Goal of the Lecture:
Understand how to properly
value a potential corporate
investment.
Basic Capital Budgeting
I.
Profit Evaluation of Investment Projects
II.
Five Steps
a. Project Identification
b. Estimate of Cash Flows
c. Determine Risk and Discount Rate (CAPM)
d. Formulate Selection Criteria
e. Control and Post Completion Audit
III.
Types of Projects
a. Expansion
b. Replacement
c. Regulatory (Government Required)
IV.
Types of Decision Scenarios
a. Screen for All Acceptable Projects
b. Mutually Exclusive
c. Capital Rationing
ACCEPT-REJECT CRITERIA - A PROJECT
SHOULD ENHANCE SHARE VALUE
V.
Project Selection Criteria - Alternate Methods
•
Payback Method
•
Net Present Value (NPV)
•
Internal Rate of Return (IRR)
ILLUSTRATIVE PROBLEM:
Suppose firm ABC has a share price of $10. The firm may
invest $500,000 in a machine that costs $100,000 each year
in operating expenses for its 10 year life. The machine
produces a product that it sells for $200,000 each year.
Should the investment be made if k = 10%? What should
be the price of the shares once the new project is accepted
if there are 100,000 shares?
PV of Annual Profits = PV of Annual Revenue - Cost
PV = ($200,000 - $100,000)
 1

1
 0.1  0.1(1  0.1)10 


= [=PV(0.10, 10, -100000, 0)] = $614,500
But the machine costs $500,000 so net profit = $114,500
Share Price = $10 + ($114,500) / (100,000 shares) = 11.14
What would you do if the machine costs $700,000?
Payback Method
“Number of years it takes a firm to recover its initial investment.”
I.
Payback Method - Accept project if
Payback < Maximum
Payback = Investment/Cash Flow Per Year
(If cash flows are annuities, otherwise, find the point in
time when the cash flows sum up to the investment
amount)
II.
Example: Suppose a $1.0M project yields net operating
cash flows of $150,000 per year for 10 years. What
is its payback?
$1,000,000/$150,000 = 6.67 Years
If the Firm’s Maximum Payback is > 6.67, then
Accept, Otherwise Reject
Second Method - Could have added cash flows as
follows:
$150,000 + $150,000 + $150,000 + $150,000 +
$150,000 + $150,000 + [$100,000 / $150,000] = 6.67
Firm Sets Maximum or Flexible Payback Period
Advantages:
a. Simple to Calculate and Understand
b. Adjust for Risk by Shortening Payback Period
Disadvantages:
a. Ignores Timing of Cash Flows (no discounting)
and ignores Cash Flows After Payback Point
|-----|-----|-----|-----|
-100 70
20 30 20
|-----|-----|-----|-----|
-100 30
70 20 20
|-----|-----|-----|-----|
-100 100 5
5
5
b. Payback Maximum is Arbitrary
Net Present Value - NPV
“The NPV is determined by discounting cash inflows back to
the present at k and then subtracting the initial investment.”
I.
Net Present Value (NPV) - Accept Project If NPV > 0
n
CF
NPV = CF0 + 
t 1 (1  k )
t
t
Note: k is given or must be determined.
Advantage: NPV gives the correct decision more often.
Disadvantage: Not intuitive and hard to explain to nonfinance managers.
II.
Example: Suppose you have a project that costs
$100,000 and yields cash flows of $50,000
in each of 3 years.
What is the NPV if k =5, 10, 15, 20, 25, and 30%?
NPV= -$100,000 + [=PV(0.05, 3, -50000, 0)] = $36,750
NPV= -$100,000 + [=PV(0.10, 3, -50000, 0)] = $24,350
NPV= -$100,000 + [=PV(0.15, 3, -50000, 0)] = $11,415
NPV= -$100,000 + [=PV(0.20, 3, -50000, 0)] = $ 5,300
NPV= -$100,000 + [=PV(0.25, 3, -50000, 0)] = $ -2,400
NPV= -$100,000 + [=PV(0.30, 3, -50000, 0)] = $ -9,200
Internal Rate of Return - IRR
“The IRR Is the Rate that Causes the Net Present Value to
Equal Zero: Set the Initial Investment Equal to the Present
Value of the Future Cash Flows and Find k = IRR.”
I.
Internal Rate of Return - Accept Project If
IRR > Hurdle
n
NPV = 0 = - Initial Investment +
or
CFt
t
t 1 (1  k )

n
In. Investment =
CFt
t
t 1 (1  k )

Advantages: Considers time value, like NPV.
It is a rate of return; easier than NPV to explain.
Disadvantage: Ignores project scale; reinvestment at IRR.
Unreliable if cash flows change signs more than once.
II.
Example: Suppose the initial investment is $1.0M
and annual cash flows are $150,000 for 10 years.
Find IRR?
[=Rate(10, -150000, 1000000, 0)]
=>
IRR = 8.14%
Note: If required (or hurdle) rate is 10%, we would
reject this project.
IRR with Unequal Cash Flows
The Excel function “Rate” gets you the IRR but only if the
cash flows are all equal. Suppose you that you have the
following cash flows, where year 0 refers to the date of
the initial investment (an outflow).
Year
Cash Flow
0
-65
1
40
2
30
3
20
In Excel, just enter each of these numbers in separate cells,
say B1, B2, B3, and B4.
Then in another cell of the spreadsheet type in [=IRR(B1:B4)],
without the square brackets and you should get 20.82%.
(or 21% if your cell is formatted with zero decimal
places).
For more detail see page 60-61 of the text or go to Excel and
select Help and search for IRR.
NPV Avoids Some of IRR Weaknesses
WEAKNESSES
1. Multiple IRRs
CFs
0
1
2
------------------------------80
500
-500
IRR
= 25% and 400%
QUESTION: How can you check whether these two IRR’s
are correct? Substitute & Calculate NPV =>0
QUESTION: Suppose the hurdle rate is 10%. Should we
accept the project?
Instead use NPV with 10%
NPV = - 80 + .500/(1.1) - .500/(1.1)2
= - 80,000 + 454,545 - 413,243 = - 38.678
=> reject
If we reject at 10% we should reject at higher
rates like 25%.
2. Mutually exclusive investments -scale problem.
PROBLEM: Suppose you have the following
investments which are mutually exclusive. Which
do you choose if you use IRR? If NPV?
TIME
Project A
Project B
0
1
2
3
4
-100
50
50
50
50
-10
5
5
5
5
[=Rate(4, -50, 100, 0)] = [=Rate(4, -5, 10, 0)]
IRR = 35% for both A and B
Assume k = 11% then:
NPVA = -100 + [=PV(0.11, 4, -50, 0)] = 55.0
NPVB = -10 + [=PV(0.11, 4, -5, 0)] = 5.50
IRR is inferior if there are scale differences because
you make more total profit from Project A.
PROBLEM: Suppose you must choose between A and B
below and the required rate is 9%. Which do you
choose using IRR? NPV? :
TIME
0
1
2
3
4
A
-35,000
20,000
15,000
10,000
4,000
B
-35,000
5,000
10,000
15,000
25,000
IRR
NPV(5%)
NPV(9%)
NPV(15%)
20%
9582
6529
2595
16%
12357
7297
1066
Here IRR always chooses A because it assumes
reinvestment of intermediate CFs at IRR.
NPV chooses B at low interest rates and A at high interest
rates. So as the k approaches the calculated IRR in value
we see that they give similar results. This is because the
NPV assumes intermediate CFAT's are invested at k, and
IRR assumes they are invested at IRR.
The NPV numbers above were computed using the Excel
NPV formula. For example, the first NPV number 9582 is:
9582 = NPV(0.05, 20000, 15000, 10000, 4000) - 35000
QUESTION: Why has the project A become more attractive
from an NPV standpoint when k increases to 15%?
Because you get larger cash flows earlier. At large interest
rates, early cash flows become relatively more attractive
25
20
15
10
10
5
0 period
1st period
At low discount rates
(below 10%) project
is preferred because it
earns greater cash
flows,55 vs. 49 for .
15
4
2nd period
3rd period
4th period
15
9
9
4
6
5
7
1
0 period
1st period
2nd period
3rd period
At high discount rates
(30%) project
is
preferred because its
large cash flows come
earlier (are worth more)
than those of project .
4th period
Present value of cash flows at 30% discount rate
When Two Mutually Exclusive Projects Have
Different Life Spans, the Longer Project Will
Have a Larger NPV, All Else Equal.
Ways to Handle Unequal Project Lives
•
Can use IRR
•
Replacement chains - assume multiple
replacements
•
Assume long-lived asset is sold at the end of the
short-lived asset’s life.
•
Use equivalent annual annuity NPV
NPVn
1

1

 k k (1  k ) n 


This method normalizes NPV for project years.
It is the simplest and most effective method.
Equivalent Annual NPV =
Example: Either of two molding machines that makes drinking
glasses requires an initial investment of $2000. Model 3SR
produces short glasses and has a 5-year life. Model 3TR
produces tall glasses and has a 9-year life. CFs expected
from the purchase of model 3SR and 3TR are $700 and $500
per year, respectively. If k =.13 and there is no resale value,
which should be chosen?
NPVS = -2000 + [=PV(0.13, 5, -700, 0)] = 462
NPVT = -2000 + [=PV(0.13, 9, -500, 0)] = 566
 1

1
 0.13  0.13(1  0.13)5   3.517


ENPVS = 462/3.517 = 131
 1

1
 0.13  0.13(1  0.13)9   5.132


ENPVT = 566/5.132 = 110
Capital Rationing
“A situation in which a constraint exists on funds available
such that not all positive NPV projects will be accepted.”
I.
Capital Rationing - Maximize the NPV Subject to
Budget
CFt
t
t 1 (1  k )
Initial Investment
n

Profit Index = PI =
Note: PI is a guide to choosing projects, it measures the
NPV per dollar invested, i.e., PI = 1.5 means that
you get and NPV of 1.5 per $1 invested.
II.
Example: Assume the following information. You
have $600,000 to spend. Which should you
choose?
Project
In. Invest.
PV(CF)
PI
NPV
1.
$300,000
$336,000
1.12
$36,000
2.
$100,000
$120,000
1.20
$20,000
3.
$100,000
$108,000
1.08
$ 8,000
4.
$200,000
$230,000
1.15
$30,000
5.
$200,000
$190,000
0.95 -$10,000
6.
$300,000
$330,000
1.10
$30,000
Choose: Projects 1, 2, 4
Suppose that Project 4 costs $225,000 (PI = 1.02).
Which projects to choose now? Choose: 1, 6
Options and Real Options
1. THE TWO BASIC OPTIONS - PUT AND CALL
•
A call (put) is the right to buy (sell) an asset.
•
Most other options are just combinations of these.
•
Options are “derivatives” and other derivatives
may include options
•
The price of an option is called a “premium”
because options are equivalent to insurance and
the price of insurance is called a premium.
2. For most of this lecture we will assume that the option
a. Can only be exercised at maturity (called
European). An American option, which is the most
common type should behave similarly because, in
most cases, American options are not exercised
until maturity. They are almost always worth more
left unexercised so very few are exercised. If they
are never exercised before expiration, there
should be no difference in value between an
American and European option.
b. Pays no dividends – most options aren’t
dividend protected so dividends will affect price.
CALL OPTION CONTRACT
Definition: The right to purchase 100 shares of a security at
a specified exercise price (Strike) during a specific period.
EXAMPLE: A January 60 call on Microsoft (at 7 1/2)
This means the call is good until the third Friday of January
and gives the holder the right to purchase the stock from the
writer at $60 / share for 100 shares.
Cost is $7.50 / share x 100 shares = $750 premium or option
contract price.
PUT OPTION CONTRACT
Definition: The right to sell 100 shares of a security at a
specified exercise price during a specific period.
EXAMPLE: A January 60 put on Microsoft (at 14 1/2)
This means the put is good until the third Friday of January
and gives the holder the right to sell the stock to the writer
for $60 / share for 100 shares.
Cost $14.25 / share x 100 shares = $1450 premium.
INTRINSIC AND TIME VALUE
•AN OPTION'S INTRINSIC VALUE IS ITS VALUE IF IT
WERE EXERCISED IMMEDIATELY.
•AN OPTION'S TIME VALUE IS ITS COST ABOVE ITS
INTRINSIC VALUE.
Microsoft Stock Price = 53.50 at the time - October 1987
QUESTION: Which Microsoft option has greater intrinsic
value? - put
QUESTION: Which Microsoft option has greater time value?
– put
a. For the Call - Time Value = 7.50 (the full premium)
Intrinsic Value = 0 (Stock price < exercise price).
b. For the Put - Time Value = $8.00 = 14. 50 - (60 - 53.50)
Intrinsic Value = (60 - 53.50) = 6.50.
QUESTION: Which option is a better deal?
REAL OPTIONS EXAMPLES
Call - option to buy another company or company's line.
Call - capital expenditures on R & D and marketing. Give
an option to make further investments if promising.
Call - buy car at the end of the lease
Call - rain check at a grocery store
Put - abandonment
Put - agreement to buy company but only if loan losses are
less than 50 million (WCIS).
Put - guarantees - government price supports - consider
farmer's incentives
Related to NU’s Business
Call – Invest in the first few electric charging stations for electric cars
Call or Put – weather or temperature options
Call – new technology batteries
Put – consumers with solar cells can sell to NU
Call – consumers with solar sells have the right to buy from NU if they
need power
Call – carbon pollution permits
Call – interruptible service – the right to turn off a businesses’ service
NET PRESENT VALUE RULE FOR
PROJECT ACCEPTANCE MUST BE
ADJUSTED IF OPTIONS ARE INVOLVED.
There are two types of options to consider for most projects
A. The call option to delay a project to the future when
the project may have a larger NPV. A project that can
be delayed effectively competes with itself in the future.
This call option is more valuable when a project can be
delayed for a longer time (t), when a project’s (returns)
are very risky (s), and when interest rates (r) are high.
This could explain why it may be rational to delay a
positive NPV project. Managers have often been
criticized by governments for not investing in plant and
equipment during recessions. Managers are not being
indecisive or too risk-averse but simply evaluating
projects based upon their option values which may be
high during recessions.
The basic idea is that if you undertake a project now, you
can’t undertake it in the future when it may have a higher
NPV. The more likely a project could have a higher NPV
in the future, the larger its option’s time value.
If the project is accepted, its time value is lost.
Thus, time value must be considered in the project selection
criteria. Thus instead of
NPVproject > 0
we use
NPVproject > time value of the option to delay > 0
Hence we should accept a project only when it
has a relatively large NPV.
A large NPV in
options terms means that the market value or
present value of the project’s cash flows greatly
exceeds its exercise price (cost of the project). In
other words - when its option is sufficiently “in the
money” i.e., it has much intrinsic value.
B. When a project’s acceptance allows one to undertake
additional projects in the future then we must make another
adjustment to the NPV criteria above.
NPVproject + Value of option on extended projects >
time value of option to delay
For example, if we delay building a new pentium
chip-making plant, it may be cheaper in the future,
all else equal. However, if not building the plant
means we may forfeit the opportunity to build the
next generation chip, then this extra option must
be considered.
Example: You have a project that requires a $20 million
investment. You expect the project to provide future cash
flows with present value of $22 million. If the option to delay
the project for two years is worth $9.5 million, should you
accept the project now or wait? What if the project gives you
the option to make future investments where this option is
worth $8 million? Assume that the investment remains $20
million whenever it is made and the present value of future
cash flows remains $22 million. Also assume that if you delay
then you lose the option to make future investments.
Time value of the option to delay = 9.5 - (22 - 20) = 7.5
Since NPV = (22 -20) = 2 < 7.5 then wait.
If the project gives us the option to make future investments
but only if we invest now, and this option is worth 8 then we
would have
NPV + Option on Future Project = 2 + 8 = 10 > 7.5
- so now we would go ahead with the project.