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?