CHAPTER 8
NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA
CHAPTER 8 QUIZ
CHAPTER ORGANIZATION

What Is Business Finance?
Imagine you were to start your own business. No matter what type you started, you would have to answer the following
three questions in some form or another:
1. What long-term investments should you take on? That is, what lines of business will you be in and what sorts of
buildings, machinery, and equipment will you need?
2. Where will you get the long-term financing to pay for your investment? Will you bring in other owners or will
you borrow the money?
3. How will you manage your everyday financial activities such as collecting from customers and paying
suppliers?
Capital Budgeting The first question concerns the firm's long-term investments. The process of planning and
managing a firm's long-term investments is called capital budgeting. In capital budgeting, the financial manager tries to
identify investment opportunities that are worth more to the firm than they cost to acquire. Loosely speaking, this
means that the value of the cash flow generated by an asset exceeds the cost of that asset. Regardless of the specific
investment under consideration, financial managers must be concerned with how much cash they expect to receive,
when they expect to receive it, and how likely they are to receive it. Evaluating the size, timing, and risk of future
cash flows is the essence of capital budgeting. In fact, whenever we evaluate a business decision, the size, timing, and
risk of the cash flows will be, by far, the most important things we will consider.
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This online capital budgeting calculator can be used to
calculate various measures of project profitability:
http://prenhall.com/divisions/bp/app/cfl/CB/CBCalculator.html
You can use it to check your calculations.
Capital budgeting criteria checklist
 Does the method account for the time value of money (TVM)?
 Are all cash flows included?
 Can we adjust for differential project risk?
 Is there a decision rule?
 Can we measure the effect on the value of the firm?
Net Present Value - FinSim - The Net Present Value is defined as the difference between an investment’s
market value and its cost.
8.1

The Basic Idea – The NPV measures the increase in firm value, which is also the increase in the value of what
the shareholders own. Thus, making decisions with the NPV rule facilitates the achievement of our goal –
making decisions that will maximize shareholder wealth.

Estimating Net Present Value: Discounted cash flow (DCF) valuation – finding the market value of assets or
their benefits by taking the present value of future cash flows by estimating what the future cash flows would
trade for in today’s dollars.



The cost of the project must be determined.
Cash flows from the project are estimated.
The riskiness of the projected cash flows is determined, so the appropriate rate of return is used to
discount the cash flows.
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


Cash flows are discounted to their present value to obtain an estimate of the asset’s value to the firm.
The present value of the future expected cash flows is compared with the required outlay, or cost. If the
asset’s value exceeds its cost, the project should be accepted; otherwise, it should be rejected.
Alternatively, the project’s expected rate of return is compared with the rate of return considered
appropriate for the project.
If a firm identifies an investment opportunity with a present value greater than its cost, the firm’s value
will increase. There is a very direct link between capital budgeting and stock values. The more effective
the firm’s capital budgeting procedures, the higher the price of its stock.
n
CFt
,
t
t  0 (1  r)
where CFt is the expected net cash flow at period t, r is the required return on the project, and n is the project’s life.
NPV  
Link to Wikipedia description
Decision rule
An investment should be accepted if the net present value is positive and rejected if it is negative.
Example 1 - Compute the Net Present Value (NPV) given a required return of 12% and the following net cash flows:
Year
CFt
0
($20,000)
1
$6,000
2
$7,000
3
$8,000
4
$5,000
5
$4,000
NPV 
 20,000 6,000
7,000
8,000
5,000
4,000





0
1
2
3
4
(1.12)
(1.12) (1.12) (1.12) (1.12) (1.12)5
NPV  $20,000  $5,357.14  $5,580.36  $5,694.24  $3,177.59  $2,269.71
NPV  $20,000  $22,079.04  $2,079.04 (Since the NPV>0, the project should be accepted).
Excel Solution (in class) , (note on Excel NPV function) , Calculator Solution (in class)
What is the NPV if the required return is 17%?
NPV 
 20,000 6,000
7,000
8,000
5,000
4,000





0
1
2
3
4
(1.17)
(1.17) (1.17) (1.17) (1.17) (1.17)5
NPV  $20,000  $5,128.21  $5,113.59  $4,994.96  $2,668.25  $1,824.44
NPV  $20,000  $19,729.45  $270.55 (Since the NPV<0, the project should be rejected).
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Calculating NPVs with a Spreadsheet
Note: It is not the rather mechanical process of discounting the cash flows that is important. Once we have the cash
flows and the appropriate discount rate, the required calculations are fairly straightforward. The task of coming up with
the cash flows and the discount rate in the first place is much more challenging.
NPV is superior to the other methods of analysis presented in the text because it has no serious flaws. The method
unambiguously ranks mutually exclusive projects, and can differentiate between projects of different scale and time
horizon. The only drawback to NPV is that it relies on cash flow and discount rate values that are often estimates and
not certain, but this is a problem shared by the other performance criteria as well.
Suppose the firm uses the NPV decision rule. At a required return of 11 percent, should the firm accept this project?
What if the required return was 16 percent? What if the required return was 27 percent?
The NPV of a project is the PV of the outflows minus by the PV of the inflows. The equation for the NPV of this
project at an 11 percent required return is:
NPV = – $130,000 + $68,000/(1.11)1 + $71,000/(1.11)2 + $54,000/(1.11)3
NPV = $28,730.79
At an 11 percent required return, the NPV is positive, so we would accept the project.
The equation for the NPV of the project at a 16 percent required return is:
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NPV = – $130,000 + $68,000/(1.16)1 + $71,000/(1.16)2 + $54,000/(1.16)3
NPV = $15,980.77
At a 16 percent required return, the NPV is positive, so we would accept the project.
The equation for the NPV of the project at a 27 percent required return is:
NPV = – $130,000 + $68,000/(1.27)1 + $71,000/(1.27)2 + $54,000/(1.27)3
NPV = – $6,074.35
At a 27 percent required return, the NPV is negative, so we would reject the project.
8.2
The Payback Rule

Defining the Rule - The amount of time required for an investment to generate cash flows sufficient to
recover its initial cost.
Decision rule
An investment is acceptable if its calculated payback period is less than some prespecified number of years.
Example 2 - Compute the Payback Period (PB) given a required return of 12% and the following net cash flows:
Year
CFt
Cumulative Cash Flow
0
($20,000)
($20,000)
1
$6,000
($14,000)
2
$7,000
($7,000)
3
$8,000
$1,000
4
$5,000
5
$4,000
Therefore, payback occurs between two and three years: PB  2 
$7,000
 2.875 years
$8,000
Excel Solution (in class)
Note: The PB period when the cash flows are in the form of an annuity is calculated as: PB 
Year
CFt
0
($5,000)
1
$2,000
2
$2,000
3
$2,000
4
$2,000
PB 
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CF0
CFn
CF0
$5,000

 2.50 years
CFn
$2,000
5

Analyzing the Rule
-No discounting involved*
-Doesn’t consider risk differences
-How do we determine the cutoff point
-Bias for short-term investments
*One of the criticisms of payback is that it doesn’t account for time value of money. Discounted payback
was developed to counter this problem. The basic idea is to compute the PV of each of the cash flows, using
the appropriate discount rate, and determine how long it takes for the investment to pay back on a
discounted basis. You still have an arbitrary cutoff and ignore the cash flows beyond the cutoff period.
Compute the Discounted Payback Period (DPB) given a required return of 12% and the following net cash flows:
Year
CFt
PVCFt @12% Cumulative CF
0
($20,000)
($20,000)
($20,000)
1
$6,000
$5,357.14
($14,642.86)
2
$7,000
$5,580.36
($9,062.50)
3
$8,000
$5,694.24
($3,368.26)
4
$5,000
$3,177.59
($190.67)
5
$4,000
$2,269.71
$2,079.04
DPB  4 
$190.67
 4.084 years
$2,269.71
While the payback period is widely used in practice, it is rarely the primary decision criterion. As William Baumol
pointed out in the early 1960s, the payback rule serves as a crude “risk screening” device – the longer cash is tied up,
the greater the likelihood that it will not be returned. The payback period may be helpful when comparing mutually
exclusive projects. Given two similar projects with different paybacks, the project with the shorter payback is often, but
not always, the better project.

Redeeming Qualities of the Rule
Despite its shortcomings, the payback period rule is often used by large and sophisticated companies when they are
making relatively minor decisions. There are several reasons for this. The primary reason is that many decisions simply
do not warrant detailed analysis because the cost of the analysis would exceed the possible loss from a mistake. As a
practical matter, an investment that pays back rapidly and has benefits extending beyond the cutoff period probably has
a positive NPV.
In addition to its simplicity, the payback rule has two other positive features. First, because it is biased towards shortterm projects, it is biased towards liquidity. In other words, a payback rule tends to favor investments that free up
cash for other uses more quickly. This could be very important for a small business; it would be less so for a large
corporation. Second, the cash flows that are expected to occur later in a project's life are probably more uncertain.
Arguably, a payback period rule adjusts for the extra riskiness of later cash flows, but it does so in a rather
draconian fashion—by ignoring them altogether.
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
8.3
Summary of the Rule
The Average Accounting Return
The average accounting return = measure of accounting profit / measure of average accounting value. In
other words, it is a benefit/cost ratio that produces a pseudo rate of return. However, due to the accounting
conventions involved, the lack of risk adjustment and the use of profits rather than cash flows, it isn’t clear
what is being measured.
AAR = average net income / average book value
Decision rule
A project is acceptable if its average accounting return exceeds a target average accounting return.
Average net income = [$100,000 + 150,000 + 50,000 + 0 + (−50,000)]/5= $50,000
Average book value = ($500,000 + 0) / 2 = $250,000
-Since it involves accounting figures rather than cash flows, it is not comparable to returns in capital
markets
-It treats money in all periods as having the same value
-There is no objective way to find the cutoff rate
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8.4
The Internal Rate of Return - The rate that makes the present value of the future cash flows equal to the initial
cost or investment. In other words, the discount rate that causes NPV to equal $0.
n
CFt
 0,
t
t  0 (1  IRR)
where CFt is the expected net cash flow at period t,
IRR is the internal rate of return on the project, and n is the project’s life.
NPV  
Decision rule
An investment should be accepted if the IRR > r and rejected if the IRR < r.
Link to Wikipedia description
Example 3 - Compute the Internal Rate of Return (IRR) given a required return of 12% and the following cash flows:
Year
CFt
0
($20,000)
1
$6,000
2
$7,000
3
$8,000
4
$5,000
5
$4,000
o Set the NPV equation equal to zero and solve for the IRR:
NPV  0 
 20,000
6,000
7,000
8,000
5,000
4,000





0
1
2
3
4
(1  IRR)
(1  IRR) (1  IRR)
(1  IRR)
(1  IRR)
(1  IRR) 5
o At this point, unless you are using a financial calculator or spreadsheet, solving for the IRR is a trial
and error process. That is, we would “plug” in different estimates for the IRR, work through the
calculations, and determine if we have found the rate that causes NPV to equal $0. We have already
computed the NPV of this project at a 12% discount rate and found the NPV to be positive. In
addition, we computed the NPV of the project at a discount rate of 17% and found NPV to be
negative. Therefore, we know that the IRR lies somewhere between 12% and 17% (in fact, we can
see that the IRR is much closer to 17%).
o Using a financial calculator, we find the IRR = 16.3757%.
o Since the IRR>r (16.38%>12%), the project should be accepted.
Excel Solution (in class) , Calculator Solution (in class)
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Note: The calculation of the project’s IRR does not depend upon the required rate of return. The IRR is compared to
the required rate of return to determine whether to accept or reject the project. Also, if a project’s NPV is positive, its
IRR will exceed the required rate of return. If a project’s NPV is negative, its IRR will be below the required rate of
return.
At this point, you may be wondering whether the IRR and NPV rules always lead to identical decisions. The answer is
yes as long as two very important conditions are met. First, the project's cash flows must be conventional, meaning that
the first cash flow (the initial investment) is negative and all the rest are positive. Second, the project must be
independent, meaning that the decision to accept or reject this project does not affect the decision to accept or reject
any other.
Net Present Value Profile
Graphical representation of the relationship between a project’s NPVs and various discount rates:
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Discount Rate
NPV
0%
$20.00
5%
$11.56
10%
$4.13
13%
$0.09
14%
-$1.20
15%
-$2.46
20%
-$8.33
The point at which the project’s NPV profile intersects with the x-axis is by definition the project’s IRR, since the NPV
at this point is equal to $0.
Special cases (IRR)

 CFn 
“Lump Sum” case: IRR  

 CF0 
(1/n)
1
Year
CFt
0
($750,000)
1
0
2
0
3
0
4
$1,350,000
 $1,350,000 
IRR  

 $750,000 

(1/4)
 1  1.80
(.25)
 1  .15829  15.83%
“Annuity” case: Use the PVIFA tables to estimate the IRR
Year
CFt
0
($32,000)
1
$14,000
2
$14,000
3
$14,000
4
$14,000
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NPV = 0 = $14,000(PVIFA 4, IRR) - $32,000
(PVIFA 4, IRR) = $32,000 / $14,000 = 2.285714
Looking down the period column to four periods, we then move to the right to find the interest rate that corresponds to
the PVIFA of 2.285714. This occurs somewhere between 24% and 28%. With a financial calculator, we find the exact
IRR to be 26.86%.

Problems with the IRR
Non-conventional cash flows – the sign of the cash flows changes more than once or the cash inflow comes
first and outflows come later. If cash flows change sign more than once, then you can have multiple
internal rates of return. This is problematic for the IRR rule, however, the NPV rule still works fine.
To find the IRR on this project, we can
calculate the NPV at various rates:
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If the cash flows are of loan type, meaning money is received at the beginning and paid out over the life of
the project, then the IRR is really a borrowing rate and lower is better.
Mutually exclusive investments – Even if there is a single IRR, another problem can arise concerning
mutually exclusive investment decisions. If two investments, X and Y, are mutually exclusive, then taking
one of them means that we cannot take the other. Given two or more mutually exclusive investments, which
one is the best?
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
Redeeming Qualities of the IRR
-People seem to prefer talking about rates of return to dollars of value
-NPV requires a market discount rate, IRR relies only on the project cash flows
Article: Internal Rate of Return: A Cautionary Tale
Investment
A
B
C

NPV
$10,000
$11,000
$8,000
IRR
22%
20%
24%
PB
2.50 years
7.00 years
3.00 years
The Modified Internal Rate of Return (MIRR)
Procedure: Method 3
1) Using the required rate of return as the compounding rate, find the terminal value (future value) of all of the cash
inflows (positive cash flows) at the end of the project life.
2) Using the required rate of return as the discounting rate, find the present value at t = 0 of all of the cash outflows
(negative cash flows).
3) Compute the MIRR.
 TV inflows 
MIRR  

 PVoutflows 
(1/n)
1 ,
Where n is equal to the life of the project.
Decision rule
An investment should be accepted if the MIRR > r and rejected if the MIRR < r.
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Example 4 - Compute the Modified Internal Rate of Return (MIRR) given a required return of 12% and the following
cash flows:
Year
CFt
0
($20,000)
1
$6,000
2
$7,000
3
$8,000
4
$5,000
5
$4,000
1) TVinflows = $6,000(1.12)4 + $7,000(1.12)3 + $8,000(1.12)2 + $5,000(1.12)1 + $4,000(1.12)0
TVinflows = $9,441.12 + $9,834.50 + $10,035.20 + $5,600.00 + $4,000.00 = $38,910.82
2) PVoutflows = $20,000
 TV inflows 
3) MIRR  

 PVoutflows 
(1/n)
 $38,910.82 
1  

 $20,000 
(1/5)
 1  1.945541
(.20)
 1  .14238  14.24%
Excel Solution (in class)
MIRR example with positive and negative cash flows:
Safeway estimates that its required rate of return is 6 percent. The company is considering two mutually exclusive
projects whose after-tax cash flows are as follows:
Year
0
1
2
3
4
Project S
($1,255)
625
905
930
(245)
Project L
($1,060)
(470)
905
780
920
For Project S:
TVinflows = $625(1.06)3 + $905(1.06)2 + $930(1.06)1 = $744.39 + $1,016.86 + $985.80 = $2,747.05
PVoutflows = $1,255 + $245(1.06)-4 = $1,255 + $194.06 = $1,449.06
MIRRS = ($2,747.05 / $1,449.06)1/4 – 1.0 = 17.34%
For Project L:
TVinflows = $905(1.06)2 + $780(1.06)1 + $920(1.06)0 = $1,016.86 + $826.80 + $920 = $2,763.66
PVoutflows = $1,060 + $470(1.06)-1 = $1,060 + $443.40 = $1,503.40
MIRRL = ($2,763.66 / $1,503.40)1/4 – 1.0 = 16.44%
Since these projects are mutually exclusive, we would choose Project S.
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8.5
The Profitability Index - present value of the future cash flows divided by the initial investment (both numerator
and denominator are positive). This definition assumes no negative cash flows after year zero. Technically, PI = PV of
inflows / PV of outflows, thus a nonconventional project’s PI will have a PV in the numerator and the denominator.
 PVinflows 
PI  

 PVoutflows 
Decision rule
An investment should be accepted if the PI > 1.0 and rejected if the PI < 1.0.
Example 4 - Compute the Profitability Index (PI) given a required return of 12% and the following net cash flows:
Year
CFt
0
($20,000)
1
$6,000
2
$7,000
3
$8,000
4
$5,000
5
$4,000
PVinflows 
6,000
7,000
8,000
5,000
4,000




 $22,079.04
1
2
3
4
(1.12) (1.12)
(1.12) (1.12)
(1.12) 5
PVoutflows  $20,000
 $22,079.04 
PI  
  1.104
 $20,000 
Therefore, the project should be accepted since the PI > 1.0.

The Practice of Capital Budgeting
There have been a number of surveys conducted asking firms what types of investment criteria they actually use. Table
8.5 summarizes the results of several of these. The first part of the table is a historical comparison looking at the
primary capital budgeting techniques used by large firms through time. In 1959, only 19 percent of the firms surveyed
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used either IRR or NPV, and 68 percent used either payback periods or accounting returns. It is clear that, by the 1980s,
IRR and NPV had become the dominant criteria.
Panel B of Table 8.5 summarizes the results of a 1999 survey of chief financial officers (CFOs) at both large and small
firms in the United States. A total of 392 CFOs responded. What is shown is the percentage of CFOs who always or
almost always use the various capital budgeting techniques we described. Not surprisingly, IRR and NPV are the two
most widely used techniques, particularly at larger firms. However, over half of the respondents always, or almost
always, use the payback criterion as well. In fact, among smaller firms, payback is used just about as much as NPV and
IRR. Less commonly used are accounting rates of return and the profitability index.
Article: HOW DO CFOS MAKE CAPITAL BUDGETING AND CAPITAL STRUCTURE DECISIONS?
Summary of investment criteria
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