Class 3
Investment Decisions and
Capital Budgeting
Value of an Investment Project

Recall the four factors that determine the
value of an investment:





Cost of the investment.
Magnitude of future cash flows.
Timing of future cash flows.
Risk of future cash flows.
We shall deal with the first three factors and
defer the discussion of risk to a future date.
The Net Present Value (NPV) Rule

Net Present Value (NPV):
NPV 
T

t 1
CFt
1 r i
d
t
I
p
CFt = after-tax cash flow in year t.
rp = risk-adjusted discount rate for that
investment.
I = initial cost of the investment.
Net Present Value (NPV)


The NPV measures the amount by which the
value of the firm’s stock will increase if the
project is accepted.
NPV Rule:
 Accept all projects for which NPV > 0.
 Reject all projects for which NPV < 0.
 For mutually exclusive projects, choose the project
with the highest NPV.
NPV Example

Consider a drug company with the
opportunity to invest $100 million in the
development of a new drug that is expected
to generate $20 million in after-tax cash
flows for the next 15 years. What is the
NPV of this investment project if the
required return is 10%? What if the
required return is 20%?
NPV Example (cont.)

rp = 10%
$20[1  1 / (110
. ) 15 ]
NPV 
 $100
.10
NPV  $52.12 million

rp = 20%
$20[1  1 / (1.20) 15 ]
NPV 
 $100
.20
NPV  $6.49 million
Eurotunnel NPV



One of the largest commercial investment
project’s in recent years is Eurotunnel’s
construction of the Channel Tunnel linking
France with the U.K.
The cash flows on the following page are based
on the forecasts of construction costs and
revenues that the company provided to
investors in 1986.
Given the risk of the project, we assume a 13%
discount rate.
Eurotunnel’s NPV
Year
Cash Flow
PV (k=13%)
Year
Cash Flow
PV (k=13%)
1986
-L457
-457
1999
636
130
1987
-476
-421
2000
594
107
1988
-497
-389
2001
689
110
1989
-522
-362
2002
729
103
1990
-551
-338
2003
796
100
1991
-584
-317
2004
859
95
1992
-619
-297
2005
923
90
1993
211
90
2006
983
86
1994
489
184
2007
1,050
81
1995
455
152
2008
1,113
76
1996
502
148
2009
1,177
71
1997
530
138
2010
17,781
946
1998
544
126
NPV
L251
Special Topics: Comparing
Projects with Different Lives




Your firm must decide which of two machines
it should use to produce its output.
Machine A costs $100,000, has a useful life of 4
years, and generates after-tax cash flows of
$40,000 per year.
Machine B costs $65,000, has a useful life of 3
years, and generates after-tax cash flows of
$35,000 per year.
The machine is needed indefinitely and the
discount rate is rp = 10%.
Comparing Projects with
Different Lives

Step 1: Calculate the NPV for each project.
$40,000[1  1 / (110
. )4]
NPV A 
 $100,000
.10
NPV A  $26,795
$35,000[1  1 / (110
. )3 ]
NPVB 
 $65,000
.10
NPVB  $22,040
Comparing Projects with
Different Lives

Step 2: Convert the NPVs for each project into
an equivalent annual annuity.
$26,795
EAA 
 $8,453
4
1  1 / (110
. ) 


.
10


$22,040
EAB 
 $8,863
3
1  1 / (110
. ) 


.10


Comparing Projects with
Different Lives
Machine A
0
1
-100,000 40,000
8,453
2
40,000
8,453
3
40,000
8,453
Machine B
0
1
- 60,000 35,000
8,863
2
35,000
8,863
3
35,000
8,863


4
40,000
8,453
Comparing Projects with
Different Lives



The firm is indifferent between the project and
the equivalent annual annuity.
Since the project is rolled over forever, the
equivalent annual annuity lasts forever.
The project with the highest equivalent annual
annuity offers the highest aggregate NPV over
time.
 Aggregate NPVA = $8,453/.10 = $84,530
 Aggregate NPVB = $8,863/.10 = $88,630
Special Topics: Replacing an
Old Machine




The cost of the new machine is $20,000
(including delivery and installation costs) and its
economic useful life is 3 years.
The existing machine will last at most 2 more
years.
The annual after-tax cash flows from each
machine are given in the following table.
The discount rate is rp = 10%.
Replacing an Old Machine
Annual After-Tax Cash Flows
Machine
Year 1
Year 2
Old
$8,000
$6,000
New
$18,000
$15,000
Year 3
$10,000
Replacing an Old Machine

Step 1: Calculate the NPVof the new
machine.
NPV New
$18,000 $15,000 $10,000



 $20,000
2
3
110
.
(110
. )
(110
. )
NPV New  $16,273
Replacing an Old Machine

Step 2: Convert the NPV for the new machine
into an equivalent annual annuity.
EANew
$16,273

 $6,544
3
[1  1 / (110
. ) ]


.
10


Replacing an Old Machine




The NPV of the new machine is equivalent to
receiving $6,544 per year for 3 years.
Operate the old machine as long as its after-tax
cash flows are greater than EANew = $6,544.
Old machine should be replaced after one more
year of operation.
How did we know that the new machine itself
would not be replaced early?
Alternatives to NPV



Internal Rate of Return (IRR)
Payback
Profitability Index
Internal Rate of Return (IRR)

The IRR is the discount rate, IRR, that
makes NPV = 0.
NPV 
T
CFt
I
b
1  IRR g
t 1

IRR Rule
 Accept project if IRR > rp.
 Reject project if IRR < rp.
t
0
IRR Example

Consider, once again, the drug company
that has the opportunity to invest $100
million in the development of a new drug
that will generate after-tax cash flows of
$20 million per year for the next 15 years.
What is the IRR of this investment?
IRR Example

The IRR makes NPV = 0.
1  (1  IRR )
NPV 
IRR


15
20  100  0
Trial and error (or a financial calculator)
gives IRR = 18.4%.
Accept the project if rp < 18.4%.
Problems with IRR



Borrowing or Lending?
Multiple IRRs
Mutually Exclusive Projects
IRR Problems:
Borrowing or Lending?

Consider the following two investment
projects faced by a firm with rp = 10%.
Project

0
1
A
-1,000
1,500
B
1,000
-1,500
IRR
50%
NPV
363.64
50% -363.64
Both projects have an IRR = 50%, but only
project A is acceptable.
NPV Profiles
600
Project A
Project B
400
NPV
200
0
-200
-400
-600
0
0.1
0.2
0.3
0.4
0.5
0.6
Discount Rate, k
0.7
IRR Problems:
Multiple IRRs

Consider a firm with the following investment
project and a discount rate of rp = 25%.
Year
Cash
Flows

0
-1,000
1
3,200
2
-2,400
IRR
20%
100%
NPV
24
This project has two IRRs: one above rp and the
other below rp. Which should be compared to rp?
NPV Profile
100
50
NPV
0
-50
-100
-150
-200
0
0.2
0.4
0.6
0.8
1
Discount Rate, k
1.2
1.4
IRR Problems:
Mutually Exclusive Projects

Consider the following two mutually exclusive
projects. The discount rate is rp = 20%.
Project

0
1
2
IRR
A
-5,000
8,000
0
B
-5,000
0
9,800
NPV
(k=20%)
60%
1,667
40%
1,806
Despite having a higher IRR, project A is less
valuable than project B.
NPV Profiles
5000
4000
Project A
Project B
3000
NPV
2000
1000
0
-1000 0
-2000
-3000
0.2
0.4
Discount Rate, k
0.6
0.8
1
Payback Period


Payback is the number of years it takes to
recoup your initial investment.
Payback Rule
 Accept the project if the payback is less than the
maximum payback allowed.
 Reject the project if the payback is greater than the
maximum payback allowed.
Payback Example

Consider the following two investment projects.
Assume that rp = 20%.
Project

0
1
2
A
-1,000
200
800
B
-1,000
200
200
3
Payback
NPV
(k=20%)
300 2.0 yrs.
-104
2,000 2.3 yrs.
463
Which project is accepted if the payback period
criteria is 2 years?
Problems with Payback




Ignores the Time Value of Money
Ignores Cash Flows Beyond the Payback
Period
Ignores the Scale of the Investment
Decision Criteria is Arbitrary
Profitability Index



Profitability Index
PI = (I + NPV)/I = 1 + NPV/I
Used when the firm (or division) has a
limited amount of capital to invest.
Rank projects based upon their PIs. Invest
in the projects with the highest PIs until all
capital is exhausted (provided PI > 1).
Profitability Index Example

Suppose your division has been given a capital
budget of $6,000. Which projects do you
choose?
Project
I
NPV
PI
A
1,000
600
1.6
B
4,000
2,000
1.5
C
6,000
2,400
1.4
D
3,000
600
1.2
E
5,000
500
1.1
Profitability Index Example




Suppose your budget increases to $7,000.
Choosing projects in decending order of PIs
no longer maximizes the aggreagate NPV.
Projects A and C provide the highest
aggregate NPV = $3,000 and stay within
budget.
Linear programming techniques can be used
to solve large capital allocation problems.