Question $1(20$ points$)$

a$.$ A company will generate $$10$ in earnings per share this year $($at time $1)$ and will pay it all in

dividends. Shareholders require an expected return of $12\mathrm{.}5\%$ per year. If the company expects to

generate the same earnings each year forever and will keep paying them out to shareholders,

then what is the price per share? Express final answer to the nearest penny.

b$.$ Suppose the company's financial manager decides to take on a new project, which will allow

the company to increase its future earnings by $8\%$ per year forever $($earnings per share at time $1$

is still $$10).$ To start up and maintain the project, the company will need to reinvest $80\%$ of its

earnings in each of the first three years $($i$.$e$.,$ at time $1,2,$ and $3)$ and plowback $50\%$ of its earnings

in the fourth year $($i$.$e$.$ at time $4).$ Then, boginning at time $5,$ the plowback ratio will be set at $20\%$

and is expected to remain constant forever. What is the per share price of the company now?

Express final answer to the nearest penny.

c$.$ What is the present value of growth opportunities of the company under the new project?

Express final answer to the nearest penny.