Use simple decision trees and a $10\%$ per year discount rate to evaluate a project, which has two phases. You may invest in the first, in both or in neither. You may not invest in the second phase without investing in the first.

Phase $1$ requires an investment of $$100.$ One year later the project delivers

either $$160$ or $$60$ with equal probability. At that time, after the phase $1$ payout has been received, you may invest an additional $$100$ for phase $2.$ One year later, phase $2$ pays out either $20\%$ more cash than phase $1$ actually delivered or $($equally likely$)20\%$ less. Assume no taxes.

$$ How much would the project be worth if it offered only the phase $1$ opportunity?

$$ How much would phase $2$ be worth if you had to choose today, once and for all, whether or not to invest in it$?$

$$ How much is the project worth if you have access to both phases and can wait to decide whether to invest in phase $2?$

$$ How would you allocate the value of the project between assets$-$in$-$place and real options?