhile projects might incorrectly appear undesirable.
COMPUTING NPV: THE TIME VALUE OF MONEY
In deciding whether a project is worthwhile, one needs to know more than
whether it will make money. One must also know when it will make money.
Time is money! Project decisions involve cash flows spread out over several pe-
riods. As we shall see, cash flows in different periods are distinct products in
the financial marketplace—as different as apples and oranges. To make deci-
sions affecting many future periods, we must know how to convert the differ-
ent periods’ cash flows into a common currency.
300 Planning and Forecasting
The concept that future cash flows have a lower present value and the set
of tools used to discount future cash flows to their present values are collec-
tively known as “time value of money” (TVOM) analysis. I have always thought
this to be a misnomer; the name should be the “money value of time.” But
there is no use bucking the trend, so we will adopt the standard nomenclature.
You probably already have an intuitive grasp of the fundamentals of
TVOM analysis, as your likely answer to the following question illustrates:
Would you rather have $100 today or $100 next year? Why?
The answer to this question is the essence of TVOM. You no doubt an-

swered that you would rather have the money today. Money today is worth
more than money to be delivered in the future. Even if there were perfect cer-
tainty that the future money would be received, we prefer to have money in
hand today. There are many reasons for this. Having money in hand allows
greater flexibility for planning. You might choose to spend it before the future
money would be delivered. If you choose not to spend the money during the
course of the year, you can earn interest on it by investing it. Understanding
TVOM allows you to quantify exactly how much more early cash flows are
worth than deferred cash flows. An example will illuminate the concept.
Suppose you and a friend have dinner together in a restaurant. You order
an inexpensive sandwich. Your friend orders a large steak, a bottle of wine, and
several desserts. The bill arrives and your friend’s share is $100. Unfortu-
nately, your friend forgot his wallet and asks to borrow the $100 from you. You
agree and pay. A year passes before your friend remembers to pay you back the
money. “Here is the $100,” he finally says one day. Such events test a friend-
ship, especially if you had to carry a $100 balance on your credit card over the
course of the year on which interest accrued at a rate of 18%. Is the $100 that
your friend is offering you now worth the same as the $100 that he borrowed a
year earlier? Actually, no; a $100 cash flow today is not worth $100 next year.
The same nominal amount has different values depending on when it is paid. If
the interest rate is 18%, a $100 cash flow today is worth $118 next year and is
worth $139.24 the year after because of compound interest. The present value
of $118 to be received next year is exactly $100 today. Your friend should pay
you $118 if he borrowed $100 from you a year earlier.
The formula for converting a future value to a present value is:
where PV stands for present value, FV is future value, n is the number of peri-
ods in the future that the future cash flow is paid, and r is the appropriate in-
terest rate or discount rate.
Discounting Cash Flows
Suppose in the brewery example that the appropriate discount rate for translat-

ing future values to present values was 20%. Recall that the brewery project
PV
FV
r
n
=
+
()
1
Planning Capital Expenditure 301
was forecast to generate $2.42 million of cash in year 1. The present value of
that cash flow, as of year 0, is $2,016,670, computed as follows:
Similarly, the year-2 cash flow was forecast to be $2.42 million also. The pres-
ent value of that second-year cash flow is only $1,680,560:
The longer the time over which a cash flow is discounted, the lower is its pres-
ent value. Exhibit 10.4 presents the forecasted cash flows and their discounted
present values for the brewery project.
Summing the Discounted Cash Flows
to Arrive at NPV
Finally, we can calculate the NPV. The NPV is the sum of all discounted cash
flows, which in the brewery example equals $614,000. To understand precisely
what this means, observe that the sum of the discounted cash flows from years
1 through 10 is $10,614,000. This means that the project generates future cash
flows that are worth $10,614,000 today. The initial cost of the project is
$10,000,000 today. Thus, the project is worth $10,614,000 but costs only
$10,000,000 and therefore creates $614,000 of new wealth. The managers of
the beer company would be well advised to adopt this project, because it has a
positive NPV and therefore creates wealth.
PV =
()

=
$, ,
.
$, ,
2 420 000
120
1 680 560
2
PV =
()
=
$, ,
.
$, ,
2 420 000
120
2 016 670
1
EXHIBIT 10.4 Discounted cash f lows for
brewery project (thousands).
Year Cash Flow Discounted Cash Flow
0 $(10,000) $(10,000)
1 2,420 2,017
2 2,420 1,681
3 2,420 1,400
4 2,420 1,167
5 2,420 973
6 2,420 810
7 2,420 675
8 2,420 563

9 2,420 469
10 5,320 859
302 Planning and Forecasting
MORE NPV EXAMPLES
Consider two alternative projects, A and B. They both cost $1,000,000 to set
up. Project A returns $800,000 per year for two years starting one year after
setup. Project B also returns $800,000 per year for two years, but the cash
flows begin two years after setup. The firm uses a discount rate of 20%. Which
is the better project, A or B?
Like project A, project C also costs $1,000,000 to set up, and it will pay
back $1,600,000. For both A and C, the firm will earn $800,000 per year for
two years starting one year after setup. However, C costs $500,000 initially and
the other $500,000 need only be paid at the termination of the project (it may
be a cleanup cost, for example). Project A requires the initial outlay all at once
at the outset. Which is the better project, A or C? Of projects A, B, and C,
which project(s) should be undertaken?
We should make the project decision only after analyzing each project’s
NPV. Exhibit 10.5 tabulates each project’s cash flows, discounted cash flows,
and NPVs. The NPVs of Projects A, B, and C, are, respectively, $222,222,
−$151,235, and $375,000. Project C has the highest NPV. Therefore, if only
one project can be selected, it should be project C. If more than one project
can be undertaken, then both A and C should be selected since they both have
positive NPVs. Project B should be rejected since it has a negative NPV and
would therefore destroy wealth.
It makes sense that project C should have the highest NPV, since its cash
outflows are deferred relative to the other projects, and its cash inflows are
early. Project B, alternatively has all costs up front, but its cash inflows are
deferred.
Suppose a project has positive NPV, but the NPV is small, say, only a few
hundred dollars. The firm should nevertheless undertake that project if there

are no alternative projects with higher NPV. The reason is that a firm’s value
is increased every time it undertakes a positive-NPV project. The firm’s value
increases by the amount of the project NPV. A small NPV, as long as it is posi-
tive, is net of all input costs and financing costs. So, even if the NPV is low,
EXHIBIT 10.5 Cash f lows and discounted cash f lows for three
alternative projects (thousands).
Project A Project B Project C
Project A Discounted Project B Discounted Project C Discounted
Year Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow Cash Flow
0 $(1,000,000) $(1,000,000) $(1,000,000) $(1,000,000) $(500,000) $(500,000)
1 800,000 666,667 0 0 800,000 666,667
2 800,000 555,556 0 0 300,000 208,333
3 0 0 800,000 462,963 0 0
4 0 0 800,000 385,802 0 0
NPV = $0,(222,222 $0,(151,235) $ 375,000
Planning Capital Expenditure 303
the project covers all its costs and provides additional returns. If accepting
the small-NPV project does not preclude the undertaking of a higher-NPV
project, then it is the best thing to do. A firm that rejects a positive-NPV proj-
ect is rejecting wealth.
Of course, this does not mean a firm should jump headlong into any proj-
ect that at the moment appears likely to provide positive NPV. Future poten-
tial projects should be considered as well, and they should be evaluated as
potential alternatives. The projects, current or future, that have the highest
NPV should be the projects accepted. For maximum wealth-creation effi-
ciency, the firm’s managerial resources should be committed toward under-
taking maximum NPV projects.
THE DISCOUNT RATE
At what rate should cash flows be discounted to compute net present values? In
most cases, the appropriate rate is the firm’s cost of funds for the project. That

is, if the firm secures financing for the project by borrowing from a bank, the
after-tax interest rate should be used to discount cash flows. If the firm obtains
funds by selling stock, then an equity financing rate should be applied. If the
financing combines debt and equity, then the appropriate discount rate would
be an average of the debt rate and the equity rate.
Cost of Debt Financing
The after-tax interest rate is the interest rate paid on a firm’s debt less the im-
pact of the tax break they get from issuing debt. For example, suppose that a
firm pays 10% interest on its debt and the firm’s income tax rate is 40%. If the
firm issues $100,000 of debt, then the annual interest expense will be $10,000
(10% × $100,000). But this $10,000 of interest expense is tax deductible, so the
firm would save $4,000 in taxes (40% × the $10,000 interest). Thus, net of the
tax break, this firm would be paying $6,000 to service a $100,000 debt. Its
after-tax interest rate is 6% ($6,000/$100,000 principal).
The formula for after-tax interest rate (R
D, after-tax
) is:
where R
D
is the firm’s pretax interest rate, and τ is the firm’s income tax rate.
Borrowing from a bank or selling bonds to raise funds is known as “debt
financing.” Issuing stock to raise funds is known as “equity financing.” Equity
financing is an alternative to debt financing, but it is not free. When a firm sells
equity, it sells ownership in the firm. The return earned by the new sharehold-
ers is a cost to the old shareholders. The rate of return earned by equity in-
vestors is found by adding dividends to the change in the stock price and then
dividing by the initial stock price:
RR
DD,
()

after-tax
=−1 τ
304 Planning and Forecasting
where R
E
is the return on the stock and also the cost of equity financing, D is
the dollar amount of annual dividends per share paid by the firm to stockhold-
ers, P
0
is the stock price at the beginning of the year, and P
1
is the stock price
at the end of the year. For example, suppose the stock price is $100 per share at
the beginning of the year and $112 at the end of the year, and the dividend is
$8 per share. The stockholders would have earned a return of 20%, and this
20% is also the cost of equity financing:
The capital asset pricing model (CAPM) is often used to estimate a firm’s
cost of equity financing. The idea behind the CAPM is that the rate of return
demanded by equity investors will be a function of the risk of the equity,
where risk is measured by a variable beta (β). According to the CAPM, β and
cost of equity financing are related by the following equation:
where R
F
is a risk-free interest rate, such as a Treasury bill rate, and R
M
is the
expected return for the stock market as a whole. For example, suppose the ex-
pected annual return to the overall stock market is 12%, and the Treasury bill
rate is 4%. If a stock has a β of 2, then its cost of equity financing would be
20%, computed as follows:

Analysts often use the Standard & Poor’s 500 stock portfolio as a proxy
for the entire stock market when estimating the expected market return. The
βs for publicly traded firms are available from a variety of sources, such as
Bloomberg, Standard & Poor’s, or the many companies that provide equity re-
search reports. How β is computed and the theory behind the CAPM are be-
yond the scope of this chapter, but the textbooks listed in the bibliography to
this chapter provide excellent coverage.
Weighted Average Cost of Capital
Most firms use a combination of both equity and debt financing to raise money
for new projects. When financing comes from two sources, the appropriate dis-
count rate is an average of the two financing rates. If most of the financing is
debt, then debt should have greater weight in the average. Similarly, the weight
given to equity should reflect how much of the financing is from equity. The
R
E
=+× −
()
[]
=4 2 12 4 20%%%%
RR RR
EF MF
=+ −
()
β
R
E
=
+−
=
$$ $

$
%
8 112 100
100
20
R
DP P
P
E
=
+−
10
0
Planning Capital Expenditure 305
resulting number, the “weighted average cost of capital” (WACC), reflects the
firm’s true cost of raising funds for the project:
where W
E
is the proportion of the financing that is equity, W
D
is the propor-
tion of the financing that is debt, R
E
is the cost of equity financing, R
D
is the
pretax cost of debt financing, and τ is the tax rate.
For example, suppose a firm acquires 70% of the funds needed for a proj-
ect by selling stock. The remaining 30% of financing comes from borrowing.
The cost of equity financing is 20%, the pretax cost of debt financing is 10%,

and the tax rate is 40%. The weighted average cost of capital would then be
15.8%, computed as follows:
This 15.8% rate should then be used for discounting the project cash flows.
Most often the choice of the discount rate is beyond the authority of the
project manager. Top management will determine some threshold discount rate
and dictate that it is the rate that must be used to assess all projects. When this
is the policy, the rate is usually the firm’s WACC with an additional margin
added to compensate for the natural optimism of project proponents. A higher
WACC makes NPV lower, and this biases management toward rejecting projects.
The Effects of Leverage
Leverage refers to the amount of debt financing used: the greater the ratio of
debt to equity in the financing mix, the greater the leverage. The following ex-
ample illustrates how leverage impacts the returns generated by a project. Sup-
pose we have two companies that both manufacture scooters. One company is
called NoDebt Inc., and the other is called SomeDebt Inc. As you might guess
from its name, NoDebt never carries debt. SomeDebt is financed with equal
parts of debt and equity. Neither company knows whether the economy will be
good or bad next year, but they can make projections contingent on the state of
the economy. Exhibit 10.6 presents balance-sheet and income-statement data
for the two companies for each possible business environment.
Each company has $1 million of assets. Therefore, the value of NoDebt’s
equity is $1 million, since debt plus equity must equal assets—the balance-
sheet equality. Since SomeDebt is financed with an equal mix of debt and eq-
uity, its debt must be worth $500,000, and its equity must also be worth
$500,000. Aside from capital structure—that is, the mix of debt and equity used
to finance the companies—the two firms are identical. In good times both com-
panies make $1 million in sales. In bad times sales fall to $200,000. Cost of
goods sold is always 50% of sales. Selling, administrative, and general expenses
are a constant $50,000. For simplicity we assume there is no depreci
ation.

WACC =×
()
+× ×−
()
[]
=07 20 03 10 1 40 158.%. % % .%
WACC W R W R
EE D D
=+ −
()
[]
1 τ
306 Planning and Forecasting
Earnings before interest and taxes (EBIT) is thus $450,000 for both companies
in good times, and $50,000 for both in bad times. So far, this example illus-
trates an important lesson about leverage: Leverage has no impact on EBIT. If
we define return on assets (ROA)
1
as EBIT divided by assets, then leverage has
no impact on ROA.
If the pre-tax interest rate is 10%, however, then SomeDebt must pay
$50,000 of interest on its outstanding $500,000 of debt, regardless of whether
business is good or bad. NoDebt, of course, pays no interest. Because this is a
standard income statement, not a capital budgeting cash-flow computation, we
must account for interest. EBT (earnings before taxes, which is the same thing
as taxable income) for NoDebt is the same as its EBIT: $450,000 in good times
and $50,000 in bad times. For SomeDebt, however, EBT will be $50,000 less in
both states: $400,000 in good times and zero in bad times. Income tax is 40% of
EBT, so it must be $180,000 for NoDebt in good times, $20,000 for NoDebt
in bad times, $160,000 for SomeDebt in good times, and zero for SomeDebt in

bad times. Here we see the second important lesson about leverage: Leverage
reduces taxes.
Net earnings is EBT minus taxes. For NoDebt, net earnings is $270,000 in
good times and $30,000 in bad times. For SomeDebt, net earnings is $240,000
in good times and zero in bad times. Return on equity (ROE) equals net earn-
ings divided by equity. ROE is the profit earned by the equity investors as a
function of their equity investment. If, as in this example, there is no deprecia-
tion, no changes in net working capital, and no capital expenditures, then net
earnings would equal the cash flow received by equity investors, and ROE
would be that year’s cash return on their equity investment. Notice that ROE
for NoDebt is 27% in good times and 3% in bad times. ROE for SomeDebt is
much more volatile: 48% in good times and 0% in bad times. This is the third
EXHIBIT 10.6 Performance of NoDebt Inc. and SomeDebt Inc.
NoDebt Inc. (thousands)
SomeDebt Inc. (thousands)
Net Earnings Good Times Bad Times Good Times Bad Times
Assets $1,000 $1,000 $1,000 $1,000
Debt 0 0 500 500
Equity $1,000 $1,000 $1,500 $1,500
Revenue $1,000 $
1,200 $1,000 $1,200
COGS 500 100 500 100
SAG 50 50 50 50
EBIT 450 50 450 50
Interest 0 0 50 50
EBT 450 50 400 0
Tax (40%) 180 20 160 0
Net Earnings $
1,270 $1,030 $1,240 $11,00
ROA 45.0% 5.0% 45.0% 5.0%

ROE 27.0% 3.0% 48.0% 0.0%
Planning Capital Expenditure 307
and most important lesson to be learned about leverage from this example: For
the equity investors, leverage makes the good times better and the bad times
worse. One student of mine, upon hearing this, exclaimed, “Leverage is a lot
like beer!”
Because leverage increases the riskiness of the cash flows to equity in-
vestors, leverage increases the cost of equity capital. But for moderate amounts
of leverage, the impact of the tax shield on the cost of debt financing over-
whelms the rising cost of equity financing, and leverage reduces the WACC.
Economists Franco Modigliani and Merton Miller were each awarded the
Nobel Prize in economics (in 1985 and 1990, respectively) for work that in-
cluded research on this very issue. Modigliani and Miller proved that in a world
where there are no taxes and no bankruptcy costs the WACC is unaffected by
leverage. What about the real world in which taxes and bankruptcy exist? What
we learn from their result, known as the Modigliani-Miller irrelevance theo-
rem, is that as leverage is increased WACC falls because of the tax savings, but
eventually WACC starts to rise again due to the rising probability of bank-
ruptcy costs. The choice of debt versus equity financing must balance these
countervailing concerns, and the optimal mix of debt and equity depends on
the specific details of the proposed project.
Divisional versus Firm Cost of Capital
Suppose the beer company is thinking about opening a restaurant. The risk in-
herent in the restaurant business is much greater than the risk of the beer
brewing business. Suppose the WACC for the brewery has historically been
20%, but the WACC for stand-alone restaurants is 30%. What discount rate
should be used for the proposed restaurant project?
Considerable research, both theoretical and empirical, has been applied
to this question, and the consensus is that the 30% restaurant WACC should be
used. A discount rate must be appropriate for the risk and characteristics of

the project, not the risk and characteristics of the parent company. The reason
for this surprising result is that the volatility of the project’s cash flows and
their correlation with other risky cash flows are the paramount risk factors in
determining cost of capital, not simply the likelihood of default on the com-
pany’s obligations. The financial analyst should estimate the project’s cost of
capital as if it were a new restaurant company, not an extension of the beer
company. The analyst should examine other restaurant companies to determine
the appropriate β, cost of equity capital, cost of debt financing, financing mix,
and WACC.
OTHER DECISION RULES
Some firms do not use the NPV decision rule as the criterion for deciding
whether a project should be accepted or rejected. At least three alternative de-
cision rules are commonly used. As we shall see, however, the alternative rules