Real Options Theory

Source: Copeland, T., T. Koller, and J. Murrin, 2000 Figure 2.7 Six Driving Variables for valuing ROA 2.5.2 Two Kinds of Real Options: Call and Put

A description for two kinds of real options can be seen here. Copeland and Antikarov states that a call option is the right to buy the underlying asset by paying the exercise price (Copeland, T. & Antikarov, V., 2003). At the time of exercise, the profit on the option is the difference between the value of the underlying asset and the exercise price.

But a put option is said as the opposite of the call option, thus it is the right to sell the underlying asset to receive the exercise price. Usually, one who has options is called as holder instead of either buyer or seller.

And one who receive obligation when option is exercised is acceptor.

Options that can be exercised only on their maturity date are called European options and exercise frequency is only one time. On the other hand, American Options are those that can be exercised at any time during the life of options and can be exercised at only time. The exercise price is the price that seller and holder have agreed to be exercised on the option. Next, the exercise date is the date on which the seller and buyer

Expected Present Value of Cash Flows from Investment

Uncertainty (Volatility) about the Present Value

1

An increase in the present value of the present of the project will increase the NPV without flexibility thus, the ROA will also increase.

4

In an environment with managerial flexibility, an increase in uncertainty will increase ROA

Exercise Price/Investment Cost Risk-free Interest Rate

2 A higher investment cost will reduce

NPV and thus, reduce ROA 5

An increase in risk-free rate will increase ROA since it will increase the time value of money advantage in deferring the investment cost.

Time to Expire Cash Flows (Dividends) Lost due to

Competitors who have Fully Committed

3

A longer time to expiration will allow the managers to learn more about the uncertainty and thus, it will increase ROA.

6 Increasing cash flows lost to competitors will clearly decrease ROA.

have agreed to be exercised on the option. Summary information of the call and put options are shown in Table 2.7.

Table 2.7 Summary Information of the Call Options and Put Options Options Kinds of

Options Exercise Timing Holder Acceptor Exercise Frequency

Call Option

European Only on maturity

date Right to BUY

asset

Obligation to SELL asset if the option is exercised

Just one time American On or before the

maturity

Put Option

European Only on maturity

date Right to SELL

asset

Obligation to BUY asset if the option is exercised

American On or before the maturity

Source: Author

2.5.3 Common Types of Real Options

Real options are classified primarily by the type of flexibility that they offer. The brief description of basic options, their effectiveness and option type are illustrated in Table 2.8.

2.5.4 Real Options Analysis (ROA) Rule and Formula

ROA takes the different perspective from NPV rule. Mathematically, ROA for call option is an expectation of maximums, not a maximum of expectations (Copeland, T. & Antikarov, V., 2003):

ROA rule for call option: E0 MAX (at t= T) [0, VT – X] (2 – 3) From a call option aspect, a project is undertaken, at a future time, if and only if VT > X. Conversely, ROA for put option is an expectation of maximum, not a maximum of expectations, if and only if VT < X:

ROA rule for put option: E0 MAX (at t= T) [0, X – VT] (2 – 4)

Table 2.8 Basic Options, Effectiveness and Option Type

Options Effectiveness Kind of Option

The option to abandon

(Abandonment option) Dispose or terminate of an unprofitable project American Put The option to shrink

(option to contract)

Reduce the size or capacity by selling a fraction of the

project depending on market conditions American Put The option to wait

(Deferral option) Wait until further information reduces uncertainties. American Call The option to scale up

(Expanding option) Expand the project capacity or scaling up the project

operations depending on the market situations American Call The option to switch

(Switching options)

Allows the owners to switch at a fixed cost between two modes of operation: switch on/open or switch off/shut down the project.

American Call and Put Growth option

(Learning option)

Create and acquire the related future opportunities of the

project. American Call

Compound options including rainbow and compound rainbow options

Option on another option to take the project to next level of the project phases based on multiple sources of uncertainties.

American Call

Source: Copeland, T. & Antikarov, V., 2003

For the real options method, the binomial model is formulated as follows:

(2 – 5)

where, C0 = current option value p = risk-neutral probabilities Cu = call value in up state Cd = call value in down state 𝑟_! = risk-free interest rate

0

[ (1 ) ]

1

u d

f

pC p C

C r

+

-= +

Risk-neutral probabilities can be calculated as:

(2 – 6)

where, u = up movement d = down movement

Strategic initiatives can no longer be looked at as stand-alone investments, but rather as links in a chain of interrelated, staged investment decisions. Moreover, if a firm’s investment decisions are contingent upon and sensitive to competitor’s moves, a more involved game-theoretic treatment might be necessary.

Appropriate competitive strategies can still be analyzed using an integration of game theory with real options analysis.