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QUESTION $4$

The current stock price of Gagah Enterprise is $$60$ per share. There are call options

available for this stock that allow the holder to acquire one share for $$50.$ These options

will expire in one year, at which point Gagah's stock will be available for purchase at one

of two prices: $$45$ or $$70.$ The risk$-$free rate is now around $7\%.$ The following duties have

been assigned to you as an assistant to the firm's treasurer in order to$|$determine the

value of the firm's call options.

a$)$ Compute the range of possible values for the closing stock price and the call

option at the option's one$-$year expiration.

b$)$ Equalize the range of payoffs for the stock and the option by buying $0\mathrm{.}8$ share

and selling one option.

c$)$ Create a riskless hedged investment by buying $0\mathrm{.}8$ share and selling one call

option.

Determine the value of the portfolio in $1$ year.

d$)$ Calculate the cost of the stock in the riskless portfolio.

e$)$ Calculate the present value of the riskless portfolio.

f$)$ From your answers in parts $d$ and e$,$ what is the value of the firm's call option.