$1.$ Answer the following short questions.

a$.$ Goose Industries does not currently pay a dividend. You expect the company to begin paying a $$10$ dividend $10$ years from now and you expect dividends to grow perpetually at $9\%$ thereafter. Goose has a beta of $1\mathrm{.}8.$ The expected return on the market is $10\%$ and the riskless rate is $5\%.$ How much is the stock currently worth? $(5\%)$

b$.$ You have sold short $100$ shares of Topley Industries at $$50$ per share. Just as you anticipated, the price falls and you cover your short position $($i$.$e$.$ repurchase the shares$)$ when the price hits $$42$ per share three months later. The company paid $$1$ per share in dividends over this period. What is your annualized rate of return on this investment? Assume an initial margin requirement of $60\%.(5\%)$

The following information pertains to parts c and d$.$

You have purchased $100$ shares of VF Technologies at $$100$ per share and borrowed as much as possible. The IMR is $60\%$ and the MMR is $30\%.$

c$.$ If the price rises to $$120$ in one year, what is the $\%$ return on your investment? Note that the company pays no dividends. $(5\%)$

d At what price are you subject to a margin call? $(5\%)$