Consider a 4-month American put option on a dividend paying stock when the stock price is $40, the exercise price is $50, and the continuously compounded risk-free rate of interest is 12% per annum. The volatility is 30% per annum and a dividend of $3 is expected in 2.5 months. Using a four-step binomial tree, calculate the value of the option. Also, show on the tree when it would be optimal to exercise the option beforeits maturity.