Question $1.(20$ points$)$ Calculate the initial cost of a warrant based on the following information.

You are buying a bond that has $25$ warrants attached to it$.$ The bond carries a coupon rate of $\backslash (3\mathrm{.}5\backslash \%\backslash ),$ has $7$ years before maturity, with $\backslash (\backslash$$ $1000\backslash )$ par value, and is sold for $\backslash (\backslash$$ $1000\backslash ),$ at the time when the going rate of interest is $\backslash (5\backslash \%\backslash ).$ Each warrant allows you to buy one share of the stock of the company at a price of $\backslash (\backslash$$ $20\backslash )$ per share five years from now. The current stock price is $\backslash (\backslash$$ $15\backslash ).$

$1$a$).$ Explain in your own wording your understanding of this warrant in terms of its potential benefit to you.

$1$b$).$ What does the warrant do for you as the bondholder in this example, if you exercise it$?$

$1$c$).$ Calculate the intrinsic value of the warrant.

$1$d$).$ Suppose the stock price will rise in the market at a constant rate of $\backslash (12\backslash \%\backslash )$ per year. Would it be beneficial to you $5$ years from now to exercise the warrant?

$1$e$).$ Calculate the net benefit to you for having this warrant $($show your net gain per share of common stock$).$