P$12\mathrm{.}13$ Convertible Bonds with an Observable Price: A company issues $$1$ million of $$1,000$ face value convertible bonds with a $6\%$ annual coupon payment. The bonds mature in $5$ years. Each bond is convertible into $200$ shares of the company's stock at the end of the $5$ years. If the company had straight debt outstanding, it would have a yield to maturity and a cost of capital of $9\%.$ The bonds were issued today at $$1,200.$ The company has $1$ million shares of stock outstanding, and its stock is trading at $$4\mathrm{.}50$ per share. Its common equity cost of capital is $15\%,$ the standard deviation of its annual stock return is $60\%,$ its continuously compounded dividend yield is $4\mathrm{.}75\%,$ and the risk$-$free rate is $3\mathrm{.}25\%.$ This is the only financing the company uses to finance the company. Calculate the value of the conversion feature of these bonds on a per convertible share value and calculate the cost of capital for this conversion feature and for the convertible bond. The income tax rate is $40\%.$