Question $3$: $(25$ points$)$

Consider a bond with a $(4\%)$ coupon, $($ $ $1000)$ par value, and $15$ years in maturity, that is issued and sold for $($ $ $1000).$ It is callable after $7$ years by the company. The bond is a convertible bond allowing the investor to exchange the bond for $40$ shares of common stock in the future.

The current stock price is $($ $ $20).$ The stock has a dividend yield of $(2\%)$ and growth rate of $(6\%)$ per year.

The current rate of interest, it is $(5\%).$

If the company decides to call back the bond at the end of the $7$th year, and give you $($ $ $1040)$ in cash, what would you do$?$ Take $($ $ $1040),$ or convert the bond? Show your calculations to prove your answer.