Problem Solving $(35$ marks$)$:

Consider the following information about Firm ABC:

$\backslash$table$[[$Firm ABC Overview$],[$Number of Shares,$100,000,,],[$Price per share,$$10,,],[$Market value of shares,$$1,000,000,,$Boom$],[$Scenarios: State of the Economy$],[,$Slump,Normal,$$175,000],[$Operating Income,$$75,000,$$$125,000,$$$1\mathrm{.}75],[$Earnings per share,$$0\mathrm{.}75,$$$1\mathrm{.}25,17\mathrm{.}5\%],[$Return on shares,$7\mathrm{.}5\%,12\mathrm{.}5\%,]]$

A prospective investor is seeking your advice. Specifically, if they have $$10$ available and can borrow another $$10$ at some interest rate $"r",$ for what value$($s$)$ of $"r"($if any$)$ is the following return profile $,15\%,25\%$ possible?

Note: a return profile means earning a return of $5\%$ in a slump, $15\%$ in normal times, and $25\%$ in a boom period.

You should clearly explain every step in your solution and provide an intuitive conclusion, i$.$e$.,$ one easily understood by a non$-$finance reader.