Copyright © 2015 by The McGraw-Hill Companies, Inc. All rights.docx

Copyright © 2015 by The McGraw-Hill Companies, Inc. All
rights reserved
Chapter 8
Net Present Value and Other Investment Criteria
8- ‹#›
Topics Covered
8.1 Net Present Value
8.2 The Internal Rate of Return Rule
8.3 The Profitability Index
8.4 The Payback Rule
8.5 More Mutually Exclusive Projects
8.6 A Last Look
8- ‹#›
2

Net Present Value
Net Present Value - Present value of cash flows minus initial
investments
Opportunity Cost of Capital - Expected rate of return given up
by investing in a project
8- ‹#›
4
Net Present Value
Example
Q: Suppose we can invest $50 today & receive $60 later today.
What is our increase in value?
Initial Investment
Added Value
$50
$10
A: Profit = −$50 + $60
= $10

8- ‹#›
6
Net Present Value
Example
Suppose we can invest $50 today and receive $60 in one
year. What is our increase in value given a 10% expected
return?
This is the definition of NPV
Initial Investment
Added Value
$50
$4.55
8- ‹#›

8
Valuing an Office Building
Step 1: Forecast cash flows
Cost of building = C0 = 350,000
Sale price in Year 1 = C1 = 400,000
Step 2: Estimate opportunity cost of capital
If equally risky investments in the capital market
offer a return of 7%, then
Cost of capital = r = 7%
8- ‹#›

Valuing an Office Building
Step 3: Discount future cash flows
Step 4: Go ahead if PV of payoff exceeds investment
8- ‹#›
Risk and Present Value
Higher risk projects require a higher rate of return

Higher required rates of return cause lower PVs
8- ‹#›
8- ‹#›
New NPV = 357,143 − 350,000 = $7,143
Higher risk = Lower value
8- ‹#›

Net Present Value
NPV = PV - required investment
8- ‹#›
11
Net Present Value
C0 = Initial cash flow (often negative)
C1 = Cash flow at time 1
C2 = Cash flow at time 2
Ct = Cash flow at time t
t = Time period of the investment
r = Opportunity cost of capital

8- ‹#›
11
Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by accepting all
projects that are worth more than they cost
Therefore, they should accept all projects with a positive net
present value
8- ‹#›
13
Net Present Value
Example
You have the opportunity to purchase an office building.
You have a tenant lined up that will generate $25,000 per year

in cash flows for three years. At the end of three years you
anticipate selling the building for $450,000. How much would
you be willing to pay for the building?
Assume a 7% opportunity cost of capital.
$$$$$$$$$$
8- ‹#›
14
Example - continued
Net Present Value
$25,000
$25,000
$25,000
$450,000
$475,000
0 1 2 3

Present Value
23,364
21,836
387,741
$432,942
$$$$
8- ‹#›
16
Net Present Value
Example - continued
If the building is being offered for sale at a price of
$375,000, would you buy the building? What is the added value
generated by your purchase and management of the building?
8- ‹#›
17

Net Present Value
Example - continued
If the building is being offered for sale at a price of
$375,000, would you buy the building and what is the added
value generated by your purchase and management of the
building?
8- ‹#›
18
Internal Rate of Return
Internal Rate of Return (IRR) - Discount rate at which NPV = 0
Rate of Return Rule - Invest in any project offering a rate of
return that is higher than the opportunity cost of capital

8- ‹#›
20
Example
You can purchase a building for $350,000. At the end of
the year you will sell the building for $400,000. What is the
rate of return on this investment?
8- ‹#›
21
IRR = 14.29%

8- ‹#›
24
NPV (,000s) 0 5 10 15 20 25 30 35 50
46.039603960396022 42.15686274509801
38.349514563106759 34.615384615384627
30.952380952380945 27.358490566037712
23.831775700934582 20.370370370370335
16.972477064220175 13.636363636363589
10.360360360360355 7.1428571428571015
3.9823008849557953 0.87719298245612298 -
2.1739130434782128 -5.17241379310342 -
8.1196581196581246 -11.016949152542336 -
13.865546218487376 -16.666666666666629 -
19.421487603305781 -22.131147540983626 -
24.796747967479693 -27.419354838709697 -30 -
32.539682539682545 -35.039370078740177 -37.5 -
39.922480620155049 -42.307692307692314 -
44.656488549618345 -46.969696969696962 -
49.248120300751879 -51.492537313432841 -
53.703703703703709
Discount rate (%)
NPV (,000s)

Example
You can purchase a building for $375,000. The investment
will generate $25,000 in cash flows (i.e. rent) during the first
three years. At the end of three years you will sell the building
for $450,000. What is the IRR on this investment?
IRR = 12.56%
8- ‹#›
23
IRR=12.56%
8- ‹#›
24

NPV (,000s) 0 5 10 15 20 25 30 35 150
135.29019674832887 121.14213236236438
107.52903058128879 94.425637232589821
81.80812007342611 69.653976101076637
57.941945711293315 46.651933140273265
35.764932677183239 25.262960180315421
15.128989471575245 5.3468932215742537 -
4.0986120284399368 -13.222017030881368 -
22.037067477603326 -30.556808397228249 -
38.793625551241043 -46.759284055331783 -
54.464964433623187 -61.921296296296291 -
69.138389815535575 -76.125865160520007 -
82.892880039250471 -89.448155483199628 -95.8 -
101.95633220954461 -107.9247020698766 -
113.71231079101562 -119.32602952733261 -
124.77241693218023 -130.05773565216001 -
135.18796783259594 -140.16882970045958 -
145.00578528608912 -149.7040593405477
Discount rate (%)
NPV (,000s)

8- ‹#›
23
Calculating the IRR can be a laborious task. Fortunately,
financial calculators can perform this function easily. Note the
previous example.
HP-10B EL-733A BAII Plus
-375,000 CFj -375,000 CFi CF
25,000 CFj 25,000 CFfi 2nd {CLR Work}
25,000 CFj 25,000 CFi -375,000 ENTER
475,000 CFj 475,000 CFi 25,000 ENTER
{IRR/YR} IRR 25,000 ENTER
475,000 ENTER
IRR CPT
All produce IRR=12.56
8- ‹#›
26

Example
You have two proposals to choice between. The initial
proposal (H) has a cash flow that is different than the revised
proposal (I). Using IRR, which do you prefer?
8- ‹#›
50
40
30
20
10
0
-10
-20
NPV $, 1,000s
Discount rate, %
8 10 12 14 16

Revised proposal
Initial proposal
IRR= 14.29%
IRR= 12.56%
IRR= 11.72%
8- ‹#›
Example
You have two proposals to choose between. The initial
proposal has a cash flow that is different than the revised
proposal. Using IRR, which do you
prefer?ProjectC0C1C2C3IRR[email protected]%Initial
Proposal-35040014.29% $ 23,832 Revised Proposal-
375252547512.56% $ 57,942
8- ‹#›

Pitfall 3 - Mutually Exclusive Projects
IRR sometimes ignores the magnitude of the project
The following two projects illustrate that problem
Pitfall 1 - Lending or Borrowing?
With some cash, the NPV of the project increases as the
discount rate increases
This is contrary to the normal relationship between PV and
discount rates
Pitfall 2 - Multiple Rates of Return
Certain cash flows can generate NPV = 0 at two different
discount rates
8- ‹#›
Profitability Index
Profitability Index
Ratio of net present value to initial investment
8- ‹#›
Profitability IndexCash FlowsProjectC0C1C2NPV @
10%Profitability IndexC-1030521.402.1D-552016.073.2E-
551511.942.4

8- ‹#›
Capital Rationing
Capital Rationing - Limit set on the amount of funds available
for investment
Soft Rationing - Limits on available funds imposed by
management
Hard Rationing - Limits on available funds imposed by the
unavailability of funds in the capital market
8- ‹#›
48
Payback Method
Payback Period - Time until cash flows recover the initial
investment of the project
The payback rule specifies that a project be accepted if its
payback period is less than the specified cutoff period
The following example will demonstrate the absurdity of this
statement

8- ‹#›
28
Payback MethodCash FlowsProjectC0C1C2PaybackNPV @
10%F-2,000+1,000+10,0002+7,249G-2,000+1,00002-264H-
2,000+2,00002-347
8- ‹#›
32
Project Interactions
When you need to choose between mutually exclusive projects,
the decision rule is simple:
Calculate the NPV of each project
From those options that have a positive NPV, choose the one
whose NPV is highest

8- ‹#›
35
Mutually Exclusive Projects
Example
Select one of the two following projects, based on highest
NPV
Assume a 7% discount rateSystemC0C1C2C3NPVFaster-
800350350350+118.5Slower-700300300300+87.3
8- ‹#›
36

Investment Timing
Sometimes you have the ability to defer an investment and
select a time that is more ideal at which to make the investment
decision
A common example involves a tree farm
You may defer the harvesting of trees
By doing so, you defer the receipt of the cash flow, yet increase
the cash flow
8- ‹#›
38
Investment Timing
Example
You may purchase a computer anytime within the next five
years. While the computer will save your company money, the
cost of computers continues to decline. If your cost of capital
is 10% and given the data listed below, when should you
purchase the computer?
8- ‹#›

39
Investment Timing
Example
You may purchase a computer anytime within the next five
years. While the computer will save your company money, the
cost of computers continues to decline. If your cost of capital
is 10% and given the data listed below, when should you
purchase the computer?
TimeCostPV SavingsNPV at PurchaseNPV
Today050702020.0145702522.7240703024.83367034Date to
purchase 25.5433703725.3531703924.2
8- ‹#›
40
Equivalent Annual Annuity
Equivalent Annual Annuity - The cash flow per period with the
same present value as the cost of buying and operating a
machine

8- ‹#›
42
Example
Given the following costs of operating two machines and a
6% cost of capital, select the lower cost machine using
equivalent annual annuity method.
Costs ($ thousands)Year:0123PV @ 6%EAAMachine I-15-4-4-
4-25.69-9.61Machine J-10-6-6-21.00-11.45
8- ‹#›
45

Example (with a twist)
Select one of the two following projects, based on highest
“equivalent annual annuity” (r = 9%).
ProjectC0C1C2C3C4NPVEAAA-154.95.25.96.2B-208.18.710.4
2.82
2.78
.87
1.10
8- ‹#›
47
Capital Budgeting TechniquesCriterionDefinitionInvestment
RuleCommentsNet present value (NPV)Present value of cash
inflows minus present value of cash outflowsAccept project if
NPV is positive. For mutually exclusive projects, choose the
one with the highest (positive) NPV.The “gold standard” of
investment criteria. Only criterion necessarily consistent with
maximizing the value of the firm. Provides appropriate rule for
choosing among mutually exclusive investments. Only pitfall
involves capital rationing, when one cannot accept all positive
NPV projects.Internal rate of return (IRR)The discount rate at
which project NPR equals zeroAccept project if IRR is greater
than opportunity cost of capital.If used properly, results in same
accept-reject decision as NPV in the absence of project
interactions. However, beware of the following pitfalls: IRR
cannot rank mutually exclusive projects—the project with

higher IRR may have lower NPV. The simple IRR rule cannot
be used in cases of multiple IRRs or an upward-sloping NPV
profile.Profitability indexRatio of net present value to initial
investmentAccept project if profitability index is greater than 0.
In case of capital rationing, accept projects with highest
profitability index.Results in same accept-reject decision as
NPV in the absence of project interactions. Useful for ranking
projects in case of capital rationing, but misleading in the
presence of interactions. Cannot rank mutually exclusive
projects.Payback periodTime until the sum of project cash flows
equals the initial investmentAccept project if payback period is
less than some specified number of years.A quick and dirty rule
of thumb, with several critical pitfalls. Ignores cash flows
beyond the acceptable payback period. Ignores discounting.
Tends to improperly reject long-lived projects.
8- ‹#›
Capital Budgeting Techniques
8- ‹#›
55
4
$
10
1
60
50
Profit

.
.
+
=
=
-
832
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PV
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07
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at
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1
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C
143
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1
400,000
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12%
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1
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832
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1
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C
t
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t
t
r
C
r
C
r
C
C
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1
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)
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C
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57
$
NPV
)

07
.
1
(
000
,
475
)
07
.
1
(
000
,
25
)
07
.
1
(
000
,
25
000
,
375
NPV
3
2
1
=
+
+
+
-
=

investment
investment
=
return
of
Rate
1
-
C
3
2
1
)
IRR
1
(
000
,
475
)
IRR
1
(
000
,
25
)
IRR
1
(
000
,
25
000

,
375
0
+
+
+
+
+
+
-
=
Calculating IRR by using a spreadsheet
YearCash FlowFormula
0(375,000.00) IRR = 12.56%=IRR(B4:B7)
125,000.00
225,000.00
3475,000.00
Sheet1Calculating IRR by using a spreadsheetYearCash
FlowFormula0(375,000.00)IRR
=12.56%=IRR(B4:B7)125,000.00225,000.003475,000.00
Sheet2
Sheet3
%
29
.
14
0
)
IRR
1
(
400
350
NPV
1
=

=
+
+
-
=
%
56
.
12
0
)
IRR
1
(
475
)
IRR
1
(
25
)
IRR
1
(
25
375
NPV
3
2
1
=
=
+
+
+
+

+
+
-
=
investment
initial
NPV
index
ity
Profitabil
=
factor
annuity
flows
cash
of
lue
present va
=
annuity
annual
Equivalent

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