1. Chapter 32 Valuing Flexibility Instructors:
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Chapter 32
Valuing Flexibility

2. Valuation Using Real Options
Decision Tree Analysis (DTA)
A simple method to evaluate uncertainty is to build a decision tree. Each branch represents a critical uncertainty. To value the entire tree as of today, each branch must be probability weighted and discounted to today’s value.
Real Option Valuation (ROV)
If the project contains substantial market risk (i.e. beta greater than zero), decision trees will be biased upwards because they underestimate the cost of capital. Replicating portfolios allow us to value the option accurately.
An Exploration of Risk
A number of factors, such as market risk, can affect the valuation process. We will explore situations in which it may be more appropriate to use one of either the Decision Tree Analysis or Real Option Valuation.
Slides 3-9
Part 1
Slides 11-14
Part 2
Slide 16-23
Part 3
LAN-ZWB ZWB

3. Decision Tree Analysis (DTA)
Your company has developed a new serotonin stimulant which could potentially treat anxiety, depression, and obesity. Development of the product is expected to cost $350 million.
Merck has offered to license the product from our company. If the product can be incorporated broadly, Merck has agreed to pay $25 million in after-tax cash flows per year every year forever. If it can only use the compound in niche products, it will generate $5 million in after-tax cash flows per year forever.
Assume the probability of wide use is 50%, the risk free rate is 5%, and the cost of capital for Merck is 15%.
What is the expected ROIC and NPV of the new investment?
Since beta is zero (only technical risk exists), the appropriate cost of capital is 5%. The present value equals $300 million:
= [ (.5)(150)+(.5)(0) ] / (1.05) = $300
Since the present value is less than initial investment ($350), the project should be turned down.

4. Product Testing
What if you had the ability to test the product’s potential over the next year before making the investment? What would the net present value be after the test is completed?
Value with Positive Results
Value with Negative Results
The NPV of a positive test equals $150 million ($25/.05 - $350). The NPV of a negative test equals $0 (since $100 minus $350 < 0).

5. Building a Decision Tree
What if you had the ability to test the product’s potential over the next year before making the investment? What is the present value of the test before the test is completed?
Good Results
Value Today?
Test
To value the project today, probability weight each branch at 50%. The present value equals $71.4 million:
= [ (.5)(150)+(.5)(0) ] / (1.05).
We divide by one plus the cost of capital because of the lost year in testing.
Bad Results

6. Valuing the Test Itself
If this test costs $60 million and delays a full product launch by a year, should we perform the test?
Because the option (test) costs $60 million, the option value is $ $60 = $11.4 million.

7. Why the Difference in Values?
Note that the ‘standard’ NPV is the maximum, decided today, of the expected discounted cash flows or zero:
The contingent NPV is the expected value of the maximums, decided when information arrives, in each future state of nature, or zero:
Real options are most valuable whenever you face a decision that is costly to reverse, such as a large initial investment (i.e. sunk cost).

8. A Slight Alteration: A Practice Example
One of your scientists has a brilliant idea. With a slight alteration in the compound, you can reduce research and development costs from $350 million to $275 million. Unfortunately, this makes any testing (of the compound) more expensive. The cost of testing will rise from $60 to $85 million.
If both compounds are available, would you change your investment & testing strategy?
The naïve answer is to replicate the earlier DTA tree:
= [ (.5)(225)+(.5)(0) ] / (1.05) = $107.1
Deducting $85 million in cost, the NPV of the option equals $22.1 million, which is higher than the earlier value of $11.4 million.
The correct answer however is to use traditional DCF. By lowering the investment by $75 million, the project’s NPV rises to $25 million, which is higher than either of the testing options.

9. Valuation Using Real Options
Decision Tree Analysis (DTA)
A simple method to evaluate uncertainty is to build a decision tree. Each branch represents a critical uncertainty. To value the entire tree as of today, each branch must be probability weighted and discounted to today’s value.
Real Option Valuation (ROV)
If the project contains substantial market risk (i.e. beta greater than zero), decision trees will be biased upwards because they underestimate the cost of capital. Replicating portfolios allow us to value the option accurately.
An Exploration of Risk
A number of factors, such as market risk, can affect the valuation process. We will explore situations in which it may be more appropriate to use one of either the Decision Tree Analysis or Real Option Valuation.
Slides 3-9
Part 1
Slides 11-14
Part 2
Slide 16-23
Part 3
LAN-ZWB ZWB

10. Using the Tools of Financial Options
Our example looks quite similar to a call option. What were the payout features of this real option?
The most difficult part of real options is distinguishing the underlying asset from the strike price.
In the first example, what is the underlying asset?
What was the strike price?

11. Real Options Valuation (ROV)
In our example, the “underlying asset” was the revenue stream. Let’s value the underlying asset using standard probability and the appropriate cost of capital.
Step 1: Value Underlying Asset
Call Option Payoff
p = 50%
Today’s “value of the market” is $285.7 (remember, the project is delayed by a year):
= [ (.5)(150)+(.5)(0) ] / (1.05) = $285.7
The call payoffs remain $150 in the upstate and $0 in the downstate.
1 - p = 50%

12. Step 2: The Replicating Portfolio
To value the call option, we can not use discounted cash flow, as we do not know the appropriate cost of capital for the option. Therefore, we use replicating portfolios.
Since there are two states of the world, we need two assets to replicate the payoff structure of the call option. As the second asset, we use a risk free bond.
N(500)+B(1.05) = 150
Continuing the same example:
Solving for N and B equals: N = and B =
N(100)+B(1.05) = 0
Value of underlying asset in down state
Value of option payoff in down state

13. Step 3: Valuing the Call Option
Because both have identical payoffs, the value of the real option equals the value of the replicating portfolio.
Today’s value of the replicating portfolio equals N shares of the underlying asset (S) financed by $b in risk free bonds.
Call Option Value = NS + B
When valuing financial options, this relation MUST hold, otherwise arbitrage is available. For instance, let’s say C > NS + B, what could an investor do?
What if a real option was mispriced? Is arbitrage available?
The value of the option equals $71.4 million, the same as with DTA:
= (.375) (285.71) - $35.71 = $71.4

14. Valuation Using Real Options
Decision Tree Analysis (DTA)
A simple method to evaluate uncertainty is to build a decision tree. Each branch represents a critical uncertainty. To value the entire tree as of today, each branch must be probability weighted and discounted to today’s value.
Real Option Valuation (ROV)
If the project contains substantial market risk (i.e. beta greater than zero), decision trees will be biased upwards because they underestimate the cost of capital. Replicating portfolios allow us to value the option accurately.
An Exploration of Risk
A number of factors, such as market risk, can affect the valuation process. We will explore situations in which it may be more appropriate to use one of either the Decision Tree Analysis or Real Option Valuation.
Slides 3-9
Part 1
Slides 11-14
Part 2
Slide 16-23
Part 3
LAN-ZWB ZWB

15. Modeling Market Based Risk
Through this point, we have assumed all risk was technological, i.e.
the primary driver of volatility was technological feasibility – the outcome of research is likely uncorrelated with the economy.
Even long-term cash flows were also uncorrelated to the market, as Cisco was absorbing all market-based risk by paying a level cash flow stream.
But what if your company decides to “play the market.” Then the company takes on both market based risk and technology risk. This change will render decision tree analysis (DTA) as theoretically flawed.

16. Analyzing Market Risk vs. Technological Risk
Your company has developed a new serotonin stimulant which could potentially treat anxiety, depression, and obesity. Development of the product is expected to cost $350 million.
You have decided to market the product yourself. If the economy rebounds, you expect to generate $75 million in after-tax cash flows per year every year forever. If it can only use the compound in niche products, it will generate $15 million in after-tax cash flows per year forever.
Assume the probability of wide use is 50%, the risk free rate is 5%, and the cost of capital for your company is 15%.
What is the expected ROIC and NPV of the new investment?
Since beta is now positive (only technical risk exists), the appropriate cost of capital is 15%. The present value equals $300 million:
= [ (.5)(150)+(.5)(0) ] / (1.05) = $300
Since the present value is less than initial investment ($350), the project should be turned down.

17. Using DTA to Solve for Option Value
What if you had the ability to test the product’s potential over the next year before making the investment? What is the net present value after the test is completed?
Good Results
Value Today?
Test
To value the project today, probability weight each branch at 50%. The present value equals $65.2 million:
= [ (.5)(150)+(.5)(0) ] / (1.15) = $65.2 million
We divide by one plus the cost of capital because of the lost year in testing.
Bad Results 15

18. Using ROV to Solve for Option Value
To value the call option, we can not use discounted cash flow, as we do not know the appropriate cost of capital. Therefore, we use replicating portfolios.
Since there are two states of the world, we need two assets to replicate the payoff structure of the call option. As the second asset, we use a risk free bond.
If the hedge ratio doesn’t change, then why does the option value change?
N(500)+B(1.05) = 150
Solving for N and B equals: N = and B =
Continuing along the same example:
N(100)+B(1.05) = 0

19. Valuing the Call Option
Because they have identical payoffs, the value of the real option equals the value of the replicating portfolio.
Today’s value of the replicating portfolio equals N shares of the underlying asset (S) financed by $B in risk free bonds.
Call Option Value = NS + B
How does this value differ from DTA?
The value of the option equals $62.11 million:
= (.375) (260.87) - $35.71 = $62.11
This is lower than the DTA value, which incorrectly overestimates the value of the option. Note the value of the underlying asset equals $260.87, which is the present value at a 15% cost of capital.

20. The Intuition Behind the Valuation Difference
In the first example, when the only risk was technological, DTA and ROV both led to a value of $71.4 million
When the risk is both market based and technological, then DTA will overstate the valuation of real options that mimic calls. In this case, DTA led to $65.2 million, while ROV was approximately 5% lower at $62.1.
A call option is identical to a levered stock portfolio
Example 2:
Do it ourselves Rf
Example 1:
Merck license
Underlying asset
Call
Option
Standard Deviation

21. When to Use DTAs versus ROV Models
When risk is nondiversifiable and the cost of capital for the underlying asset is greater than the risk free rate, only ROV models provide the correct value.
The real options model, however, requires that the underlying asset be traded, in order to prevent arbitrage.
DTAs have the added benefit of simplicity.
Underlying risk
Diversifiable
Nondiversifiable
Nontraded assets
Decision tree analysis
Decision tree analysis, real options valuation
Available data
Decision tree analysis
Real options valuation
Traded assets

22. Complex Real Option Models