Consider a $9-$month zero coupon bond issued by company XYZ with a face value of

$$100.$ Suppose that it can be exchanged for $2$ shares of company XYZ$\text{'}$s stock at any time

during the $9$ months. Assume also that it is callable for $113$ at any time. The initial stock

price is $$50,$ its volatility is $35\%$ per annum, there are no dividends and risk$-$free rates for

all maturities are $5\%.$ What is the value of this convertible bond?