For part b, how to we get the value of 3.1111? I dont understand why the payoffs are 3.1111 x the payoffs in (a). Please explain in details.

Eagleton's current stock price is $10. Suppose that over the current year, the stock price will either increase by 95% or decrease by 45%. Also, the risk-free rate is 25% (EAR) a. What is the value today of a one-year at-the-money European put option on Eagletron stock? b. What is the value today of a one-year European put option on Eagletron stock with a strike price of $19.50? c. Suppose the put options in parts (a) and (b) could either be exercised immediately, or in one year. What would their values be in this case? a. What is the value today of a one-year at-the-money European put option on Eagletron stock? In one year, the stock price will either increase to S $19.50 or decrease to Sd $5.50, meanwhile, the put option will be worth Cy $0 or Cd $4.50, respectively. To compute the delta of the option, use the following formula: Cu-Cd where ? is the sensitivity of option price to stock price, Cu is the put option value if the stock prices goes up, Cd is the put option value if the stock prices goes down, Su is the stock price after the increase, and Sd is the stock price after the decrease. Therefore, $O $4.50 $19.50-$5.50 =-0.3214 The delta of the option is 0.3214. fA