$2.$ A company has a $$100$ par convertible preferred stock with a $12\%$ annual

dividend. Each share of the convertible preferred stock is convertible into $4$

shares of common stock. The current price of the firm's common stock is

$$26\mathrm{.}00$ and the current price of the convertible stock is $$110\mathrm{.}00.$

a$.$ What is the value of the preferred stock in terms of common stock?

b$.$ What is the premium over the preferred stock's value as common stock?

c$.$ Assume that the preferred stock is perpetual and comparable preferred

stock offers a dividend yield of $11\%,$ would would the minimum price of this

stock be if it was not convertible?

d$.$ If the price of the common stock rose to $$32,$ by how much would you

expect the preferred stock to increase in value?