Investment in Next Generation Networks and the Role of Regulation: A Real Option Approach

model inputs (stock volatility, risk free interest rate, pay out ratio, option lifespan, etc).
Finally, we develop the parallel between a financial option and a business opportunity and
we examine how it works in a discrete time setting.

The example is framed within a discrete multiplicative binomial event tree. Differently
from models in continuous time, such as those by Black and Scholes (1973) and Merton
(1973), a discrete setting helps to clarify the economic principles underlying option pricing.
The logic that lies behind the solution of discrete time problems and that of continuous time
problems is exactly the same: often solutions to continuous time problems are found by
converting them into equivalent discrete settings. The numbers in this example are chosen
to make computations simpler, but nothing of substance is lost.

Let us consider a 3-year time horizon (see Figure 4). At time t=t₁, there are two possible
states of nature (“Up” and “Down”); at t=t₂, there are four possible states of nature (“A”,
“B”, “C” and “D”); finally at t=t₃ there are eight possible states of nature (“1”, “2”, “3”,
“4”, “5”, “6”, “7” and “8”).

Let us suppose that a firm can choose between a risk-free security, worth 1,000$, which
earns 3% per annum, and an investment project which requires a 480$ disbursement, and
whose expected net cash flow are equal to 500$ (again, the numbers are chosen for the sake
of simplicity). The investments opportunity ceases to exist at t₃ i.e. three periods after the
investment opportunity arises.

The firm opportunity to invest can be thought as a call option on a stock whose price
evolves following the same stochastic process as the expected net cash flow. The strike
price, worth 480$, is equal to the up-front disbursement required to implement the
investment and is exogenously given. The financial equivalent of the last date at which the
investment can be carried out (i.e. t₃) is to be considered as the option expiry date.

Let us now look at the cost associated with keeping the investment opportunity at bay
for one period: each year of delay implies less payout (extra revenues and cost savings) to
the company. The equivalent of the opportunity cost in the case of a call option on a quoted

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