# How Do Capital Expenditures Affect the Income Statement

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```							Capital Budgeting

Duke University

January 14, 2008
• Topics:
1. Capital budgeting under certainty

1. Brealey, Myers and Allen, chapter 2;
2. Brealey, Myers and Allen, sections 7.1 and 7.2;
3. Brealey, Myers and Allen, sections 6.1, 6.2 and 6.3
1
Capital Budgeting under Certainty

• At the most general level, an investment is a claim to a stream of cash
ﬂows.

• This deﬁnition encompasses both real and ﬁnancial investments.

• In order to choose between alternative investments, we must therefore ﬁnd
a way to compare cash ﬂows diﬀering in size (more is better than less),
timing (the sooner the better), and risk (the less the better).

• It is easy to compare two single cash ﬂows along any of these dimensions;
it is hard to compare two streams of cash ﬂows.

• The techniques of compounding and discounting allow us to compare cash
ﬂow streams diﬀering in size and timing.

• We will at ﬁrst ignore risk and compare certain cash ﬂows.
2
The NPV Formula

• We have seen that ﬁnancial managers act in the best interest of the share-
holders by undertaking investments with positive NPV.

• Also, we have seen that for a one-period investment the NPV formula is
C1
N P V = C0 + 1+r1
where C0 is the initial cash ﬂow (which is generally negative) and C1 is the
end-of-period cash ﬂow (which is usually positive).

• The general formula is

T     Ct           T     Ct
N P V = C0 +   t=1 (1+rt )t   =   t=0 (1+r)t

• In this course, we will discuss how to ﬁnd the cash ﬂows and the appropriate
rate at which to discount them.
3
Estimating Cash Flows

• Only cash ﬂows are relevant.

• Cash ﬂows are simply the diﬀerence between dollars received and dollars paid out. Do not
confuse cash ﬂows with accounting proﬁts or losses.

• Estimate cash ﬂows on an after-tax basis.

• Make sure that cash ﬂows are recorded at the time they actually occur (example: credit
sales, tax liabilities).

• Forget sunk costs.

• Include opportunity costs.

• Treat inﬂation consistently.
1. Discount nominal cash ﬂows at the nominal rate.
2. Discount real cash ﬂows at the real rate.
4
Example: IM&C’s Fertilizer Project

• International Mulch and Company (IM&C) is considering a project requiring
an initial investment of \$10 million in plant and machinery.

• The project is expected to generate the following sales and to require the fol-
lowing costs. The project will also require an initial and ongoing investment
in working capital.
C0      C1      C2       C3            C4     C5       C6

Sales                          523    12,887   32,610     48,901    35,834   19,717
Costs of goods sold            837    7,729    19,552     29,345    21,492   11,830
Other costs           4,000   2,200   1,210    1,331      1,464     1,611    1,772
Working capital                550     1,289    3,261      4,890    3,583     2,002

• Even though the machinery is expected to be resold for \$1.949 million in
7 years, it has been decided that it will be depreciated on a straight-line
basis over 6 years down to a \$500, 000 book value.

9.5
• This means that the yearly depreciation will be           6
= 1.583M.
5

• The ﬁrm’s tax rate is 35% and its opportunity cost of capital (discount
rate)is 20%.
Example: IM&C’s Fertilizer Project (cont’d)

• First, let us calculate the after-tax operating proﬁts of the ﬁrm.
C0       C1       C2       C3       C4       C5       C6

(1)   Sales                           523     12,887   32,610   48,901   35,834   19,717
(2)   Costs of goods sold             837     7,729    19,552   29,345   21,492   11,830
(3)   Other costs           4,000    2,200    1,210    1,331    1,464    1,611    1,772
(4)   Depreciation                   1,583     1,583    1,583    1,583    1,583    1,583

(5) Pre-tax proﬁts          -4,000   -4,097   2,365    10,144   16,509   11,148   4,532
(6) Tax                     -1,400   -1,434    828     3,550    5,778    3,902    1,586

(7) After-tax proﬁts        -2,600   -2,663   1,537    6,594    10,731   7,246    2,946

• The proﬁts of the ﬁrm are not the project’s cash ﬂows. We need to make
some adjustments to get the cash ﬂows.

• Depreciation is not a cash ﬂow; we need to add it back.

• Capital expenditures (and sales) have not been taken into account yet.
6

• Changes in working capital are cash ﬂows.
IM&C’s Fertilizer Project: Depreciation

• Depreciation is an accounting number that does not directly aﬀect cash
ﬂows.

• Capital expenditures do not ﬂow directly through the income statement;
instead the assets are depreciated over time to match their cost with their
use.

• For cash ﬂow purposes we want to account for capital expenditures when
the cash is paid, i.e. when the assets are purchased.

• So if we did not add back depreciation, we would double-count the costs.

• However, depreciation still plays an important role because it is tax de-
ductible, so we cannot completely ignore it.

• This is why we calculate book income ﬁrst, then adjust it to get cash ﬂows.
7

• The adjustment here is simple – just add back the depreciation number each
year.
IM&C’s Fertilizer Project: Capital Expenditures

• Clearly, the initial capital investment of \$10 million in plant and machinery
is a negative cash ﬂow, but it has not been accounted for on the income
statement.

• In year 7, the machine sale will generate a positive cash ﬂow of \$1.949 million,
which will be taxed.

• Only the excess over the book value of the machine (\$0.5 million) is taxed;
this is considered a taxable gain. The tax is 35% × (1.949 − 0.5) = 0.507.

• Therefore, the net capital inﬂow in year 7 is 1.949 − 0.507 = 1.442.

• There are no other interim capital expenditures for this project.
8
IM&C’s Fertilizer Project: Working Capital

• Working capital essentially represents a ﬁrm’s net investment in short-term
assets:

working capital = inventory + accounts receivable − accounts payable.

• For example:
1. An increase of \$1 in accounts receivable means that part of the sales
ﬁgure in line (1) has not yet been received (i.e., it is not a cash inﬂow
ﬂow yet, but it was counted as such on the income statement).
2. An increase of \$1 in inventory means that the ﬁrm has spent cash to
buy products that have not yet been sold (ie, it is a cash outﬂow that
has not been accounted for on the income statement).
3. An increase of \$1 in accounts payable means that some of the costs
have not yet been paid (so this is a cash outﬂow that is in the income
statement but is not yet a physical outﬂow).
9

• More generally, working capital is often deﬁned as (non-cash) current assets
minus (non-debt) current liabilities. It is not always clear how to treat cash;
we will ignore this for most of the course.
IM&C’s Fertilizer Project: Working Capital (cont’d)

• The changes is working capital from year to year are as follows.
C0   C1     C2      C3      C4      C5       C6       C7

(10) Working capital        550   1,289   3,261   4,890   3,583    2,002
(11) Change in WC           550    739    1,972   1,629   -1,307   -1,581   -2,002

• We now have all of the ingredients to calculate the project’s cash ﬂows.
10
Example: IM&C’s Fertilizer Project (cont’d)

• The project’s cash ﬂows are as follows.
C0      C1    C2    C3    C4     C5     C6     C7

(7) After-tax proﬁts     -2,600 -2,663 1,537 6,594 10,731 7,246 2,946

(4) Depreciation                  1,583 1,583 1,583 1,583 1,583 1,583

(11) Change in WC                 550   739 1,972 1,629 -1,307 -1,581 -2,002

(12) Capital expenditure 10,000                                         -1,442

(13) Project cash-ﬂows   -12,600 -1,630 2,381 6,205 10,685 10,136 6,110 3,444

• We can now calculate the net present value (NPV) of the project as follows:
2,381     6,205    10,685    10,136     6,110     3,444
N P V = −12, 600 + −1,630 + (1.20)2 + (1.20)3 + (1.20)4 + (1.20)5 + (1.20)6 + (1.20)7 =
1.20
3, 519.

• Since the NPV is greater than zero, IM&C should undertake the project.
11
Alternatives to NPV: The Internal Rate of Return Rule

• The internal rate of return (IRR) of a project is deﬁned as the constant
discount rate y which makes N P V = 0. In other words, y solves
T     Ct
NP V =     t=0 (1+y)t   =0

• The IRR rule says that a project should be accepted if and only if y exceeds
the yield on ﬁnancial securities (bonds) with comparable maturity, cash ﬂows
and risk (the opportunity cost of capital or hurdle rate).

• Notice that with a ﬂat term structure (discount rate is r for all maturities t),
the IRR rule implies that we should accept a project if and only if y > r.

• Given that we have assumed a ﬂat term structure and considered only riskless
projects so far, the IRR rule implies that we should accept a project if y
exceeds the riskfree rate.

• Essentially, the IRR measures the return of the project, i.e. the return on
the initial investment.
12

• If the project’s return (i.e.IRR) beats what can be obtained in capital markets
(i.e. r), then the project should be undertaken
The Internal Rate of Return Rule (cont’d)

• For example, consider the following project:

C0         C1      C2      C3
-5,000   2,000   2,000   2,000

• The internal rate of return (IRR) for this project is calculated as follows.
2,000    2,000
We want to ﬁnd y that solves −5, 000 + 2,000 + (1+y)2 + (1+y)3 = 0. We ﬁnd
1+y
y = 9.7%; this is the IRR.

• Notice that in this case the IRR rule corresponds exactly to the NPV rule.

• For any discount rate lower than 9.7%, the NPV is positive; this is precisely
when the IRR rule says that we should undertake the project.

• For any discount rate higher than 9.7%, the NPV is negative; this is precisely
13

when the IRR rule says that we should drop the project.
Alternatives to NPV: Multiples

• Multiples are used extensively by research analysts and investment bankers
for valuations of whole companies, but are less common in project valuation.

• The acquisition of a whole company is really just a type of project, though,
so the topic is important for this course.

• The multiple approach uses the market price multiples for comparable com-
panies to provide an appropriate valuation range.

• The use of multiples is predicated on the Eﬃcient Markets Hypothesis
(EMH) and the Arbitrage Pricing Theory (APT). Simply stated, the multiple
approach says that comparable companies should sell at comparable prices.
14
How to use Multiples

• To implement the multiples method, ﬁrst ﬁnd a set of comparable compa-
nies.

• You are looking for ﬁrms with similar cash ﬂow characteristics, i.e., similar
risk, timing, and expected growth rates (technically need proportionality).

• Next, divide the comparable ﬁrms’ value by some operating statistic to get
a pricing multiple for each. Depending on the operating statistic, use either
equity market value or total ﬁrm value (equity plus debt). Commonly used
multiples include:
1. Equity Value-to-Net Income (or P/E)
2. Equity Value-to-Book Value of Equity
3. Firm Value-to-EBITDA
4. Firm Value-to-EBIT (Operating Income)
5. Firm Value-to-Sales
15

6. Firm Value-to-Book Value of Assets
How to use Multiples (Cont’d)

• Next, just take an average of the comparable ﬁrms’ multiples (or use the
entire range), and multiply that by the analogous operating statistic for the
company you are trying to value.

• If you used an Equity Value multiple, this gives you an estimate of your
company’s (or project’s) Equity Value; if you used a Firm Value multiple, it
gives you an estimate of Firm Value (or just Total Value if it’s a project).

• To go from Equity Value to Firm Value, just add the value of existing debt.

• To go from Firm Value to Equity Value, just subtract existing debt.
16
Multiples: An Example

• Assume you are trying to value Project X, and you have three comparable
ﬁrms, A, B, and C. You have the following information on the three ﬁrms:

Shares Outs.    Mkt Price    Debt Outs.   Revenues      Op. Inc.
Company A         100          \$5.00         \$100         \$100         \$68
Company B         200           2.00          150          95           65
Company C          50           7.50          200          150          63

• From this information you calculate their multiples as follows:

Firm Value    Firm Value
Equity Value    Firm Value    Revenues      Op. Inc.
Company A        \$500            \$600          6.0           8.8
Company B         400            550           5.8           8.5
Company C         375            575           3.8           9.1
17

Average                                        5.2           8.8
Multiples: An Example (cont’d)

• Now, just apply these multiples to get an estimate of the value of Project
X (note that we are looking for the total value here, which is analogous to
Firm Value for a stand-alone ﬁrm):

Valuation Based On
Revenues Op. Inc.
Average multiple                   5.2        8.8
Project X operating statistic     \$195       \$105
Implied value of Project X       \$1, 015     \$924

• NOTE: Multiples are not really an alternative to NPV. They are just a
diﬀerent way to estimate NPV.

• Our normal approach is to discount future cash ﬂows to ﬁnd PV, then
subtract the initial investment to get NPV.
18

• Multiples just give us an alternative way to estimate PV, so we can still
subtract the initial investment to get an estimate of NPV.
NPV’s Competitors

• In spite of the fact that the NPV rule always leads to investment decisions
which are in the shareholders’ best interests, alternative investment rules
have been—and to some extent are still—used by businesses.

• Four common alternatives to the NPV rule are:
1. Payback period.
2. Average return on book value (or average accounting return).
3. Internal rate of return.
4. Proﬁtability index.

• The internal rate of return and the proﬁtability index, when properly used,
lead to the same decisions as the NPV rule. We will concentrate on these
two rules.
19
NPV’s Competitors (cont’d)

• As the following survey shows, many of the above investment rules were still

U.S.       U.S.      Japan
Capital Budgeting Method        (1950’s)   (1980’s)   (1980’s)
Payback period                    34%        12%        40%
Average accounting return         34%         8%        19%
Internal rate of return (IRR)     19%        49%        15%
Net present value (NPV)                      19%         9%
Other                             6%         10%        2%
None                              6%          2%        15%
20
NPV’s Competitors (cont’d)

• In a 1984 survey of large U.S. multinational ﬁrms, Stanley and Block ﬁnd
that over 80% of the responding ﬁrms used NPV or IRR as their primary
decision rule.

Primary    Secondary
Capital Budgeting Method        Technique   Technique
Internal rate of return (IRR)    65.3%       14.6%
Net present value (NPV)          16.5%       30.0%
Average accounting return        10.7%       14.6%
Payback period                    5.0%       37.6%
Other                             2.5%        3.2%
21
NPV’s Competitors (cont’d)

• More recently, Graham and Harvey (2002) surveyed 392 CFOs about their
capital budgeting methods. The following table shows the percentage of
CFOs who “always or almost always” use a given method.

Internal rate of return (IRR)   75.6%
Net present value (NPV)         74.9%
Payback period                  56.7%
Average accounting return       30.3%
Discounted payback period       29.5%
Proﬁtability index              11.9%
22
Features of the NPV Rule

• When looking at NPV’s competitors, it is important to keep in mind the
main features of the NPV rule:

• Time value of money: a dollar today is worth more than a dollar tomorrow.

• NPV depends only on all the forecasted cash ﬂows from the project and the
opportunity cost of capital.

• Any rule ignoring some of the project’s cash ﬂows will lead to suboptimal
decisions.

• Any rule aﬀected by the manager’s tastes such as the accounting methods,
the proﬁtability of the company’s existing business, or the proﬁtability of
other independent projects will lead to inferior decisions.

• Because present values are all measured in today’s dollars, you can add them
up and you can compare them.

• As a result, the NPV rule can easily identify whether joint projects are better
than single projects, and identify which mutually exclusive project is better.
23

• As we shall see, the alternatives to the NPV rule often fail to satisfy one or
more of these critical features.
The Payback Period Rule

• The payback period of a project is the number of years it takes to recover the initial
investment. The payback period rule says that a project should be accepted if the payback
period is less than some given cutoﬀ.

• Here are some examples:

Cash ﬂows                Payback       NPV
Project      C0       C1     C2        C3       Period      at 10%
A          -2,000   2,000                         1        -181.82
B          -2,000   1,000 1,000       1,000       2         486.85
C          -2,000   1,000 1,000      10,000       2        7,248.69

• The basic weaknesses of the payback rule are:

• It ignores the time value of money (as well as the risk of the project).

• It ignores the cash ﬂows beyond the cutoﬀ period.

• It gives no indications on what the cutoﬀ rule should be.
24

• Some companies discount the cash ﬂows before computing the payback rule. This modiﬁ-
cation surmounts the ﬁrst weakness, but is still subject to the others.
The Average Return on the Book Rule

• The average return on the book value is computed by dividing the average
yearly proﬁt from a project (after depreciation and taxes) by the average
book value of the investment. This ratio is then compared with the book rate
of return for the ﬁrm as a whole (or some other equally absurd yardstick).

• This criterion suﬀers from several defects:
1. It ignores the relevant cash ﬂow from investment and instead considers
the accounting proﬁts (in particular, it depends critically on the accoun-
tants’ choice of a depreciation method).
2. It ignores the time value of money (as well as the risk of the project).
3. The choice of a yardstick is totally arbitrary.
25
Limitations of the IRR Rule: Non-Flat Term Structure

• One of the main limitations of the IRR rule is that it is very diﬃcult to
apply with a non-ﬂat term-structure, since in this case the opportunity cost
of capital depends on the maturity and cash-ﬂow proﬁle of each investment
and is a complicated average of the interest rates r1 , r2 , . . ., rT .

• As an example, assume the following term structure,

t
1       2          3        4           5
rt   4.00%   4.50%      5.00%    5.50%       6.00%

• and consider the two projects:

Project     C0     C1    C2       C3    C4      C5     IRR     NPV
A         -1,000   20    20       20    20    1,200   5.24%   -32.32
B         -1,000   50    50     1,050                 5.00%     0.89
26

Why does project A have higher IRR but lower NPV?
Limitations of the IRR Rule:Non-Flat Term Structure (cont’d)

• The answer is that the IRR of project A should be compared to a cutoﬀ
diﬀerent from that of project B. In particular, the IRR for project A (B)
should be compared to the yield on a 5-year (3-year) bond with the same
cash ﬂows.

• The prices P5 and P3 of such 5-year and 3-year bonds are
20           20             20             20           1,200
P5 =   1.04
+   (1.045)2
+   (1.045)3
+   (1.045)4
+   (1.06)5
= 967.68

50           50           1,050
P3 =   1.04
+   (1.045)2
+   (1.05)3
= 1, 000.89.

The yields on these two bonds can be calculated as follows:

20          20             20                 20      1,200
967.68 =      1+yA
+   (1+yA )2
+ + (1+yA )3 +         (1+yA )4 (1+y )5
A
⇒ yA = 5.96%.

50          50            1,050
1, 000.89 =              +              +              ⇒ yB = 4.97%.
27

1+yB       (1+yB )2       (1+yB )3
Limitations of the IRR Rule: Non-Flat Term Structure (cont’d)

• Since IRRA < yA , we should reject project A. However, Since IRRB > yB ,
we should accept project B.

• Note that, since N P VA = −1, 000 + 967.68 and N P VB = −1, 000 + 1, 000.89,
we have essentially gone back to the NPV rule!

• Typically (in practice), do we perform this type of computation for the hurdle
rate? No, because the step before that essentially involves calculating the
project’s NPV (i.e., we rediscovered the NPV formula).

• Do we often take the riskfree term structure into account with IRR? No
but, as we will see later, a diﬀerent risk implies a diﬀerent discount rate.
Many projects will have diﬀerent phases in which their risk diﬀers, and so
the appropriate hurdle rate may not be obvious with the IRR. This slide
shows how to get the hurdle rate in those situations too.
28
Limitations of the IRR Rule: Multiple IRRs

• In the example presented in the previous lecture, we noted that the IRR rule
corresponded exactly to the NPV rule. This is not always the case.

• For example, a project can have more than one IRR (in general, there can
be as many diﬀerent IRRs as there are changes in the sign of cash ﬂows).
In fact, it is also possible that the IRR does not exist for some projects.

• Consider the following two projects:

• and consider the two projects:

Project     C0       C1      C2           IRR
A         -1,000   2,300   -1,320     10% and 20%
B         -1,000   3,000   -2,300        none

• If the appropriate hurdle rate is 15%, it is diﬃcult to tell whether these
projects should be undertaken based solely on their IRR.
29

• With a discount rate of 15%, the NPV of project A is 1.89 > 0 (undertake),
and that of project B is −130.44 < 0 (reject).
Limitations of the IRR Rule: Mutually Exclusive Projects

• The IRR rule can be misleading when choosing between mutually exclusive
projects, as the following example shows (we assume that the hurdle rate is
15%):

Project     C0       C1      C2     IRR     NPV at 15%
A         -2,000   1,500   1,500   31.9%       439
B         -5,000   1,000   6,500   24.5%       784

• Essentially, it is better to realize a yield of 24.5% on a larger project than
31.9% on a smaller project.

• The IRR rule can be salvaged in the case of mutually exclusive projects by
computing the IRR for the incremental cash ﬂows.

Project     C0      C1       C2     IRR
B-A       -3,000   -500    5,000   21.0%
30

• Since the IRR of the incremental cash ﬂows is greater than 15%, we should
choose project B over project A.
Limitations of the IRR Rule: Mutually Exclusive Projects (cont’d)

• This can be seen more easily in the following ﬁgure:

• Notice that the incremental project’s IRR of 21.0% also represents the break-
even discount rate between the two projects.

NPV
1500
Project B
1000
Project A
500
35%   40% Discount
0
10%   15%   20%     25%    30%               rate
-500

-1000
31
Limitations of the IRR Rule: Mutually Exclusive Projects (cont’d)

• With project scaling, the IRR rule can also be adjusted by thinking about
what the ﬁrm can do with the excess cash when it invests in the smaller
project.

• In the previous example, there are no other projects, so the excess \$3,000
(assuming that the ﬁrm has \$5,000 in cash) can be invested in capital
markets at an annual rate of 15%.

• Over two years, such a project will generate the cash ﬂows of a coupon
bond with a 15% annual coupon (check that the NPV is zero):
Project              C0       C1     C2    NPV at 15%
Capital markets    -3,000    450   3,450       0

• So, if project A is undertaken and the rest of the money is invested in capital
markets, the project’s cash ﬂows will be as follows:
Project               C0        C1      C2     IRR     NPV at 15%
A with cap. mkt.    -5,000    1,950   4,950   20.9%       439
32

• Notice that the IRR is now lower than that of project B (24.5%).
Limitations of the IRR Rule: Mutually Exclusive Projects (cont’d)

• Because IRR assumes that the proceeds of a project are reinvested at a
rate equal to the IRR, cash ﬂow timing may also create problems when
comparing mutually exclusive projects. In what follows, we assume a hurdle
rate of 10%.
Project     C0       C1      C2     C3     IRR    NPV at 10%
A         -1,200   1,000    500    100    22.8%      197
B         -1,200    100     600   1,100   17.4%      213

• As before, the IRR rule can be salvaged by computing the IRR for the
incremental cash ﬂows.
Project   C0    C1     C2     C3     IRR
B-A       0    -900   100   1,000   11.1%

• Since the IRR of the incremental cash ﬂows is greater than 10%, we should
choose project B over project A.
33
Limitations of the IRR Rule: Mutually Exclusive Projects (cont’d)

• Again, this can be seen graphically:

NPV
600         Project B

400
Project A
200
Discount
5%      10%      15%   20%   25%   30% rate
-200
34
Potential Advantages of the IRR Rule

• In short, the IRR rule yields the same answers as the NPV rule when it is
used properly.

• The IRR rule is sometimes preferred to the NPV rule for a number of reasons.
1. People understand and can relate to rates better than to present values.
2. The IRR is the yield on each dollar I invest.
3. This can be useful when diﬀerent investors invest a diﬀerent amount in
a given project/ﬁrm/fund (e.g., venture capital, hedge funds).
4. Also, the size of a project’s net present value can be misleading when
capital is not easy to raise. For example, a net present value of \$1 million
is good if the initial investment is \$1 million, but not so good (and maybe
not worth it) if the initial investment is \$100 million.
5. Because the IRR rule splits the capital budgeting problem into two dis-
tinct parts (cash ﬂow estimation, hurdle rate estimation), the source of
35

value may be more apparent than with the NPV rule.
The Proﬁtability Index Rule

• The proﬁtability index is deﬁned as the present value of future cash ﬂows
divided by the initial investment:

T
PV              Ct /(1+rt )t
PI =   −C0
=   t=1
−C0
.

• The PI rule consists in accepting a project if and only if P I > 1.

PV      N P V − C0     NP V
• Note that since P I = −    =−             =1+      , the PI rule is equiv-
C0          C0         −C0
alent to the NPV rule (provided that C0 < 0).
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The Proﬁtability Index Rule (cont’d)

• As with the IRR rule, the PI rule can be misleading when applied to mutually
exclusive projects, unless we look at the incremental cash ﬂows.

• This is shown in the following example (where we assume that the hurdle is
10%):
Project     C0        C1       PI    NPV at 10%
A          -1,000    2,000    1.82       818
B         -10,000   15,000    1.36     3,636
B-A        -9,000   13,000    1.31     2,818

• Even though project A has a larger proﬁtability index than project B, project B
should be undertaken because the incremental project from A to B has a PI
over one.
37

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