# Call/Put Options, Net Present Value, Put-call parity

1. Applied Materials' long-term call options with a maturity of two years and an exercise price of $30 are selling for $3. AMAT's current stock price is $20 and it not expected to pay a cash dividend over the next two years. Assume an annual risk-free rate of 1.5 percent.

(a) Is the call option in or out of the money?

(b) What would be the value of an AMAT put with the same maturity and exercise price?

(c) Is the put in or out of the money?

(d) What is the implied volatility of AMAT? [Use the Black-Scholes spreadsheet model I sent you to answer this - it should take only a couple of minutes if you followed what was going on with that model. Attach a printout of the results.]

2. Your college buddy, Bags Blackwell, is an entrepreneur. He imports and makes stuff sold in "bargain" stores. He has just "invented" Softerskin, a lotion he claims enhances skin softness and reduces wrinkles. He is thinking about getting into that business and selling the product through bargain stores. Market research (Bag's best guesses) has indicated that there is an equal likelihood that sales will be high (500,000 units/year) or low (100,000units/year) at a wholesale (fob plant) price of $2.30/bottle, so that the expected sales are 300,000 units per year. Raw materials, plastic bottles with painted labels, and other variable operating costs are $1.00 per bottle, resulting in a margin of $1.30/bottle and expected annual profit margin of $390,000. The level of market acceptance will be known only after one year of sales. The initial investment required to set up manufacturing/packaging facilities and launch the product is $3 million. If necessary and appropriate, the product can be abandoned and the facilities sold for $1.5 million after one year. The cost of capital in the health and beauty industry is 10 percent and the risk-free rate is 5 percent. Sales beyond 10 years are assumed zero. Assume zero income taxes.

(a) Taking Bag's "research" and cost estimates at face value, would you recommend he enter the business? If so why so; if not, why not? [Be sure to specify the expected net present value of the decision to enter the business as part of your answer?]

(b) If abandoned facilities could be sold for only $500,000 after one year, would that change your recommendation? If so, why so; if not, why not?

3. "You are scheduled to retire two years from today. Over the past several years you have been awarded stock options that are well "in the money" today but they cannot be exercised until the day you retire. We understand you are considering several post-retirement options and would like some "peace-of-mind" so that, when retirement day comes, you are assured you will have the funds you need to pursue those "other interests." We have a plan that permits you to 'lock in' the value of the options you own without incurring a cost today. Call us for further details."

Suppose you work for the brokerage firm that sent out the above paragraph to several soon-to-retire folks. The idea is that you will get the pre-retiree to simultaneously purchase put options and sell call options on the stock of the company. The proceeds from selling the calls equals the cost of the puts - hence, no cost today. Assume there is no perception problem with employees selling puts on the company for which they work.

Further suppose the underlying stock is currently selling for $100/share and the target retiree has options on 100,000 shares at an exercise price of $20/share. The company is expected to pay no dividends. The time value of money is 5%. Ignore transaction costs (transmission expenses).

(a) Using the put-call parity theorem, at what exercise price could calls be sold and puts be purchased so that the premium (price) of the calls sold equal the premium (price) of the puts bought?

(b) If the standard deviation of the return on the stock of the company is 40 percent per annum, according to Black-Scholes, what would be the premium (price) of a single put or call? [Use the Black-Scholes spreadsheet model I sent you to answer this - it should take only a couple of minutes if you followed what was going on with that model. Attach a printout of the results.]

(c) Draw the diagram that clearly shows net profit (ending wealth) for the target retiree as a function of the stock price on retirement day associated with the original stock option and the two options from (a). ]

(Questions and more info in attachments)

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#### Solution Summary

Answers to 3 questions

1) Value of call and put options-in or out of money, implied volatility of options

2) Net Present value of an investment

3) Put-call parity, Exercise price, Black Scholes

Option and Warrants Part 1

4 Questions for you to familiarize with option and warrants, especially the Call/Put Parity, formula and relations.

Question 1

Pintail's stock price is currently $200. A one-year American call option has an exercise price of $50 and is priced at $75. How would you take advantage of this great opportunity? Now suppose the option is a European call. What would you do?

Question 2

In June 2001 a six-month call on Intel stock, with an exercise price of $22.50, sold for $12.30. The stock price was $27.27. The risk-free interest rate was 3.9 percent. How much would you be willing to pay for a put on Intel stock with the same maturity and exercise price?

Question 3

Suppose that Mr. Colleoni borrows the present value of $100, buys a six-month put

option on stock Y with an exercise price of $150, and sells a six-month put option on Y with an exercise price of $50. Suggest two other combinations of loans, options and the underlying stock that would give Mr. Colleoni the same payoffs.

Question 4

a.) If you can't sell a share short, you can achieve exactly the same final payoff by a combination of options and borrowing or lending. What is this combination?

b.) Now work out the mixture of stock and options that gives the same final

payoff as a risk-free loan.