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Real Options
in Capital Budgeting
© Copyright 2004, Alan Marshall
1
Capital Budgeting
> Value of Follow-on Opportunities
• Gaining a foothold so that future projects are
possible
> Value of Waiting
> Abandonment Options
© Copyright 2004, Alan Marshall
2
Follow-on Opportunities
> Suppose your firm is evaluating the Lev-I, a
personal levitation transport device. The
cash flows are shown on the next slide
• They are extremely simplified, but that is not
important to what we are illustrating
© Copyright 2004, Alan Marshall
3
Lev-I Project Cash Flows
Lev-I PLTD Project
2004
After-tax OCF
PV @ 20%
1,294.37
Investment
1,500.00
NPV
(205.63)
© Copyright 2004, Alan Marshall
2005
500
2006
500
2007
500
2008
500
4
Why We Might Accept
> We want to preempt the competition from
entering the PLTD market which we believe
will be highly profitable in the long run
> The Lev-I might teach us things that will be
useful for developing the next generation
Lev-II
© Copyright 2004, Alan Marshall
5
Lev-II Cashflows
Lev-II PLTD Project
2004 …
PV @ 20% 1,248.43
Investment 2,049.04
(800.62)
NPV
2008
2009
1000
2010
1000
2011
1000
2012
1000
2,588.73
3,000.00
(411.27)
Note: Since the investment in 2008 is fixed and known, we
are discounting it at the risk free rate of 10%
© Copyright 2004, Alan Marshall
6
Proceed?
> The Lev-II doesn’t look any better
> The NPV is twice as bad as the Lev-I
> This business does not look promising!
© Copyright 2004, Alan Marshall
7
The Lev-II as an Option
> Undertaking the Lev-I gives us an option to
do the Lev-II, which will not be available
without the Lev-I
> Can we value the option?
© Copyright 2004, Alan Marshall
8
Call Option Valuation
C  S  N(d1)  Xe
 rT
 N(d2 )
 S  T
ln rT  
Xe 
2

d1 
 T
2
 S  T
ln rT  
Xe 
2

d2 
 d1   T
 T
2
© Copyright 2004, Alan Marshall
9
Option Valuation Parameters
BSOPM Parameters
S Today's PV of the cash flows
Value
1,248.43
X Cost (Investment) of the Project 3,000.00
rf Risk free rate
T Term of the option (Years)
 Standard Deviation (assumed)
© Copyright 2004, Alan Marshall
10%
4
50%
10
Option Valuation
BSOPM Calculator
Exercise Price of Option
$3,000.00
Current Price of Underlying
$1,248.43
Annualized Standard Deviation
50.00%
Annual Riskfree Rate
10.00%
Term to Expiry (in Years)
4.0000
Call Price
$305.30
© Copyright 2004, Alan Marshall
11
Re-evaluating the Lev-I
> The DCF valuation of the Lev-I was
(205.63)
> The Lev-II option is worth 305.30
> With the Lev-II option, the Lev-I is worth
99.67 > 0, accept
© Copyright 2004, Alan Marshall
12
How Can It Be So Valuable?
> The option valuation only considers those
outcomes that will result in positive NPVs
for the Lev-II
> If we get to 2008 and find the expected
cash flows are better than we anticipated,
we will proceed with the Lev-II
> Otherwise, we do not proceed
© Copyright 2004, Alan Marshall
13
Cautionary Note
> Option theory can be used to justify very
optimistic valuations
> What happens is all of the firm’s projects
are accepted based on the value of options
and none of the options expire in the
money?
© Copyright 2004, Alan Marshall
14
Value of Waiting
> You have a claim that will allow your firm to
obtain a 100% interest in an oil well by
simply investing the $10 million needed to
develop the well
> If development has not begun by next year,
the claim will expire and revert back to the
government
© Copyright 2004, Alan Marshall
15
Value of Waiting
> Currently, you forecast annual perpetual
cash flows of $1.1 million
> The discount rate is 10%
> NPV = 1.1MM/10% - $10MM = $1MM
> This is positive, so you could proceed
immediately
© Copyright 2004, Alan Marshall
16
Price Uncertainty
> Suppose that the price of oil is volatile
> If the price of oil next year falls, the
expected perpetual annual cash flows
would be $0.8MM, resulting in a project
NPV of ($2MM)
> If the price rises, these cash flows will rise
to $1.4MM, resulting in a project NPV of
$4MM
© Copyright 2004, Alan Marshall
17
First Year Returns
> Low Price:
• (0.8MM + 8.0MM)/$10MM = -12%
> High Price
• (1.4MM + 14MM)/$10MM = 54%
© Copyright 2004, Alan Marshall
18
Risk Neutral Expected Return
> Assume an risk free rate of 10%
> Let pH be the probability of high price
• The probability of low price is (1- pH)
E(r) =(-12%)(1-pH)+54%(pH) = 10%
pH = 1/3
© Copyright 2004, Alan Marshall
19
Option to Wait
> If you wait until next year, what is the well
be worth today?
> [(1/3)x4MM + (2/3)(0)]/(1.1) = $1.21MM,
compared to the $1MM is developed now
© Copyright 2004, Alan Marshall
20
Why Is Waiting Valuable?
> The passage of time resolves uncertainty
> If a year from now, the conditions
deteriorate, we can decide not to invest in a
bad project
> We are cutting of some of the left tail of the
distribution
© Copyright 2004, Alan Marshall
21
Abandonment Option
> We can invest $12MM in a project that will
generate gross margin of $1.7MM annually.
This margin is expected to grow at 9%
annually Fixed costs are $0.7MM annually
and will not grow.
© Copyright 2004, Alan Marshall
22
DCF Analysis
Project Abandonment Example
YEAR
Forecast Revenues
Present value
Fixed Costs
Present value
NPV
0
17.00
0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70
5.15
(0.15)
Investment =
12
Year 1 cash flow =
1.7
Cash flow growth = 9.00%
Fixed costs =
0.7
Discount rate = 9.00%
RF = 6.00%
© Copyright 2004, Alan Marshall
1
2
3
4
5
6
7
8
9 10
1.85 2.02 2.20 2.40 2.62 2.85 3.11 3.39 3.69 4.02
Note Since fixed costs are not uncertain,
they are evaluated at the risk free rate
23
Abandonment
> Ignored in the previous example is the fact
that there are many possible outcomes or
paths where it may be better to stop the
project and collect the project salvage
values.
> Suppose that $10MM of the $12MM project
cost is for fixed assets that have a salvage
value that declines at 10% annually.
© Copyright 2004, Alan Marshall
24
Building a Binomial Tree
> Suppose that historically prices have
evolved according to a random walk with a
 = 14%
ue
 T
e
0.14
 1.15
d  1/ u  1/ 1.15  0.87
© Copyright 2004, Alan Marshall
25
Risk Neutral Expected Return
> With a risk free rate of 6%
> Let pH be the probability of high price
• The probability of low price is (1- pH)
E(r) =(-13%)(1-pH)+15%(pH) = 6%
pH = 0.6791
> Note, there is a minor rounding error in the source
example
© Copyright 2004, Alan Marshall
26
Binomial Tree
> See the spreadsheet
© Copyright 2004, Alan Marshall
27
Discussion
> Again, the value is created by the flexibility
of being able to eliminate the unfavourable
results or branches
© Copyright 2004, Alan Marshall
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