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 of $$expenses$$ 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$,$ it is 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 at $16\mathrm{.}5\%.$

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

Case $1$ Case $2$ Case $3$

Bank loan $20\%20\%10\%$

LPF

$40\%20\%30\%$

PF $20\%40\%$

Family Fund $40\%40\%20\%$

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 $($instead of 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$)$