A non-dividend paying stock price is currently selling for $X. It is known that at the end of three months the stock price will be either $3.50 or $5.50. The risk-free rate of interest is 10 percent per annum (quarterly compounding). The value of a three-month European put option on the stock with an exercise price of $5.00 is currently selling for $0.75.

Use a one-period binomial model.

Required

Determine the fair value today of the share (i.e. $X) based on a replicating portfolio constructed by taking a position in shares and a riskless asset or a risk-free bond.