Your dream finally comes true! You opened your coffee shop at HKMU bookstore. It is a very popular area, and many students come by and buy your brewed coffee. You price each cup at $$25,$ and estimate it to have a variable cost at $$10$ per cup. You project that there will be $100$ cups sold on a day, and you only open $30$ days a month $($to give yourself a day of rest$).$ The initial investment is about $$250,000.$ You hope that this business can last at least five years and therefore, expected salvage value will be around $$50,000$ at the end of Year $5.$ Working capital needed is about $$400,000$ and shall release the same amount at the end of Year $5.$ Hong Kong$$s tax rate is one of the best in the world, at $16\%.$ Your alternate use of your initial capital shall generate about $15\%,$ which you will use as your cost of your capital.

a$.$ Build a simple pro forma business budget to show the free cash flow for each of the five years. $(14$ marks$)$

b$.$ Calculate the Net Present Value $($NPV$)$ of the business, Internal Rate of Return $($IRR$)$ and Payback $($PB$)$ period. $(6$ marks$)$