# Stock Values and Options

1. The exercise price on a call option is $30 and the price of the underlying stock is $35. The option will expire in 35 days. The option is currently selling for $5.75.

a. Calculate the option's exercise value?

b. Calculate the value of the premium over and above the exercise value? Why is an investor willing to pay more than the exercise value?

c. Is this an out-of-the money, at-the-money, or in-the-money option? Why?

d. What will happen to the value of the option if the underlying stock price changes to $30? Why?

e. Is this an example of a covered call option or a naked call option? Why?

2. The Marcus Company is evaluating the proposed acquisition of a new machine. The machine's base price is $350,000, and it would cost another $125,000 to modify it for special use. The machine falls into the MACRS 3-year class, and it would be sold after 4 years for $40,000. The machine would require an increase in net working capital of $20,000. The machine would have no effect on revenues, but it is expected to save the firm $170,000 per year for 4 years in before-tax operating costs. . The company's marginal tax rate is 30 percent and its cost of capital is 10 percent.

a. Calculate the cash outflow at time zero.

b. Calculate the net operating cash flows for Years 1, 2, 3, and 4

c. Calculate the non-operating terminal year cash flow.

d. Calculate NPV. Should the machinery be purchased? Why or why not?

3. Company Z's stock trades at $45 a share. The company is contemplating a 3-for-2 stock split. Currently, the company has EPS of $3.00, DPS of $0.50, and 20 million shares of stock outstanding. Assuming that the stock split will have no effect on the total market value of its equity, what will be the company's stock price following the stock split?

a. How many shares of stock will be outstanding after the split?

b. Calculate EPS after the split.

c. Calculate DPS after the split. -

d. Calculate price per share after the split -

e. Calculate price after the split if the PE increases by 2 points (for example, if PE was 10 prior to split, it increases to 12 after the split)

f. Why do companies split their stock? Why might a split cause the P/E to increase?

4. Shown below are exchange rates for several currencies.

US$ per 1 euro US$ per 1 franc Mexican peso per US$1

Spot rate 1.38 1.12 12.9

30-day forward rate 1.36 1.13 13.1

60-day forward rate 1.33 1.18 13.9

a. Is the euro appreciating or depreciating against the U.S. dollar? Explain.

b. Is the Swiss franc appreciating or depreciating against the U.S. dollar? Why?

c. Is the Mexican peso appreciating or depreciating against the U.S. dollar? Why?

d. Using cross-rates, based on the spot rate, how many francs will the euro buy, how many pesos will the franc buy, and how many euro will the peso buy?

Euro Swiss Franc Mexican Peso

Spot rate 1.38 1.12 12.90

Cross-rate: euro- buys francs franc buys peso peso buys euro

e. A U.S. company purchases goods from several foreign companies with payment due in euros, francs, and pesos. Would the company be better off paying now or waiting for 60 days? Why?

5. An investment banker enters into a best efforts arrangement to try and sell 10 million shares of stock at $12 per share for Pierre Imports. The investment banker incurs expenses of $2,000,000 in floating the issue and the company incurs expenses of $1,000,000. The investment banker will receive 8 percent of the proceeds of the offering.

a. If the offering is successful and sells out at the expected price of $12, how much money will the company receive?

b. If the offering is successful and sells out at the expected price of $12, how much money will the investment banker receive?

c. If the offering is partially successful; all shares are sold, but at a price of $10. How much does the company receive?

d If the offering is partially successful; all shares are sold, but at a price of $10. How much does the investment banker receive?

e. Who bears more risk with a best efforts deal, the company or the investment banker? Why?

6. Wesley Corporation is evaluating whether to lease or purchase equipment. Its tax rate is 30 percent. If the company purchases the equipment for $1,500,000 it will depreciate it over 5 years, using straight-line depreciation. If the company enters into a 5-year lease, the lease payment is $350,000 per year, payable at the beginning of each year. If the company purchases the equipment it will borrow from its bank at an interest rate of 10 percent.

a. Calculate the cost of purchasing the equipment.

b. Calculate the cost of leasing the equipment with debt.

c. Calculate the net advantage to leasing. Should the company purchase or lease the equipment?

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#### Solution Preview

Dear student,

All solutions attached with all possible workings and explanations for better understanding.

I have a point to say. For question 5, the investment ...

Textbook: Essentials of Investments. Chapter 16 (1, 2, 5, 6, 7 & 12). Problems on call and put options.

We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? In each of the following questions, you are asked to compare two options with parameters as given. What is the hedge ratio of the put? Verify that the put-call parity relationship is satisfied by your answers. Use the Black-Scholes formula to find the value of a call option on the following stock. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

1.We showed in the text that the value of a call option increases with the volatility of the stock. Is this also true of put option values? Use the put-call parity relationship as well as a numerical example to prove your answer.

2.In each of the following questions, you are asked to compare two options with parameters as given. The risk-free interest rate for all cases should be assumed to be 6%. Assume the stocks on which these options are written pay no dividends.

I.

Put T X s Price of Option

0.5 50 0.20 10

B 0.5 50 0.25 10

Which put option is written on the stock with the lower price?

(1) A

(2) B

(3) Not enough information

II.

Put T X s Price of Option

A 0.5 50 0.2 10

B 0.5 50 0.2 12

Which put option must be written on the stock with the lower price?

a. A

b.B

c. Not enough information

III.

Call S X s Price of Option

A 50 50 0.20 12

B 55 50 0.20 10

Which call option must have the lower time to expiration?

a. A

b. B

c. Not enough information

IV.

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 50 55 12

Which call option is written on the stock with higher volatility?

a. A

b. B

c. Not enough information

Call T X S Price of Option

A 0.5 50 55 10

B 0.5 55 55 7

Which call option is written on the stock with higher volatility?

a. A

b. B

c.Not enough information

5. We will derive a two-state put option value in this problem. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.

1. Show that the range of S is 50 while that of P is 30 across the two states. What is the hedge ratio of the put?

2. Form a portfolio of three shares of stock and five puts. What is the (nonrandom) payoff to this portfolio? What is the present value of the portfolio?

3. Given that the stock currently is selling at 100, show that the value of the put must be 10.91.

6. Calculate the value of a call option on the stock in Problem 5 with an exercise price of 110. Verify that the put-call parity relationship is satisfied by your answers to Problems 5 and 6. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective annual yield.)

7. Use the Black-Scholes formula to find the value of a call option on the following stock:

Time to expiration = 6 months

Standard deviation = 50% per year

Exercise price = $50

Stock price = $50

Interest rate = 10%

12. All else being equal, is a put option on a high beta stock worth more than one on a low beta stock? The firms have identical firm-specific risk.

Please see attached for problem. Thanks.

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