Question $1$

Suppose Sigma Industries and Pi Technology have identical assets that generate identical cash flows. Sigma Industries is an all$-$equity firm, with $7$ million shares outstanding that trade for a price of $ $25\mathrm{.}00$ per share. Pi Technology has $17$ million shares outstanding, as well as debt of $ $52\mathrm{.}50$ million.

a$.$ According to MM Proposition I, what is the stock price for Pi Technology?

b$.$ Suppose Pi Technology stock currently trades for $ $14\mathrm{.}97$ per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity?

Question $2$

Suppose PayPal $($PYPL$)$ has no debt and an equity cost of capital of $9\mathrm{.}1\%.$ The average debt$-$to$-$value ratio for the credit services industry is $15\mathrm{.}2\%.$ What would its cost of equity be if it took on the average amount of debt for its industry at a cost of debt of $5\mathrm{.}6\%?$

Cost of equity is$?$

Question $3$

Indell stock has a current market value of $ $200$ million and a beta of $1\mathrm{.}20.$ Indell currently has risk$-$free debt as well. The firm decides to change its capital structure by issuing $ $55\mathrm{.}32$ million in additional risk$-$free debt, and then using this $ $55\mathrm{.}32$ million plus another $ $15$ million in cash to repurchase stock. With perfect capital markets, what will the beta of Indell stock be after this transaction?

Part $1$

The beta of Indell stock after the recapitalization is $?$