Assume a two$-$period world, perfect certainty, and perfect capital market. A firm has an initial endowment of $$115$ million. The firm has identified the following available investment opportunities:

Proposal

Period$-0$ Outlay

Period$-1$ Return

M

$$19\mathrm{.}31$ million

$$21\mathrm{.}95$ million

N

$$30\mathrm{.}94$ million

$$40\mathrm{.}07$ million

Q

$$25\mathrm{.}00$ million

$$28\mathrm{.}45$ million

R

$$20\mathrm{.}86$ million

$$24\mathrm{.}13$ million

S

$$14\mathrm{.}91$ million

$$16\mathrm{.}01$ million

These are not divisible projects, which cannot be invested in a fraction $($the firm must invest $100$ percent of each proposal or none of it$).$ Assume that the average market rate of return is $13\mathrm{.}80$ percent.

Which projects will the firm undertake to maximise the value of the firm?

If the firm undertakes projects that will maximise the value of the firm, how much money will it invest in period $0($now$)?$

Does the firm need borrowing in period $0?$ If yes, how much? Why?

What period$-0$ dividend will be paid to shareholders $($owners$)?$

What will the period$-1($next$)$ dividend be$?$

What is the Present Value $($PV$)$ of period$-1$ returns from optimum investment in $($ii$)?$

What is the Net Present Value $($NPV$)$ from optimum investment in $($ii$)?$

How will the value of the firm change due to the decision of optimum investment in $($ii$)?$

How would your answers from $($i$)$ to $($viii$)$ above change if the firm had an initial endowment of $$31$ million