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Stocks, Bonds, Futures, and Options

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1. Why most of the largest stock market declines have occurred in periods when interest rates increased substantially. Please use one of the stock valuation theories to explain this and also provide an intuitive explanation.

2.
a). Find the price of a corporate bond maturing in 5 years that has a 5% coupon (annual payments), a $1,000 face value, and an Aa rating. A local newspaper's financial section reports that the yield on 5-year bonds are : Aaa, 6 percent; Aa,7 percent; and A, 8 percent.

b. If the yield on Aa bonds changes to 8%, what is the bond price?

c. Given the above changes in the price of the bond and the yield, calculate the bond price elasticity.

3. A bond you are interested in pays an annual coupon of 5%, has a yield to maturity of 6% and has 13 years to maturity. The face value is $1,000,000. If interest rates remain unchanged, at what price would you expect this bond to be selling 8 years from now?

4. Company A currently has earnings of $10 per share, and investors expect that the earnings per share will grow by 4% per year. Furthermore, the mean PE ratio of all other firms in the same industry is 15. Company A is expected to pay a dividend of $2 per share over the next four years. The required rate of return on company A's stock is 10%.

a) What is the forecasted stock price of company A in four years? (Hint, use the PE method. You need to figure out the expected earnings per share 4 years from now)

b) Use the adjusted dividend discount model to figure out today's stock price of company A. (Hint: P0 = , P0 is today's price. P4 is the price in 4 years.)

5. Bill purchased a futures contract on Treasury bonds at a price of 102-12. Two months later, Bill sells the same futures contract in order to close out the position. At that time, the futures contract specifies 103-15. What is Bill's nominal profit? The par value (size) of the futures contract is $100,000.

6. Today is October 1. Your grandmother has just purchased 100 shares of Microsoft at $50 per share. She plans to give them to you as a Christmas present. However, you intend to sell the shares on Dec. 28 in order to buy a 50" plasma TV with a price of $5000. Your broker provides information about the following options:

Call Put
Exercise Price Dec. Jan. Feb. Dec. Jan. Feb.
$55 1.50 2.00 2.50 6.50 7.00 8.00
$50 2.50 3.50 4.50 1.50 2.50 3.50
$45 6.50 7.50 8.50 1.00 .75 .50
$40 12.50 .75 .50 .25
a. What option would you buy on Oct. 1 to hedge your price risk?
b. What is the total cost of your premium?
c. Suppose the Dec. 28 price of Microsoft is $55. What do you do with your option? What is the net amount of cash that you have for the purchase of the plasma TV?
d. Suppose the Dec. 28 price of Microsoft is $40. What do you do with your option? What is the net amount of cash that you have for the purchase of the plasma TV?

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Solution Summary

Answers to 6 questions on stock market declines, bond price, bond price elasticity, stock price, futures contract on Treasury bonds, Options.

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Options, Warrants , Futures and Bonds

Please see the attached file.

Q1- Consider a European call option on stock (A) that that expires on December 21 and has a strike price of $50.
a. If stock A is trading at $55 on December 21, what is the payoff to the owner of the option?
b. If stock A is trading at $55 on Dec. 21, what is the payoff to the seller of the option?
c. If stock A is trading at $45 on Dec. 21, what is the payoff to the owner of the option?
d. If stock A is trading at $45 on Dec. 21, what is the payoff to the seller of the option?
e. Draw the payoff diagram to the owner of this option with respect to the stock price at expiration.
f. Draw the payoff diagram to the seller of this option with respect to the stock price at expiration.
g. If the seller of a call option never receives cash at expiration, why should anyone ever sell a call option?

Q2- MMInc. Must purchase gold in three months to use in its operations. The management has estimated that if the price of gold were to rise above $375 per ounce, the firm would go bankrupt. The current price of gold os $350 per ounce;. The firm's CFO believes that the price f gold will either rise to $400 per ounce or fall to $325 per ounce over the next three months. Management wishes to eliminate any risk of going bankrupt . MMInc. Can borrow and lend at the risk free interest rate of 16.99% per annum(effective annual yield) .
a. Would MMInc. be interested in buying a call option or a put option on the price of gold? In order to avoid bankruptcy, what strike price and time to expiration would the firm like this option to have?
b. How much should such an option sell for in the open market?
c. If no option currently trade on gold, is there a way for the company to creat a synthetic option which identifies payoffs to the option described above? If there is, how would the firm do it?
d. How much does the synthetic option cost? Is this greater than , less than, or equal to what the actual option costs? Does this make sense?

Q3
a. What is the primary difference between warrants and call options?
b. Why is this difference important? What is dilution?

Q4 Explain three ways in which futures contracts differ from forward contracts

Q5 Consider three zero-coupon, $1000 face value bonds . bond A matures one year from today, bond B matures five years from today, and bond C matures ten years from today. The current market interest rate is 11% per annum (effective annual yield).
a. What is the current price of each bond?
b. If the market interest rate suddenly rises to 14% per annum , what wil be the price of each of these bonds?
c. Which bond experienced the greatest percentage change in price?

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