Question $3(20$ points$)$

A company is considering whether to start a large project. It will cost the company $$20$ billion

in year $0,$ and generate profits of $$10$ billion and $$13$ billion in years $1$ and $2,$ respectively.

The risk$-$free rates in years $0$ and $1$ are the same, $2$ percent, and the expected market returns

in years $0$ and $1$ are also the same, $6$ percent. The company's $$ is a constant $0\mathrm{.}75.$ Use the

discretely compound rate to calculate results.

a$)$ Given the above information, should the company start the project? $(5$ points$)$

b$)$ Suppose the company has an option to pay a maintenance $$5$ billion in year $1$ to raise its

profit by $$5\mathrm{.}26$ in year $2.$ Should the company take the option in year $1?(5$ points$)$

c$)$ Following the setting of part $b.$ Suppose the monetary authority raises the risk$-$free in year

$1$ to $3$ percent, should the company start the project and$/$or take the maintenance option in

year $1?(10$ points$)$