CHAPTER 9
NET PRESENT VALUE AND OTHER INVESTMENT
CRITERIA
CHAPTER OUTLINE
• Net Present Value
• The Payback Rule
• The Discounted Payback
• The Average Accounting Return
• The Internal Rate of Return
• The Profitability Index
• The Practice of Capital Budgeting
9-2
GOOD DECISION CRITERIA
• We need to ask ourselves the following
questions when evaluating capital budgeting
decision rules:
 Does the decision rule adjust for the time value of
money?
 Does the decision rule adjust for risk?
 Does the decision rule provide information on
whether we are creating value for the firm?
9-3
資本預算(CAPITAL BUDGETING)
•
所謂資本預算，是指為了使資本投資活動的進行能
獲得有效的控制，並為企業尚未實現的資本投資活
動而進行未來現金流出量與流入量的事前規劃。它
(capital budgeting)涉及分配資金與預算資金的過程，
所以是企業規劃長期固定資產支出的過程，亦即資
本預算的規劃所產生的經濟效應會長於1年，所支出
的成本也有長於1年的利用。

一般而言，對長期專案的支出即稱為資本

投資案被接受的準則在於，提案的報酬率大於投資人所要
求的必要報酬率
2023/9/12
資本預算的程序
•
資本預算程序有5個步驟:
1.產生與公司策略目標一致的投資專案的計畫
2.為投資專案估計稅後的增量/額營運現金流量
3.根據資本預算決策準則/方法，評估專案的增量/額(營運)
現金流量





還本期間法則(PBP)與折現還本期間法則(Discounted PBP)
淨現值法則(NPV)
平均會計報酬率法則(AAR)
內部報酬率法則(IRR)
獲利指數法則(PI)
4.根據價值極大化接受準則，選擇專案
5.為已完成之專案，持續對所履行的投資專案作再評估並
執行後續的會計審計工作
2023/9/12
PROJECT TYPES AND RISK
•
根據專案的風險程度而分類
替代型(replacement)專案的風險最小；擴張型(expansion)
專案的風險次之；新市場開發型(new venture)專案的風
險最大。
•
根據專案間的相依程度而分類
Stand-alone projects (獨立專案): 代表對該專案所作的取
捨決策不會影響對其他專案的取捨考量，IRR、NPV、
及PI等評估方法會得到相同的接受或拒絕之決策結果。
Mutually exclusive projects (互斥專案): 亦稱為排序型的
專案，此類型專案的取捨決策無法單獨進行分析，因為
它們的接受與否會影響其他的專案的取捨。 只有 NPV
對互斥專案的排序是正確的。
2023/9/12
專案的現金流量
• As a rule, only incremental cash flows should be counted--that is, the cash flows that will occur only if the project is
accepted. (基本原則:只有增量現金流量才應納入考慮與計
算，i.e., 被納入分析的現金流量是指在只有專案被接受時
所發生的現金流量。增量現金流量又稱為攸關的現金流
量(relevant cash flows)，包括所有與該特定專案有攸關的
成本與利益。)
2023/9/12
NET PRESENT VALUE
• The difference between the market value of
a project and its cost
• How much value is created from
undertaking an investment?
 The first step is to estimate the expected future
cash flows.
 The second step is to estimate the required return
for projects of this risk level.
 The third step is to find the present value of the
cash flows and subtract the initial investment.
9-8
ESTIMATING NET PRESENT VALUE
• Imagine we are thinking of starting a business to produce
and sell a new product—say, organic fertilizer. We can
estimate the start-up costs with reasonable accuracy
because we know what we will need to buy to begin
production. Would this be a good investment?
• How should we estimate the value of our fertilizer
business?
1. Estimate future cash flows we expect the business to
product
2. Apply basic discounted cash flow procedure to estimate
the PV of those cash flows (from step 1)
3. Estimate NPV as the difference between the PV of the
future cash flows and the cost of the investment
• Recall, discounted cash flow (DCF) valuation is the
process of valuing an investment by discounting its
future cash flows
• The task of coming up with the cash flows and the
discount rate is much more challenging than the
calculations themselves
ESTIMATING NET PRESENT VALUE
(CONTINUED)
• Suppose we believe cash revenues from our fertilizer
business will be $20,000 per year. Cash costs (including
taxes) will be $14,000 per year. We will wind down the
business in eight years. The plant, property, and
equipment will be worth $2,000 as salvage at that time.
The project costs $30,000 to launch. We use a 15%
discount rate on new projects such as this one. Is this a
good investment? If there are 1,000 shares of stock
outstanding, what will be the effect on the price per
share of taking this investment?
Present value = $6,000 × [1 − (1/1.158)]/.15 + ($2,000/1. 158)
= ($6,000 × 4.4873) + ( $2,000/3.0590 )
= $26,924 + 654
= $27,578
NPV = −$30,000 + 27,578 = −$2,422
• This is not a good investment! Estimated impact of taking
this project is a loss of value of $2,422/1,000 = $2.42 per
share
PROJECT CASH FLOWS ($000)
• Net present value rule:
• Cash flows for fertilizer business example (on
previous slide):
USING THE NPV RULE
PROJECT EXAMPLE
INFORMATION
• You are reviewing a new project and have
estimated the following cash flows:
 Year 0: CF = -165,000
 Year 1: CF = 63,120; NI = 13,620
 Year 2: CF = 70,800; NI = 3,300
 Year 3: CF = 91,080; NI = 29,100
 Average Book Value = 72,000
• Your required return for assets of this risk
level is 12%.
9-13
NPV – DECISION RULE
• If the NPV is positive, accept the project
• A positive NPV means that the project is
expected to add value to the firm and will
therefore increase the wealth of the owners.
• Since our goal is to increase owner wealth,
NPV is a direct measure of how well this
project will meet our goal.
9-14
COMPUTING NPV FOR THE
PROJECT
• Using the formulas:
 NPV = -165,000 + 63,120/(1.12) + 70,800/(1.12)2 +
91,080/(1.12)3 = 12,627.41
• Using the calculator:
 CF0 = -165,000; C01 = 63,120; F01 = 1; C02 =
70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12;
CPT NPV = 12,627.41
• Do we accept or reject the project?: Accept
9-15
DECISION CRITERIA TEST - NPV
• Does the NPV rule account for the time
value of money?
• Does the NPV rule account for the risk of the
cash flows?
• Does the NPV rule provide an indication
about the increase in value?
• Should we consider the NPV rule for our
primary decision rule?
9-16
CALCULATING NPVS WITH A
SPREADSHEET
• Spreadsheets are an excellent way to
compute NPVs, especially when you
have to compute the cash flows as well.
• Using the NPV function
 The first component is the required return
entered as a decimal
 The second component is the range of cash
flows beginning with year 1
 Subtract the initial investment after computing
the NPV
9-17
PAYBACK PERIOD(回收期間法)
• How long does it take to get the initial cost
back in a nominal sense?
• Computation
 Estimate the cash flows
 Subtract the future cash flows from the initial cost
until the initial investment has been recovered
• Decision Rule – Accept if the payback
period is less than some preset limit
9-18
COMPUTING PAYBACK
• Assume we will accept the project if it pays
back within two years.
 Year 1: 165,000 – 63,120 = 101,880 still to recover
 Year 2: 101,880 – 70,800 = 31,080 still to recover
 Year 3: 31,080 – 91,080 = -60,000 project pays
back in year 3
• Do we accept or reject the project?
9-19
DECISION CRITERIA TEST PAYBACK
• Does the payback rule account for the time
value of money?
• Does the payback rule account for the risk
of the cash flows?
• Does the payback rule provide an
indication about the increase in value?
• Should we consider the payback rule for our
primary decision rule?
9-20
ADVANTAGES AND
DISADVANTAGES OF PAYBACK
• Advantages
 Easy to
understand
 Adjusts for
uncertainty of
later cash flows
 Biased toward
liquidity
• Disadvantages
 Ignores the time value
of money
 Requires an arbitrary
cutoff point
 Ignores cash flows
beyond the cutoff date
 Biased against longterm projects, such as
research and
development, and new
projects
9-21
DISCOUNTED PAYBACK PERIOD
• Compute the present value of each cash
flow and then determine how long it takes to
pay back on a discounted basis
• Compare to a specified required period
• Decision Rule: Accept the project if it pays
back on a discounted basis within the
specified time
9-22
COMPUTING DISCOUNTED
PAYBACK
• Assume we will accept the project if it pays back on
a discounted basis in 2 years.
• Compute the PV for each cash flow and determine
the payback period using discounted cash flows
 Year 1: 165,000 – 63,120/1.121 = 108,643
 Year 2: 108,643 – 70,800/1.122 = 52,202
 Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in
year 3
• Do we accept or reject the project?
9-23
DECISION CRITERIA TEST –
DISCOUNTED PAYBACK
• Does the discounted payback rule account for
the time value of money?
• Does the discounted payback rule account for
the risk of the cash flows?
• Does the discounted payback rule provide an
indication about the increase in value?
• Should we consider the discounted payback
rule for our primary decision rule?
9-24
ADVANTAGES AND DISADVANTAGES OF
DISCOUNTED PAYBACK
• Advantages
 Includes time value
of money
 Easy to understand
 Does not accept
negative estimated
NPV investments
when all future cash
flows are positive
 Biased towards
liquidity
• Disadvantages
 May reject positive
NPV investments
 Requires an arbitrary
cutoff point
 Ignores cash flows
beyond the cutoff
point
 Biased against longterm projects, such as
R&D and new products
9-25
AVERAGE ACCOUNTING RETURN(平均
會計報酬率法)
• There are many different definitions for
average accounting return
• The one used in the book is:
 Average net income / average book value
 Note that the average book value depends on
how the asset is depreciated.
• Need to have a target cutoff rate
• Decision Rule: Accept the project if the AAR
is greater than a preset rate
9-26
THE AVERAGE ACCOUNTING RETURN
• Average accounting return (AAR) is an investment’s
average net income divided by its average book value
• Different definitions of AAR, but in one form or another,
the AAR is always defined as some measure of average
accounting profit divided by some measure of average
accounting value
• Suppose we are deciding whether to open a store in a
new shopping mall. The required investment in
improvements is $500,000. The store would have a fiveyear life because everything reverts to the mall owners
after that time. The required investment would be 100%
depreciated (straight-line) over five years, so the
depreciation would be $500,000/5 = $100,000 per year.
The tax rate is 25%.
• Table 9.4, on the next slide, contains projected revenues
and expenses
• Net income in each year, based on these figures, is also
shown
PROJECTED YEARLY REVENUE AND COSTS
FOR AVERAGE ACCOUNTING RETURN
THE AVERAGE ACCOUNTING RETURN
(CONTINUED)
• We started out with a book value of $500,000 (the initial
cost) and ended up at $0, so the average book value is:
• ($500,000 + 0)/2 = $250,000
• Average net income is:
• [$100,000 + 150,000 + 50,000 + 0 + ( − 50,000)]/5 = $50,000
• Average accounting return is:
• If the firm has a target AAR of less than 20 percent, then
this investment is acceptable; otherwise, it is not
• Average accounting return rule is:
AVERAGE ACCOUNTING RETURN SUMMARY
• Use of this rule has a number of problems
• Chief drawback is that the AAR is not a rate of return in any
meaningful economic sense, but rather the ratio of two
accounting numbers, and therefore is not comparable to the
returns offered in financial markets
• One reason AAR is not a true rate of return is that it ignores
time value
• Lacks an objective cutoff period
• Target AAR may be specified by calculating AAR for the firm
as a whole and using this as a benchmark
• Does not look at cash flow and market value, but instead
focuses on net income and book value, which are poor
substitutes
COMPUTING AAR
• Assume we require an average accounting return
of 25%
• Average Net Income:
 (13,620 + 3,300 + 29,100) / 3 = 15,340
• AAR = 15,340 / 72,000 = .213 = 21.3%
• Do we accept or reject the project?
9-31
DECISION CRITERIA TEST - AAR
• Does the AAR rule account for the time
value of money?
• Does the AAR rule account for the risk of the
cash flows?
• Does the AAR rule provide an indication
about the increase in value?
• Should we consider the AAR rule for our
primary decision rule?
9-32
ADVANTAGES AND
DISADVANTAGES OF AAR
• Advantages
 Easy to calculate
 Needed
information will
usually be
available
• Disadvantages
 Not a true rate of
return; time value of
money is ignored
 Uses an arbitrary
benchmark cutoff rate
 Based on accounting
net income and book
values, not cash flows
and market values
9-33
INTERNAL RATE OF RETURN(內部報酬
率法)
• This is the most important alternative to NPV
• It is often used in practice and is intuitively
appealing
• It is based entirely on the estimated cash flows and
is independent of interest rates found elsewhere
9-34
IRR – DEFINITION AND DECISION
RULE
• Definition: IRR is the return that makes
the NPV = 0
• Decision Rule: Accept the project if the
IRR is greater than the required return.
9-35
COMPUTING IRR
• If you do not have a financial calculator,
then this becomes a trial and error process
• Calculator
 Enter the cash flows as you did with NPV
 Press IRR and then CPT
 IRR = 16.13% > 12% required return
• Do we accept or reject the project?
9-36
NPV PROFILE FOR THE
PROJECT
70,000
IRR = 16.13%
60,000
50,000
NPV
40,000
30,000
20,000
10,000
0
-10,000 0
0.02 0.04 0.06 0.08
0.1
0.12 0.14 0.16 0.18
0.2
0.22
-20,000
Discount Rate
9-37
DECISION CRITERIA TEST - IRR
• Does the IRR rule account for the time value
of money?
• Does the IRR rule account for the risk of the
cash flows?
• Does the IRR rule provide an indication
about the increase in value?
• Should we consider the IRR rule for our
primary decision criteria?
9-38
ADVANTAGES OF IRR
• Knowing a return is intuitively appealing
• It is a simple way to communicate the value
of a project to someone who doesn’t know
all the estimation details
• If the IRR is high enough, you may not need
to estimate a required return, which is often
a difficult task
9-39
CALCULATING IRRS WITH A
SPREADSHEET
• You start with the cash flows the same
as you did for the NPV
• You use the IRR function
 You first enter your range of cash flows,
beginning with the initial cash flow
 You can enter a guess, but it is not
necessary
 The default format is a whole percent – you
will normally want to increase the decimal
places to at least two
9-40
SUMMARY OF DECISIONS FOR
THE PROJECT
Summary
Net Present Value
Accept
Payback Period
Reject
Discounted Payback Period
Reject
Average Accounting Return
Reject
Internal Rate of Return
Accept
9-41
NPV VS. IRR
• NPV and IRR will generally give us the same
decision
• Exceptions:
 Nonconventional cash flows – cash flow
signs change more than once
 Mutually exclusive projects(互斥方案)
• Initial investments are substantially
different (issue of scale)
• Timing of cash flows is substantially
different
9-42
IRR AND NONCONVENTIONAL
CASH FLOWS(非傳統現金流量)
• When the cash flows change sign more
than once, there is more than one IRR
• When you solve for IRR you are solving
for the root of an equation, and when
you cross the x-axis more than once,
there will be more than one return that
solves the equation
• If you have more than one IRR, which
one do you use to make your decision?
9-43
ANOTHER EXAMPLE:
NONCONVENTIONAL CASH FLOWS
• Suppose an investment will cost
$90,000 initially and will generate the
following cash flows:
 Year 1: 132,000
 Year 2: 100,000
 Year 3: -150,000
• The required return is 15%.
• Should we accept or reject the project?
9-44
NPV PROFILE
IRR = 10.11% and 42.66%
$4,000.00
$2,000.00
NPV
$0.00
($2,000.00)
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
($4,000.00)
($6,000.00)
($8,000.00)
($10,000.00)
Discount Rate
9-45
PROBLEMS WITH THE IRR:
NONCONVENTIONAL CASH FLOWS
• Suppose we have a strip-mining project that requires a
$60 investment. Our cash flow in the first year will be $155.
In the second year, the mine will be depleted, but we will
have to spend $100 to restore the terrain.
• The cash flows for this project are shown below:
• To find the IRR on this project, calculate the NPV at various
rates:
PROBLEMS WITH THE IRR:
NONCONVENTIONAL CASH FLOWS
(CONTINUED)
• What’s the IRR? To find out,
we draw the NPV profile
• Notice the NPV is zero
when the discount rate is
25%, as well as when it is
33.33%
• Which of these is correct?
• Both or neither; there is no
unambiguously correct
answer
• Multiple rates of return
problem is the possibility
that more than one discount
rate will make the NPV of an
investment zero
• We should take this
investment only if our
required rate of return is
between 25% and 33.33%
WHAT’S THE IRR?
PROBLEMS WITH THE IRR:
MUTUALLY EXCLUSIVE INVESTMENTS
• Mutually exclusive investment decisions is a situation in
which taking one investment prevents the taking of
another
• Two projects that are not mutually exclusive are
independent
• Given two or more mutually exclusive investments, which
one is the best? Can we also say that the best one has the
highest return?
• The best one is the one with the largest NPV
• No, we cannot say the best one has the highest return
• Consider the following cash flows from two mutually
exclusive investments, where the IRR for A is 24% and the
IRR for B is 21%:
PROBLEMS WITH THE IRR: MUTUALLY
EXCLUSIVE INVESTMENTS (CONTINUED)
• Simple intuition suggests Investment A is better because of
its higher return, but let’s calculate the NPV of these
investments for different required returns:
• IRR for A (24%) is larger than the IRR for B (21%), but in
comparing the NPVs, the higher NPV investment depends
on our required return
• If our required return is 10%, B has the higher NPV, but if our
required return is 15%, A has the higher NPV
• When we have mutually exclusive projects, we shouldn’t
rank them based on their returns
• Look at relative NPVs to avoid the possibility of choosing
incorrectly
NPV PROFILES FOR MUTUALLY
EXCLUSIVE INVESTMENTS
• Conflict between IRR and
NPV for mutually
exclusive investments
can be illustrated by
plotting the investments’
NPV profiles
• NPV profiles cross at
about 11.1%
• At any discount rate less
than 11.1%, the NPV for B
is higher
• In this range, taking B
benefits us more than
taking A, even though
A’s IRR is higher
• At any rate greater than
11.1%, Investment A has
the greater NPV
CALCULATI
NG THE
CROSSOVER
RATE
INVESTING OR FINANCING?
• Consider the following two independent investments:
• Company initially pays out cash with Investment A and
initially receives cash for Investment B. Suppose the
required return for each investment project is 12%.
According to the IRR decision rule, which, if either, project
should we accept?
• IRR is 30% for both projects, so according to the IRR
decision rule, we should accept both projects
• However, NPV of B at 12 percent is: $100 – ($130/1.12) = $16.07
• In this case, the NPV and IRR decision rules disagree
INVESTING OR FINANCING?
(CONTINUED)
• To see what’s going on, plot the NPV profile for each
project
• NPV profile for B is upward sloping; project should be
accepted if the required return is greater than 30%
• Investment B has financing type cash flows, whereas
Investment A has investing type cash flows
• You should take a project with financing-type cash flows
only if it is an inexpensive source of financing (i.e., IRR is
lower than required return)
IRR AND MUTUALLY EXCLUSIVE
PROJECTS
• Mutually exclusive projects
 If you choose one, you can’t choose the
other
 Example: You can choose to attend
graduate school at either Harvard or
Stanford, but not both
• Intuitively, you would use the following
decision rules:
 NPV – choose the project with the higher
NPV
 IRR – choose the project with the higher IRR
9-55
EXAMPLE WITH MUTUALLY
EXCLUSIVE PROJECTS
Period
0
Project Project
A
B
-500
-400
1
325
325
2
325
200
IRR
19.43% 22.17%
NPV
64.05
The required return
for both projects is
10%.
Which project
should you accept
and why?
60.74
9-56
REDEEMING QUALITIES OF THE IRR
• Despite its flaws, the IRR is very popular in practice—more
so than even the NPV
• When analyzing investments, people tend to prefer talking
about rates of return rather than dollar values, and the IRR
appears to provide a simple way of communicating
information about a proposal
• IRR may have a practical advantage over the NPV, as we
can still estimate the IRR if we do not know the appropriate
discount rate
• Advantages and disadvantages of the IRR are
summarized as follows:
THE MODIFIED INTERNAL RATE OF
RETURN (MIRR)
• To address some of the problems that can crop up with
the standard IRR, it is often proposed that a modified
version be used
• Several different ways to calculate a modified IRR, or MIRR,
but basic idea is to modify the cash flows first and then
calculate an IRR using the modified cash flows
• To illustrate, consider again the cash flows in Figure 9.6,
shown below
• As discussed previously, there are two IRRs, 25% and
33.33%
• Next, we will calculate three different MIRRs, all of which
have the property that only one answer will result,
eliminating the multiple IRR problem
METHOD 1: THE DISCOUNTING
APPROACH
• Discount all negative cash flows back to the present at the
required return, add them to the initial cost, and then
calculate the IRR
• Because only the first modified cash flow is negative, there
will be only one IRR
• Discount rate used might be the required return, or it might
be some other externally supplied rate
• If the required return on the project is 20%, the modified
cash flows look like this:
• If you calculate the MIRR now, you should get 19.74%
METHOD 2: THE REINVESTMENT
APPROACH
• Compound all cash flows (positive and negative) except
the first out to the end of the project’s life and then
calculate the IRR
• Rate we use could be the required return on the project, or
it could be a separately specified “reinvestment rate”
• Here are the modified cash flows:
• Time 0: − $60
• Time 1: +0
• Time 2: − $100 + ($155 × 1.2) = $86
• MIRR on this set of cash flows is 19.72%, a little lower than
we got using the discounting approach
METHOD 3: THE COMBINATION
APPROACH
• Combination approach blends our first two methods
• Negative cash flows are discounted back to the present,
and positive cash flows are compounded to the end of
the project
• With the combination approach, the modified cash flows
are as follows:
• MIRR is 19.87%, the highest of the three methods
MIRR OR IRR:
WHICH IS BETTER?
• MIRRs are controversial
• On the bright side, by design, MIRRs don’t suffer from the
multiple rate of return problem
• One disadvantage with MIRRs is that there are different
ways of calculating them, and there is no clear reason to
say one of the three methods is better than any other
• Calculating an MIRR requires discounting, compounding,
or both:
1. If we have the relevant discount rate, why not calculate
the NPV and be done with it?
2. Because an MIRR depends on an externally supplied
discount (or compounding) rate, the answer you get is
not truly an “internal” rate of return, which, by definition,
depends on only the project’s cash flows
• Value of a project does not depend on what the firm does
with the cash flows generated by that project
• Generally, no need to consider reinvestment of interim
cash flows
SUMMARY OF DECISION RULES
• The NPV is positive at a required return of 15%, so
you should Accept
• If you use the financial calculator, you would get an
IRR of 10.11% which would tell you to Reject
• You need to recognize that there are nonconventional cash flows and look at the NPV profile
9-64
NPV PROFILES
IRR for A = 19.43%
$160.00
IRR for B = 22.17%
$140.00
$120.00
Crossover Point = 11.8%
NPV
$100.00
$80.00
A
B
$60.00
$40.00
$20.00
$0.00
($20.00) 0
0.05
0.1
0.15
0.2
0.25
0.3
($40.00)
Discount Rate
9-65
CONFLICTS BETWEEN
NPV AND IRR
• NPV directly measures the increase in value
to the firm
• Whenever there is a conflict between NPV
and another decision rule, you should
always use NPV
• IRR is unreliable in the following situations
 Nonconventional cash flows
 Mutually exclusive projects
9-66
修正內部報酬率法(MIRR)(1/2)
• 將再投資報酬率修正為以「資金成本」從事再投資。
• MIRR將投資計畫各期所有的現金流出量以資金成本折現
計算現值（通常只有期初一次的現金流出量），也將所有
現金流入量以資金成本複利計算終值到計畫的最後一期，
而使現金流入量終值等於現金流出量現值的那個「折現
率」，即是MIRR。
n
CF0 
財務管理專題
n－t
CF

(1

k)
 t
t 1
(1  MIRR) n
67
2023/9/12
修正內部報酬率法(MIRR)(2/2)
• 例：若一項期初成本15,000元的投資計畫，未來4
年預估可產生之現金流量分別為5,000、6,000、
8,000、10,000，且公司的資金成本為5%，則
MIRR為何?
• IRR法：
NPV  $15,000 
$5,000
$6,000
$8,000
$10,000



0
(1  IRR )1
(1  IRR ) 2
(1  IRR ) 3
(1  IRR ) 4
 IRR  28.37%
• MIRR法：
$5,000(1  5%) 3  $6,000(1  5%) 2  $8,000(1  5%)1  $10,000
$15,000 
(1  MIRR ) 4
 MIRR  19.71%
2023/9/12
PROFITABILITY INDEX(獲利指數法)
• Measures the benefit per unit cost, based on the
time value of money
• A profitability index of 1.1 implies that for every $1 of
investment, we create an additional $0.10 in value
• This measure can be very useful in situations in
which we have limited capital
9-69
ADVANTAGES AND DISADVANTAGES OF
PROFITABILITY INDEX
• Advantages
 Closely related to
NPV, generally
leading to identical
decisions
 Easy to understand
and communicate
 May be useful
when available
investment funds
are limited
• Disadvantages
 May lead to
incorrect decisions
in comparisons of
mutually exclusive
investments
9-70
CAPITAL BUDGETING
IN PRACTICE
• We should consider several investment criteria
when making decisions
• NPV and IRR are the most commonly used primary
investment criteria
• Payback is a commonly used secondary
investment criteria(作為補充之評估法)
9-71
CAPITAL BUDGETING IN
PRACTICE
SUMMARY – DCF CRITERIA
• Net present value




Difference between market value and cost
Take the project if the NPV is positive
Has no serious problems
Preferred decision criterion
• Internal rate of return




Discount rate that makes NPV = 0
Take the project if the IRR is greater than the required return
Same decision as NPV with conventional cash flows
IRR is unreliable with nonconventional cash flows or mutually
exclusive projects
• Profitability Index




Benefit-cost ratio
Take investment if PI > 1
Cannot be used to rank mutually exclusive projects
May be used to rank projects in the presence of capital rationing
9-73
SUMMARY – PAYBACK CRITERIA
• Payback period
 Length of time until initial investment is recovered
 Take the project if it pays back within some specified
period
 Doesn’t account for time value of money, and there
is an arbitrary cutoff period
• Discounted payback period
 Length of time until initial investment is recovered on
a discounted basis
 Take the project if it pays back in some specified
period
 There is an arbitrary cutoff period
9-74
SUMMARY – ACCOUNTING
CRITERION
• Average Accounting Return
 Measure of accounting profit relative to book value
 Similar to return on assets measure
 Take the investment if the AAR exceeds some specified
return level
 Serious problems and should not be used
9-75
QUICK QUIZ
• Consider an investment that costs $100,000
and has a cash inflow of $25,000 every year
for 5 years. The required return is 9%, and
required payback is 4 years.
 What is the payback period?
 What is the discounted payback period?
 What is the NPV?
 What is the IRR?
 Should we accept the project?
• What decision rule should be the primary
decision method?
• When is the IRR rule unreliable?
9-76
COMPREHENSIVE PROBLEM
• An investment project has the following cash
flows: CF0 = -1,000,000; C01 – C08 = 200,000
each
• If the required rate of return is 12%, what
decision should be made using NPV?
• How would the IRR decision rule be used for
this project, and what decision would be
reached?
• How are the above two decisions related?
9-77