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Time Value Money, Rate of return

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1. U have been tracking a non-dividend paying share that you purchased. Its price since you purchased it (t = 0) until today (t = 3) has been P0 = $27.50, P1 = $17.50, P2 = $31.50 and P3 = $26.50.

a) Compute the periodic rates of return.

b) Compute the arithmetic and geometric rate of return for this stock over the past three years. Which is the most appropriate measure?

2. With an 8% annual interest rate, how long does it take a sum of money to double given
a) annual compounding,
b) semi-annual compounding and
c) daily compounding?

3. You are considering selling for $6,250 a Volvo which you purchased five years ago for $4,670. What would be your annualized rate of return on the Volvo investment?

4. Some day, you will buy an Acura NSX, drive it for 10 years and sell it for more than you paid for it. If you pay $89,000 for it and your expected rate of return is 6%, how much must you sell it for?

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1. U have been tracking a non-dividend paying share that you purchased. Its price since you purchased it (t = 0) until today (t = 3) has been P0 = $27.50, P1 = $17.50, P2 = $31.50 and P3 = $26.50.

a) Compute the periodic rates of return.

Time period Price Return=
0 P0= $27.50
1 P1= $17.50 -36.36% =(17.5-27.5)/27.5
2 P2= $31.50 80.00% =(31.5-17.5)/17.5
3 P3= $26.50 -15.87% =(26.5-31.5)/31.5

Answer:
Time period Return
1 -36.36%
2 80.00%
3 -15.87%

b) Compute the arithmetic and geometric rate of return for this stock over the past three years. Which is the most appropriate measure?

Arithemetic rate of return= 9.26% ={(-36.36%)+(80.%)+(-15.87%)}/3

Time period Price Current price/ Previous period price
0 P0= $27.50
1 P1= $17.50 0.6364 =17.5/27.5
2 P2= $31.50 1.8 =31.5/17.5
3 P3= $26.50 0.8413 =26.5/31.5

Geometric rate of return= -1.22% ={(0.6364)*(1.8)*(0.8413)}^(1/3) ...

Solution Summary

Answers questions on Time Value Money, Rate of return.

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Value of outstanding bonds and rates of returns

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 inventors 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 stock for 2 years, while the other normally holds stock for 10 years. Should 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 sock, and to a share of preferred stock?

5. Describe the effect on a call option's price caused by an increase in each of the following factors: (1) stock price, (2) strike price, (3) time to expiration, (4) risk-free rate, and (5) variance of stock return.

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

7. Consider Triple Trice's call option with a $25.00 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 $25.00

(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?

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