Download Project Interactions (Real Options)

Project Interactions
Applying the models
So far we have discussed simple projects that are
mutually exclusive and made some assumptions
Competing projects have the same lives
We know the future cash flows with certainty
Management does not have the ability to make
decisions that change the cash flows after the project
is started.
This chapter expands on the basic decision variables
(NPV, IRR etc) in cases where projects with different lives
are compared, cash flows are uncertain, and we discuss
the value & impact of management.
Capital Rationing
Choosing among projects when limited by the
amount of resources available.
Previously we assumed that the firm could
undertake any positive NPV project, however it
may be limited by available resources.
Spending Limits
Assume that the company has a limit on the
amount of funds that it believes it can raise.
Example: 3 projects Spending limit of 12M
Project
A
B
C
Investment
12,000,000
7,000,000
5,000,000
NPV
18,000,000
14,000,000
10,000,000
Which project(s) should it undertake?
Using Profitability Index
Given the spending limits, the firm should also
look at the return per dollar invested.
Project
A
B
C
Investment
12,000,000
7,000,000
5,000,000
NPV
18,000,000
14,000,000
10,000,000
PI
1.5
2.0
2.0
While B & C have a lower NPV individually they
both have a higher profitability index.
Problems
Profitability index can be misleading if looked at
alone.
Project
A
B
C
Investment
10,000,000
5,000,000
5,000,000
NPV
14,000,000
6,000,000
10,000,000
PI
1.4
1.2
2.0
The firm should still look at the total amount of
NPV!
Problems with Profitability Index
If more than one constraint is to be rationed
then PI can be misleading. For example, if one
project depends upon another.
Also PI ignores the amount of wealth created.
Comparing Projects
with Unequal Lives
Replacement Chain Approach
Repeat projects until they have the same life
span.
Compare a two year project with a four year
project by repeating the two year project
Comparing Projects
with Unequal Lives
Equivalent Annual Annuity (finding an
annualized NPV)
To Find EA
find the NPV of the Project
Use the NPV as the PV of an annuity and solve
for payment
Choose the project with the highest EAA
Abandonment Decisions
Often one question is when to stop a project.
By quitting at different points in time the NPV
and EAA will vary due to the changes in salvage
value.
Use EAA and treat each abandonment time as a
separate project.
Uncertain Cash Flows
So far we have assumed that we can estimate
the cash flows from the project with certainty.
However, it is difficult to correctly forecast
future cash flows – how can the risks
associated with changes in the economic
environment and the difficulties with forecasting
cash flows be accounted for?
Three Types of Risk
Stand Alone Risk
Views project in isolation
With-in firm (Corporate Risk)
Looks at the firms portfolio of projects and how
they interact
Market Risk
Risk from the view of a well diversified investor.
Definitions
Risk
Exposure to a chance of injury or loss
Probability
The likelihood an event occurs
Risk vs. Uncertainty
Risk – the probability of the outcome is known
Uncertainty – includes judgment concerning the
probability
Definitions and Terms Continued
Objective Prob –can measure prob. precisely
Subjective Prob. – Includes judgment or
opinion
Variation Risk – We want to look at a range
of possible outcomes
Issues in Risk Measurement
1.
2.
3.
Stand Alone Risk is the easiest to measure
Market Risk is the most important to the shareholder
To evaluate risk you need three things
i. Standard deviation of the projects forecasted
returns
ii. Correlation of the projects forecasted returns with
the firms other assets
iii. Correlation of the projects forecasted returns with
the market
Issues in Risk Management con’t
4. Using the numbers in 3) you can find the corporate
beta and market beta coefficient (equal to ((s/s)r)
5. Most projects have a + correlation with other
projects and a coefficient < 1
6. Most projects are positively correlated with the
market with coefficient < 1
7. Corporate risk should also be examined
1. More important to small business
2. Investors may look at things other than market risk
3. Firm Stability is important to creditors, suppliers etc
Stand Alone Risk (Review)
The easiest approach to measuring stand alone
risk is to use the standard deviation of the
projects returns.
Just like security analysis you need to be careful
looking at only standard deviation – don’t forget
coefficient of variation
Measuring Stand Alone Risk
Quick Review
Sensitivity Analysis
Scenario Analysis
Monte Carlo Simulation
Applying Sensitivity
and Scenario Analysis
In our examples we simplified the problem by
changing the aggregate cash flows.
When evaluating the project, any
assumptions about inputs can change –
impacting the incremental cash flows.
A few of many possible examples:
Changes in variable input costs
Changes in sales
Changes in tax laws
Probability Review
Mutually exclusive events
If A occurs then B cannot. Example considering
building a new sports arena. There are two
sites North and South.
Prob North = .5 Prob South = .25
This implies the prob that the stadium is built is
.5 + .25 = .75
Probability Review 2
Independent Events
Example Exxon is considering two drilling sites, gulf
coast and Alaska
P(A) = New oil from gulf coast = .7
P(B) = Prob of oil in Alaska = .4
Event B
No Event B
(.4)
(.6)
Event A
(.7)
.28
.42
No event A (.3)
.12
.18
Probability Review 3
Dependent Events Prob of one event depends
upon the other
North Side is voting on bonds for the new
arena, 80% chance of the bond passing If
passed there is a 60% chance the stadium gets
built in North. If the bonds fail there is a 30%
chance that the stadium gets built in North
Prob Review 3 con’t
Bond
Passes (.8)
North
Selected
(.8)(.6)
=.48
Bond
Fails (.2)
(.2)(.3)
=.06
North
Rejected
(.8)(.4)
=.32
(.2)(.7)
=.14
Decision Trees
So far our decision making has ignored the role
of management.
We know that things change as a project
progresses and decision trees attempt to
account for this.
Project Example
Peripherals Inc. is considering making a new copier/printer.
Stage 1: Conduct a market study to investigate potential
sales, cost = $500,000
Stage 2: If sizable market exists at time t=1 spend 1,000,000
to build prototype (80% prob)
Stage 3: If it passes all test spend $10,000,000 at time t=2
60% prob
Stage 4: Year t = 3 to t = 6
High demand (20% prob) $12M in CF each yr
Avg Demand (60% prob) $5M in CF each yr
Low Demand (20% prob) –$2M in CF each yr
Building the decision tree
t=0
t=1
-1,000,000
80%
-500,000
20%
0
Stage 1 and Stage 2 represented on the tree
Building the decision tree
t=1
t=2
-10,000,000
60%
-1,000,000
40%
0
Stage 2 and Stage 3 represented on the tree
Stage 1 to 3
t=0
t=1
t=2
-10,000,000
60%
-1,000,000
80%
-500,000
40%
0
20%
0
Decision Tree
Continue to Build the tree (on the board in
class)
When finished find the NPV of each branch and
multiply it times the probability for each branch
to find the expected NPV.
Real Options
Opportunities arise that present the management with
the ability to make a choice. The decision points in the
above decision tree represent this.
For example: At time t=2, if we realize that the project is
going to produce only
-$2,000,000 each year we would not proceed with the
project. There is an option to abandon the project.
Real Options
Three main components
1.
2.
3.
Determining the value of a real option.
Identifying the optimal response to changing
conditions.
Structuring projects to create real options.
Valuing a Real Option
Using the Decision Tree
In the earlier decision tree. Assume we can abandon
the project if we find out that it is going to result in –
2,000,000 CF each year.
We would need to recalculate the NPV of that branch
without the –2,000,000 CF’s
NPV = -9,364,795.92
instead of –14,207,508.52
The total NPV is then 1,235,339.21 instead of 770,438.80
an increase of 464,900.41
Other Benefits
If the reduction in uncertainty decreases the
risk the firm can lower the WACC increasing the
NPV even further.
The key is building the decision points into the
capital budgeting process from the beginning
Real Options and
Financial Management
Flexibility Option -- Switch inputs during the production
process.
Capacity options – Ability to manage capacity in
response to changing economic conditions.
New Product Options – May accept initial negative NPV
if it allows rights to future goods.
Timing Options – Allow you to postpone or increase
production.
Value of Real Options
In each case the option can add value to the
project.
You would want to compare the added value
of the option to the cost of implementing the
option.
Example – it costs an extra 10Million to build a
plant that could allow inputs to be switched.
Given the volatility in the price of the inputs –
you estimate the real option to switch inputs is
worth $20 Million
Characteristics of Real Options
Real options often increase the value of a
project
The value of most real options increases:
As the longer the amount of time that exists
before the option needs to be exercised
increases
The source of risk becomes more volatile
If interest rates increase.
Options
Call Option – the right to buy an asset at some
point in the future for a designated price.
Put Option – the right to sell an asset at some
point in the future at a given price
Call Option Profit
Call option – as the price of the asset increases the
option is more profitable.
Once the price is above the exercise price (strike price)
the option will be exercised
If the price of the underlying asset is below the
exercise price it won’t be exercised – you only loose
the cost of the option.
The Profit earned is equal to the gain or loss on the
option minus the initial cost.
Profit Diagram Call Option
Profit
S-X-C
S
Cost
X
Spot
Price
Call Option Intrinsic Value
The intrinsic value of a call option is equal to
the current value of the underlying asset
minus the exercise price if exercised or 0 if
not exercised.
In other words, it is the payoff to the investor
at that point in time (ignoring the initial cost)
the intrinsic value is equal to
max(0, S-X)
Payoff Diagram Call Option
Payoff
S-X
X
X
S
Spot
Price
Put Option Profits
Put option – as the price of the asset decreases
the option is more profitable.
Once the price is below the exercise price
(strike price) the option will be exercised
If the price of the underlying asset is above the
exercise price it won’t be exercised – you only
loose the cost of the option.
Profit Diagram Put Option
Profit
X-S-C
S
Cost
Spot Price
X
Put Option Intrinsic Value
The intrinsic value of a put option is equal to
exercise price minus the current value of the
underlying asset if exercised or 0 if not
exercised.
In other words, it is the payoff to the investor
at that point in time (ignoring the initial cost)
the intrinsic value is equal to
max(X-S, 0)
Payoff Diagram Put Option
Profit
X-S
S
Cost
X
Spot Price
Pricing an Option
Black Scholes Option Pricing Model
Based on a European Option with no dividends
Assumes that the prices in the equation are
lognormal.
Inputs you will need
S = Current value of underlying asset
X = Exercise price
t = life until expiration of option
r = riskless rate
s2 = variance
PV and FV in continuous time
e = 2.71828 y = lnx x = ey
FV = PV (1+k)n for yearly compounding
FV = PV(1+k/m)nm for m compounding periods
per year
As m increases this becomes
FV = PVern =PVert
let t =n
rearranging for PV
PV = FVe-rt
Black Scholes
Value of Call Option = SN(d1)-Xe-rtN(d2)
S = Current value of underlying asset
X = Exercise price
t = life until expiration of option
r = riskless rate
s2 = variance
N(d ) = the cumulative normal distribution
(the probability that a variable with a standard
normal distribution will be less than d)
Black Scholes (Intuition)
Value of Call Option
SN(d1)
The expected
Value of S
if S > X
-
Xe-rt
N(d2)
PV of cost
Risk Neutral
of investment Probability of
S>X
Black Scholes
Value of Call Option = SN(d1)-Xe-rtN(d2)
Where:
S
s
ln(
)  (r 
)t
X
2
d1 
s t
2
d 2  d1  s
t
Application to Real Options
Investment
Option
Stock Price
Exercise Price
Real Option
PV of projects Cash Flows
Expenditure required to
acquire projects assets
Time to Expire Length of time the decision
can be deferred
Variance
Riskiness of projects assets
Example
Disney – Can spend 100M to create a
Spanish version of the Disney channel
PV of future CF’s = $80M
Initial investment = $100M
The resulting NPV of the project is
80M – 100M = -$20 Million
A Real Option
Assume the expansion will provide political
connections resulting in an advantage if they expand
into South America. Assume the expansion would
cost $150M and could be taken at any time over the
next ten years The firm believes that the NPV of
expanding is 100M.
S = 100M X = 150M r = .065 Variance = .40
Plugging into the
Black Scholes Model
Value of Call Option = SN(d1)-Xe-rtN(d2)
= 100(.8648) – 150e(-.065)(10)(.435)
= 52.3 Million
Original NPV = 80M – 100M = - 20M
Add the value of the option = Total Value of Project
-20M+52.3 = 32.3M
Put Option
The black scholes value is similar for a put
option
Value of put option = Xe-rtN(-d2)-SN(-d1)
Option to Abandon
An example of a real option that corresponds to
a put option would be an option to abandon a
project in the future.
Developing Prob Estimates
History – What happened last year…
Experiments – Test programs, market surveys
etc…
Judgment – Subjective adjustment
Structuring Project Cash Flows
to Help Manage Risk
Variable and Fixed Costs
Pricing Strategy
Sequential Investment
Financial Leverage
Measuring Corporate
and Market Risk
Corporate and Market beta’s