We will derive a two$-$state call option value in this problem. Data: S$0=$ $$150$; X $=$ $$160$; $1+$ r $=1\mathrm{.}10.$ The two possibilities for ST are $$180$ and $$100.$ The portfolio consists of $1$ share of stock and $4$ calls short.

Required:

a$.$ The range of S is $$80$ while that of C is $$20$ across the two states. What is the hedge ratio of the call? $($Round your answer to $2$ decimal places.$)$

b$.$ Calculate the value of a call option on the stock with an exercise price of $$160.($Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective per$-$period rate.$)($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$