$As$ a start$-up$ business owner, you try your best $to$ focus $on$ your business growth. $In$ the past, you had great support from your family funding. However, $as$ business gets more footings, you need more outside capital $to$ continue the growth. Here $is$ a list $of$ options you can consider:

$1.$ Bank loan $-$ borrowing directly from bank

$2.$ Limited Partnership Fund $(LPF)-$ debt raising from private side

$3.$ Private Fund $(PF)-$ equity capital raising $by$ selling part $of$ your holdings $in$ the company

Each $of$ the above involves some sort $ofexpenses$ your company has $to$ pay $in$ order $to$ attract these capitals. For instance, borrowing from a bank $(bank$ loan$)$ will cost about $7\%$ interest rate. For $LPF,itis$ about $9\%$ interest your company has $to$ pay annually. Lastly, the cost $of$ using a private fund $to$ attract equity capital $is$ about $15\%.$ The family fund$s$ capital was originally considered $to$ focus $on$ the stock market $in$ Hong Kong, which you expect $to$ have about $12\%$ return going forward. Hong Kong has one $of$ the world$s$ best taxation schemes, only charging owners$$ profits $at16\mathrm{.}5\%.$

You work $asan$ owner, and also the CFO $of$ your firm. You were considering three different capital structure $of$ your company:

Case $1$ : Bank loan $20\%,LPF40\%,$ Family Fund $40\%$

Case $2$ : Bank loan $20\%,LPF20\%,PF20\%,$ Family Fund $40\%$

Case $3$ : Bank loan $10\%,LPF30\%,PF40\%,$ Family Fund $20\%$

$a.$ Calculate the cost $of$ capital $in$ each case $(3$ marks$)$

$i.$ before any tax effect consideration.

$ii.$ after tax effect consideration.

$b.$ Illustrate using your findings above $to$ see $if$ borrowing $(insteadof$ selling owners$$ equity $or$ shares$),$ regardless $of$ tax effect, always lowers the cost. $(2$ marks$)$

$c.$ Propose your optimal capital structure given the above situation $(and$ you can use other sources $of$ funding$)$ and explain why your proposed capital structure $is$ your optimal choice.

$(15$ marks$)$