We are on $12/31/23.$ You are asked to evaluate the potential LBO of a listed company called M&M$.$ These are some useful information. Listed company called M&M These are some useful information:

Data as of $12/31/23$

EBITDA $($$ million$)20$

Pre$-$LBO Debt $[$to be refinanced$]($$ million$)10$

Current market cap $($$ million$)100$

Excess cash at entry $($$million$)0$

Transactions assumption

LBO Debt $($$ million$)80$

Required IRR for equity investors $20\%$

No dividends can be paid $10$

Assumption about exit

Exit date $30$

EBITDA at exit $($$ million$).50$

Debt at exit $($$ million$)10$

Exit EV $/$ Exit EBITDA $6$x

$1.$ What are the sources and uses of funds if the price paid for the equity is $20\%$ above the current market cap of M&M$?$ What is the IRR for equity investors in that case?

$2.$ What is the highest premium for the equity as a percentage of the current market cap that the LBO sponsors would be willing to pay?

$3.$ Suppose the deal is completed at an equity price of $$140$ million but the exit is expected two years earlier on $12/31/26$ at the conditions described above. What is the IRR for equity investors in that case?