stock is the dividend periodically paid by the company to its shareholders13. In the example
we assume that the payout is a fixed percentage (10%) of the net present value of the
project at the different nodes (in financial terms, this would correspond to the stock price).
At each node the company can either invest 480$ (exercise the option by paying the
strike price) and receive the project NPV14 (one share of the company) plus the period
payout15 (the dividend) or, conversely, it can decide to postpone the beginning of the
investment to the next date (hold the option unexercised). The company decides what to do
after the state of nature has revealed itself (i.e. the company knows how much the net
present value is worth at that date). We suppose that at t3 the business opportunity ceases to
exist and thus t3 represents the last chance the company has to start the project (to exercise
the option).
We can now describe the company decision process, as illustrated in Figure 4. Each
node of the binomial tree is identified by an array of seven numbers. In the first row, we
indicate the business opportunity value and whether it is optimal to undertake the
investment (grey area) or not. In the second row, first column, we represent the NPV of the
project; in the second column, the payout of the project, i.e. the extra revenues and cost
savings, at the current date. In the third row, first column, we show the value of the risk free
security; in the second column, the period project payout. In the third row, first column, we
show the value of the risk free security; in the second column, the state prices of the project
payoff which encompass all future information on the states of the nature. Finally, the
fourth row includes the value of the business opportunity if not exercised (first column) or
exercised (second column): clearly, the value of the option is the greater of the two.
The market formed by the risk-free security and the project allows no arbitrage and it is
dynamically complete. Under no arbitrage a set of state prices exist; due to market
completeness, it is also unique. We can thus price all contingent claims by the no arbitrage.
13 In the case of a NGN deployment the incremental revenues and cost savings (i.e. the investment payout)
corresponds respectively to the extra revenues arising from, say, TV on Internet plus the cost savings - mainly
in terms of less maintenance and provisioning - induced by the replacement of the current copper access with
NGNs.
14 The NPV of the project is equal to the sum of the payouts from the next date to the date the projects ends.
15 The period payout is equal to the difference between the extra revenues and cost savings realised by
investing today and those that would arise by investing one period later.
12