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

At t₀ the value of the project, denoted by S, is assumed to be equal to 500$. In the
following period, t₁, following the multiplicative binomial stochastic process, the NPV of
the project can either go up by 60% to St₁=St₀ *(1+0.6) or go down by 20% to St₁=St₀*(1-
0.2). At t₂ the NPV can either go up to St₂=St₁*(1+0.25) or go down to St₂=St₁*(1-0.15).
At t₃ the stock price can either go up to St₃=St₂*(1+0.1) or go down to St₃=St₂*(1-0.1).

Note that in the example the range of the price changes in each node is chosen to make
calculations simple. However it is greater (in absolute value) at the beginning of the project
than at the end (60%, -20% versus ±10%) in order to capture the idea that as information
flows in with time, demand uncertainty falls, and hence the project becomes less risky
while earning a constant return. In fact the payout ratio (i.e. the ratio between the one
period payout and the NPV) is kept constant through all the project lifespan.

How do we compute the values of the option whether it is exercised or not at each node?
If it is exercised, the value of the option, shown in the orange cell (fourth row; second
column), is equal to the sum of the current NPV plus the period payout minus the option
strike price. If it is not exercised, the value of the option, shown in the green cell (fourth
row; first column), is equal to the next period payoffs (associated with adopting the optimal
exercise policy) times the state prices¹⁶. The American call option value, contained in the
blue cell, is equal to the greater between these two values.

What is the intuition? If the option is exercised, i.e. if the investment is made in the
current period, the company will gain the extra revenues and lower costs linked to the
immediate investment (the payout) plus the value of the project in all future periods, as
captured by the NPV. In exchange, the company has to pay the strike price: for instance,
the cost of deploying fibre in the access network. On the other hand, if the option is not
exercised at tn, i.e. the investment has not been yet carried out, its value is a function of the
payoffs at tn+1, associated with the optimal exercise policy across all future states of nature.
In order to compute the value of the option when not exercised, one has to work backwards
through the binomial tree, determining at each node whether or not it is optimal to exercise.

¹⁶ The next period payoffs (associated with adopting the optimal exercise policy) are equal to the value of the
American call option at the next date.

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