Katie owns 1000 shares of the company whose shares are now priced at $100.00 each. Katie is worried that the price of a share of may in one year be a good bit less than it is today, but she does not want to sell her shares. Katie is comfortable with a loss of 5%, but no more. To offset the cost of buying puts with strike 95 Katie decides to sell calls with strike 115, thereby conceding any gain above 15%. Assume the following:

(a.) the Black-Scholes context is applicable, (b.) the continuously compounded risk free rate is .04, (c.) pays continuous dividends at the rate of 1%, (d.) the volatility of is .40.

Determine each of the following: (u.) sketch the payoff graph for Katie's position consisting of shares, long puts, and short calls

(v.) the cost of a 1-year call on with strike 115,

(w.) the cost of a 1-year put on with strike 95? (x.) the total cost for the options that Katie will buy ( and sell )? (y.) what is Katie's profit at expiration if rises to 112? (z.) what is Katie's profit at expiration if drops to 80?

Note: profit with respect current time meaning profit relative to value at the time the options are purchased. The option position is a collar.