Consider a convertible bond as follows:

par value $=$ $$1,000$;

coupon rate $=9\mathrm{.}5\%$

market price of convertible bond $=$ $$1,000$

conversion ratio $=37\mathrm{.}383$

estimated straight value of bond $=$ $$510$

yield to maturity of straight bond $=18\mathrm{.}7\%$

If the price of the common stock increases from $$23$ to $$46.$

$1)$ What will be the approximate return realized from investing in the convertible bond? $($Note: approximate the realized return by assuming the bond will be converted at $$46.)(5$ points$)$

$2)$ What would be the return realized if $$23$ had been invested in the common stock and the stock price increased to $$46?(5$ points$)$

$3)$ Why would the return on investing in the common stock directly be higher than investing in the convertible bond? $(5$ points$)$