REAL OPTIONS IN INVESTMENTS
 In general, once an investment is undertaken there are opportunities to modify the
investment.
Change the price
Change the method of production
Change the scale of production
Abandon the project
 These opportunities to modify are called managerial options or real options.
 Analysis of projects using basic net present value does not incorporate such managerial
flexibility.
 Options are valuable because they provide an opportunity to exploit a future change in
conditions.
But there is no obligation to take some action.
NPV underestimates the value of an investment because it misses the value of real options.
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 These include the opportunities to modify an investment and the option to wait before
investing.
Expanded NPV = Static NPV + Value of managerial flexibility
Types of real options:
1.
Investment timing options – delay the decision until later, when more information is
available.
2.
Growth options – allow a company to increase its capacity if market conditions are
better than expected.
3.
Abandonment options – allow a company to abandon a project if market conditions
deteriorate and cause lower than expected cash flows.
4.
Flexibility options – permit a firm to alter operations depending on how conditions
change during the life of the project.
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POSSIBLE APPROACHES TO DEAL WITH REAL OPTIONS
1.
Use discounted cash flow (DCF) valuation and ignore any real options by assuming
their values are zero.
2.
Use decision tree analysis.
3.
Use a standard model for a financial option.
Five basic variables affect the value of real options when using financial option models:
1.
The value of the underlying risky asset – a project, investment, or acquisition
2.
The strike price – the amount of money invested to exercise the option if you are
“buying” the asset (with a call option), or the amount of money received if you are
“selling” it (with a put option)
3.
The time to expiration of the option
4.
The standard deviation of the value of the underlying risky asset
5.
The risk-free rate of interest over the life of the option
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SIMPLIFIED EXAMPLE OF A REAL OPTION
 You want to buy some computers that, whenever they are purchased, will provide benefits
with a PV of $70. Suppose the price of computers is falling every year. When do we buy?
 Buy when the rate of increase in NPV is less than the discount rate or when the NPV is
greatest measured today.
Year of
Purchase
Cost of
Computer
PV of
Benefits
NPV at
Year of
Purchase
Growth in NPV
NPV if
today
you wait. (r=10%)
0
50
70
20
25  20
.25
20
20.0
1
45
70
25
30  25
.20
25
22.7
2
40
70
30
34  30
.13
30
24.8
3
36
70
34
37  34
.09
34
25.5
4
33
70
37
39  37
.05
37
25.3
5
31
70
39
0
24.2
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AN EXAMPLE OF THE OPTION TO ABANDON A PROJECT
 Ignoring flexibility
Investment amount is $550.
Required rate of return is 20%.
There is a 50% chance that cash flow will be $150 per year thereafter and 50% chance
that cash flow will be $50 thereafter.
Thus, your expected cash flows are the average: $100 per year into perpetuity.
NPV = -$550 + $100 = -$50.
.20
 Incorporating flexibility using decision trees
In one year we will know more about market demand.
The project or assets can be sold in one year for $400. That is, we have the option to
abandon the investment.
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DECISION TREE FOR THE PROJECT
$150
$150
(High demand)
T=2
T=3
$50
$50
(P = .50)
$150
-$550
T=0
$50
T=1
(At time 1 there
is an option to
sell assets for
$400)
(P = .50)
(Low demand)
T=2
T=3
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ESTIMATING THE VALUE OF FLEXIBILITY TO ABANDON A PROJECT
 Contingency planning:
Low cash flow outcome leads us to sell the assets in one year for $400.
PV of cash flow =
50
 $250 < Abandonment value ($400)
.20
High cash flow outcome leads us to continue the project.
PV of cash flow =
150
 $750 > Abandonment value ($400)
.20
 In one year the going-forward value of the project is either $400 or $750, or an expected
value of $575.
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 We will also receive a cash flow of either $150 or $50 in one year. So the total value of the
project is either $900 or $450, which gives us an expected value of (0.5)($900) + (0.5)($450) =
$675 on year from today.
Expanded NPV = Static NPV + Value of managerial flexibility, so
Expanded NPV =  $550 
$675
 $12.50
1.20
Value of managerial flexibility = Expanded NPV - Static NPV
Value of Flexibility = $12.50 - (-$50) = $62.50
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INVESTMENT TIMING
 Investment timing is like a call option on a stock. It gives you the right to delay investment
to see if market conditions are favorable.
 Cash flows may all be discounted at the same rate (see earlier computer example).
However, there is no possibility of losing money if you delay an investment since the lowdemand cash flows are eliminated.
 To account for this, the initial investment is typically discounted at a lower rate (e.g., the
risk-free rate).
Using financial options models (i.e., Black-Scholes):
 The value of the underlying risky asset (S) is the present value of the future cash
flows of the investment.
 The exercise price (X) is the initial investment.
 The time to expiration (t) is the length of time you can delay the investment.
 The risk-free rate (r) is typically the Treasury bill rate.
 The standard deviation (σ) is the riskiness of the project's return.
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How do we estimate the variance (or standard deviation) of a project's return?
1. Judgment
Recall that a company is a portfolio of projects, with each project having its own risk.
Since returns on the company's stock reflect the diversification gained by combining
many projects, we might expect the variance of the stock's returns to be lower than the
variance of one of its average projects. So you could use the variance of the overall
stock's returns as a base and add a premium to account for the project's risk.
2. Direct Method
Estimate the annual rate of return for each possible outcome and then calculate the
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variance of those returns using the formula:  2   Pi ri  r̂ 2
i 1
3. Indirect Method
This method recognizes that a wide range of outcomes in the project's return is possible.
Based on advanced mathematics, the variance is defined as:
In  CV 2  1
 , where CV is the coefficient of variation of the underlying asset's
2  
t
price at the time the option expires.
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