Consider an investment with the following cash flows:

$\backslash$table$[[$First cost$,$$$1$ million$],[$Year $1,$$$1$ million$],[$Year $2,$$$1\mathrm{.}1$ million$],[$Year $3,$$$1\mathrm{.}3$ million$],[$Year $4,$$$1$ million$],[$Year $5,$$$3\mathrm{.}7$ million$]]$

$($a$)$ What's the maximum nurnber of IRRs for this cash flow.

$($b$)$ Find all rates of return between $0\%$ and $100\%.$ Hint: One way to do that is to plot the present worth of the cash flows as a function of the interest rate and change your guess when invoking the Excel IRR function. Attach a screenshot with the values of the PW as a function of the interest rate and the graph you generate. Solution: $5\mathrm{.}07\%$ and $82\mathrm{.}43\%.$

$($b$)$ Now determine what happens to the rate of return if the payment in year $5$ is $-$$$5\mathrm{.}7$ million. For what interest rates is this investment economically viable? Explain.