To start up a business its founders must invest as follows:

Year : $01234$

Investment: $$4,000,800$ $$2,000,400$ $$1,000,200$ $$500,100$ $$250,050$

Following the times when you are investing, the business is projected to make positive cash flows. For year $5,$ the cash inflow is expected to be $$16,300$ and this is expected to triple each year ending with the cash flow that occurs at year $10.$ In year $11$ and into the future, the cash flows are expected to grow at a rate of $2\%$ per year $($and continuing in perpetuity$).$

c$)$ Suppose the owners of the business do a public offering of the business on the stock market at the end of year $4($just after the last investment cash flow$)$ and the market has the same expectations of future cash flows $($as stated above for years $5$ onward$).$

i$)$ What will be the market price of the business when it goes public $($at year $4)?$

ii$)$ What would be the present value of this amount discounted back to year $0?$

iii$)$ What does this imply about the economic profit expected to be received by the people who buy the stock in the public offering?