1. Real Options Traditional capital budgeting analysis:
estimates cashflows each period
discounts to get NPV
firm decides to invest/not invest
BIG PROBLEM: Traditional analysis assumes that a firm’s
only choice is accept/reject the project.
THIS IS NOT TRUE!!

2. In a real business situation, firms face many choices with
respect to how to operate a project, both before it starts
and after it is underway.
Eg.
Flexibility:
use a production technology that is adaptable
can produce more than one product
if market for one product goes down, can switch production
to the other
the option to change production if the firm wants
to (the flexibility) is valuable
makes the project worth more
traditional NPV analysis assumes cashflows fixed,
will not change with future business conditions – ignores
the value of this option

3. Eg.
Abandonment
firm invests in project
after a time the firm may be able to shut down production
if things are not going well
option to abandon
traditional analysis assumes that the firm either takes
the project and runs it for its life, or rejects it
But…the ability to start a project and shut it down
(perhaps temporarily) if conditions warrant is valuable

4. Eg.
Option to Delay
traditional analysis assumes firm accepts project now
or never invests
But…what if firm has choice to delay making decision?
Wait and see how things develop and then decide to invest
or not
The choice to delay if the firm wants is valuable
Other examples of valuable options (choices) a firm may have include:
option to expand/shrink production
option to move into new market
R&D gives the option to develop new products if
they become viable
development options on natural resources
et cetera

5. Real Options
Any time a firm has the ability to make choices, there is a
value added to the project in question
traditional NPV analysis ignores this value
the study of real options attempts to put a dollar value on the
ability to make choices

6. How are real options valued? Three major ways:
Use methods developed for pricing financial options
We look at financial options later in the course
Black-Scholes Model
May be problems
2) Decision trees
look at this method here
3) Stochastic optimization problems
like (2) but using far more complicated
(and realistic) models for the probability
of different events occurring

7. Option to Delay
simple example from “Irreversibility, Uncertainty and Investment”,
Robert Pindyck [Journal of Economic Literature, 1991]
for $800 a firm can build widget factory
makes 1 widget per year
factory is built instantly
investment is irreversible
if factory built, first widget produced immediately
no costs of manufacturing
no taxes
appropriate discount rate is 10%

8. Option to Delay the price of widgets is currently $100
next year the price will be either $150 (50% probability) or
$50 (50% probability)
whatever price holds next year will hold forever after

9. year 2 year 0 year 1 Price = $150 Price = $150 Price = $100
prob. = 0.5
Price = $100
prob. = 0.5
Price = $50
Price = $50

10. Traditional NPV Analysis
Expected year 1 price = E[price]
= 0.5($150) + 0.5($50) = $100
Standard analysis says NPV > 0, so start project.

11. Option to Delay
BUT… firm has another option. Delay the choice of whether
to invest or not.
Wait until next year to decide.
Can see what price turns out to be before making decision.
If you delay, you lose on the year 0 sales ($100).
The bad part of delaying – lost sales.
But, you get to see what price will be before making
irreversible investment.
The good part of delaying, reduced uncertainty.

12. CASE 1:
If delay and price turns out to be $50:
NPV < 0 , so firm will not invest.
From today’s perspective, NPV = 0 if price turns out to be $50.

13. CASE 2:
If delay and price turns out to be $150:
Firm will invest if the price goes to $150.

14. the essence of the option to delay is that it allows the firm to avoid
the “bad” outcome
delay deciding until you see what the state of the world is:
you lose some sales on delay
if the market turns out to be bad, you do not invest
and do not take the loss
does the avoided loss make the foregone sales
worthwhile?
Price = $150
NPV =
NPV = ??
Price = $50
NPV = 0

15. NPV in year 0 of delaying project
= (0.5)(772.73) + (0.5)(0)
= $386.36
the NPV of delaying ($386.36) is more than the NPV of
starting immediately ($300)
therefore, firm should delay start of project
the flexibility of being able to wait another year to decide
whether to invest or not is worth an additional $86.36
Does this mean that firms should always delay projects?
No, if probability of high price in this example was
90% it would be best to start immediately

16. Option to Abandon
ability to abandon a project if things are not going well is valuable
allows firm to avoid bad outcomes
value of the option to abandon can be calculated in similar
way to option to delay
see example handout