A convertible bond is selling for $$1,222\mathrm{.}70.$ It has $10$ years to maturity, a $$1,000$ face value, a coupon rate of $10$ percent, and semiannual interest payments. Similar non$-$convertible bonds are priced to yield $4$ percent per six months. The conversion ratio is $40.$ The stock currently sells for $$30\mathrm{.}13$ per share. Calculate the convertible bond's option value.