HARDWARE’s industrial engineers are also contemplating the option to expand the size of the factory building five years from now. The limited space on the site means that increasing the size of the building requires adding a second story. This would require spending now on stronger foundations and a stronger structure costing €1 million. The question is whether it is worth spending this sum now to create the expansion option.

The expected cost of adding the second story to the building is C¼6.5 million, and the discount rate for this is 6%. The assumed expected value to the company of building the extra story is the same as the cost of doing so. The following table summarizes the analyst’s views concerning the different possible outcomes for the expansion’s PI five years from now.

The discount rate for these possible values is 14%.

(a) Recompute the spread of the intervals in the table such that the value of the expansion option equals the cost of strengthening the foundations and structure.

(b) What does the recomputed spread tell us about the desirability of investing in the stronger structure?

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Interval Average value Probability 0.00 < x < 0.76 0.38 0.07 0.76 < x < 0.91 0.84 0.24 0.91 x 1.10 1.00 0.38 1.10x1.32 1.21 0.24 1.32 x 1.59 1.45 0.07 1.00