Iota Industries is an all$-$equity firm with $50$ million shares outstanding. Iota has $$200$ million in cash and expects future free cash flows of $$75$ million per year. Management plans to use the cash to expand the firm$$s operations, which will in turn increase free cash flows by $12\%.$ Iota$$s cost of capital is $10\%.$ Assume that capital markets are perfect.

$($a$)$ The value of Iota if they use the $$200$ million to expand is closest to:

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$(1)$ $$825$ million

$(2)$ $$688$ million

$(3)$ $$840$ million

$(4)$ $$950$ million

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$($b$)$ The value of Iota if they do not use the $$200$ million to expand and hold the cash instead is closest to:

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$(1)$ $$840$ million

$(2)$ $$825$ million

$(3)$ $$950$ million

$(4)$ $$688$ million

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$($c$)$ The price per share of Iota if they use the $$200$ million to expand is closest to:

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$(1)$ $$13\mathrm{.}75$

$(2)$ $$16\mathrm{.}50$

$(3)$ $$19\mathrm{.}00$

$(4)$ $$16\mathrm{.}80$

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$($d$)$ The price per share of Iota if they do not use the $$200$ million to expand and hold the cash instead is closest to:

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$(1)$ $$16\mathrm{.}50$

$(2)$ $$16\mathrm{.}80$

$(3)$ $$19\mathrm{.}00$

$(4)$ $$13\mathrm{.}75$

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$($e$)$ The NPV of Iota$$s expansion project is closest to:

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$(1)-$$$110$ million

$(2)-$$$137\mathrm{.}5$ million

$(3)$ $$0$

$(4)$ $$75$ million

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$($f$)$ A member of Iota$$s board of directors suggests that Iota$$s stock price would be higher if they used the $$200$ million to repurchase shares instead of funding the expansion. If you were advising the board, what course of action would you recommend, expansion or repurchase? Which provides the higher stock price? Explain.

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$($g$)$ Suppose that Iota is able to invest the $$200$ million in excess cash into a project that will increase future cash flows by $30\%.$ If you were advising the board, what course of action would you recommend, investing the $$200$ million in an expansion project that will raise future free cash flows by $30\%$ or use the $$200$ million to repurchase shares? Which provides the higher stock price? Explain.

$($a$)$ The price of a share of JRN$$s stock is closest to:

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$(1)$ $$20\mathrm{.}00$

$(2)$ $$24\mathrm{.}00$

$(3)$ $$25\mathrm{.}00$

$(4)$ $$18\mathrm{.}00$

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$($b$)$ Assume that management makes a surprise announcement that JRN will no longer pay dividends but will use the cash to repurchase stock instead. The price of a share of JRN$$s stock is now closest to:

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$(1)$ $$20\mathrm{.}00$

$(2)$ $$25\mathrm{.}00$

$(3)$ $$18\mathrm{.}00$

$(4)$ $$24\mathrm{.}00$

$$

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$(1)$ $$4\mathrm{.}50$

$(2)$ $$5\mathrm{.}00$

$(3)$ $$4\mathrm{.}00$

$(4)$ $$9\mathrm{.}00$