You are evaluating a potential $$50$ million investment that will generate

estimated operating cash flows of $$10\mathrm{.}6$ million per year for the next $10$ years.

The final $($i$.$e$.,10$th$)$ year will also include a $$0\mathrm{.}5$ million recapture of net working

capital and net proceeds of $$1\mathrm{.}2$ million from a fixed asset sale. The project cost

of capital is $15\%.$ You further estimate that if things go well in the first four years

of the project that you will have the option to invest an additional $$8$ million at

the end of the fourth year to increase the remaining six years of annual operating

cash flows by $20\%.$ Assume the recapture of working capital and asset salvage

value are not affected by this expansion. If the predicted volatility of returns to

the project is $42\%,$ and the risk$-$free rate is $5\%,$ what is the NPV of the proposed

project including the option to expand? Use the Black$-$Scholes calculator to solve

this problem.