*3.2. Economical Model*

All the used figures were elaborated in accordance with a proposed scenario as in Table 1 below, where the real figures can be introduced according to the data of each project (all prices are given in millions of US\$):



We apply here the technique of real option valuation, as illustrated in Brealey et al. [40] (p. 584), where we have replaced:


We have therefore calculated, at first, the call value, based on the annual StD estimation of 0.031, as 57.05 million \$US. This StD estimation of 0.031 is based on the data of the Electric Power Monthly report of the U.S. Energy Information Administration (EIA), Table 5.3 "Average Retail Price of Electricity to Ultimate Customers" [41].

Our assumption of the first unit's building cost is equal, as mentioned above, to 50 million \$US, where such high expenses of the first turbine's launching include, among others, research and development to adapt the turbine to the specific area under consideration and the cost of connecting it to the power grid, subtracted by the profit from operation.

We stress that the current work is based on assumed values, and, in this sense, it is an exercise in applying the real option technique. Future work will depend on a more realistic estimation of both the investment costs in infrastructure and current energy prices.

Hence, the results indicate that the investment in the first turbine stage is warranted, and the fact that there is the option to follow-on adds significant value to the investment. It follows that the net profit of the first stage is 57.05 − 50 = 7.05 million \$US for the standard deviation value of 0.031, according to the following data of Table 2 (in a column for the case of StD = 0.031), which includes the intermediate values and the option to follow-on:


**Table 2.** Intermediate and output data for the Black–Scholes option value.

For comparison with a scenario lacking an option to abandon, the project value is estimated as the present discounted value of a difference between (i.e., the earnings from) the future cash flow raised from the second stage realization subtracted by the second stage building cost, which is subtracted additionally by the first stage building cost.

Applying to our numerical example, this yields just the negative benefit, meaning merely loss, of the (114.7 <sup>−</sup> 60)/1.06<sup>2</sup> <sup>−</sup> 50 = <sup>−</sup>1.3 million \$US.

However, using StD of 0.031 yields a profit of 7.05 million \$US, as was calculated above. This is so because one can make a choice to abandon the project while it is still underway. This is the economic meaning of the real option.
