You are attempting to value a call option with an exercise price

of $$108$ and one year to expiration. The underlying stock pays no

dividends, its current price is $$108,$ and you believe it has a $50\%$

chance of increasing to $$145$ and a $50\%$ chance of decreasing to $$71.$

The risk$-$free rate of interest is $9\%.$ Calculate the call option's

value using the two$-$state stock price model.$$