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# Interest Rates, YTM, Options, Stocks, Bonds

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1) "The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.

2) The rate of return you would get if you bought a bond and held it to its maturity date is called the bond's yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price?

3) Two investors are evaluating General Motors' stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the risk of the stock. However, one investor normally holds stocks for 2 years, while the other normally holds stocks for 10 years. They should both be willing to pay the same price for General Motors' stock. True or false? Explain.

4) A bond that pays interest forever and has no maturity date is a perpetual bond. In what respect is a perpetual bond similar to a no-growth common stock, and to a share of preferred stock?

5) Assume you have been given the following information on Purcell Industries:

Current stock price = \$15 Strike price of option = \$15
Time to maturity of option = 6 months Risk-free rate = 6%
Variance of stock return = 0.12 d1= 0.24495
d2 = 0.00000 N(d1) = 0.59675
N(d2) = 0.50000

Using the Black-Scholes Option Pricing Model, what would be the value of the option?

6) Mini Case

Assume that you have just been hired as a financial analyst by Triple Trice Inc., a mid-sized California company that specializes in creating exotic clothing. Because no one at Triple Trice is familiar with the basics of financial options, you have been asked to prepare a brief report that the firm's executives can use to gain at least a cursory understanding of the topic.

To begin, you gathered some outside material on the subject and used these materials to draft a list of pertinent questions that need to be answered. In fact, one possible approach to the paper is to use a question-and-answer format. Now that the questions have been drafted, you have to develop the answers.

a. What is a financial option? What is the single most important characteristic of an option?

c. Consider Triple Trice's call option with a \$25 strike price. The following table contains historical values for this option at different stock prices:

Stock Price Call Option Price

\$25 \$3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50

(1) Create a table that shows (a) stock price, (b) strike price, (c) exercise value, (d) option price, and (e) the time value, which is the option's price less its exercise value.
(2) What happens to the time value as the stock price rises? Why?

#### Solution Preview

1) "The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.

FALSE
The % change in price of a bond is directly proportional to the DURATION of the bond and the longer the time to maturity the larger is the Duration of the bond. Therefore, the long -term bond prices are more sensitive to interest rate changes than are short-term bond prices

2) The rate of return you would get if you bought a bond and held it to its maturity date is called the bond's yield to maturity. If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price?

If interest rates in the economy rise after a bond has been issued, what will happen to the bond's price and to its YTM?

When interest rates rise, the price of the bond decreases and the YTM increases. This is because the YTM of the bond for an investor who buys the bond after the interest rate raises also increases. Bond prices and YTM have an inverse relationship. When yields get higher, the bond price will be lower

Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price?

Yes, the length of time to maturity affects the extent to which a given change in interest rates will affect the bond's price. The longer the time to ...

#### Solution Summary

The solution gives the answers to 5 questions and a mini-case on Interest rates, yields to maturity, stock, bond, financial option, Black-Scholes Option pricing model. Attached in Word for table formatting.

\$2.49