Consider a European put option on a stock, with a $50 strike and 1-year to expiration. The stock has a continuous dividend yield of 6%, and its current price is $46. Suppose the volatility of the stock is 22%. The continuously compounded risk-free interest rate is 8%. Use a two-period lognormal tree to calculate the following: (a) The payoff at time 2: Up movement. (b) The payoff at time 2: Middle movement. (c) The payoff at time 2: Down movement. (d) The payoff at time 1: Up movement. (e) The payoff at time 1: Down movement. (f) The option cost at time 0.