$5.$ 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$).$

a$)$ If the risk of the business implies an appropriate discount rate of $17\%$ per year, what is the economic profit generated by this business venture $($i$.$e$.,$ what is the NPV of starting this business$)?$

b$)$ What is the present value of the investment in the business $($just the investing cash flows, which are the cash flows from year $0$ to year $4)?$ Show how this can be calculated with the PV growing annuity equation using the year $0$ cash flow as the first cash flow of the growing annuity $($show the equation with the numbers in it $$ use Word$$s equation editor in a professional manner with the appropriate numbers in it$).$

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?

iv$)$ What does this imply about the economic profit expected to be received by the original founders of the business? In answering this, use the result from parts c$.$i$,$ c$.$ii$,$ and b$.$ Compare this result to your answer in part a$.$

d$)$ What is the IRR of this business? Hint, you may want to set up the first $10$ years of cash flows on a spreadsheet and then bring in the growing perpetuity formula to handle the cash flows from year $11$ onward. Make sure all discounting references one rate cell. Then you can use Goal Seek or Solver to determine the IRR by solving for NPV $=0$ by changing the rate. $($Please use a clear high$-$resolution screen capture printout to show the setup of Goal Seek or Solver and the result following running Solver.$)$

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