# Time Value of Money, Bond & Stock Valuation, Risk & Return

For problems 1 - 4:

It is January 2004, and you observe the following price quote:

IBM 9 1/2s26 Close 98 1/4

1. What is today's annual yield to maturity for this bond?

2. Suppose interest rates were to remain constant. What would be the bond price on Jan. 1, 2006?

3. Suppose interest rates were to fall by 2.5% three years later. What would be the rate of return from buying the bond, holding it for three years, and selling it at its new market price?

4. You would like to make a bid on Jan. 1, 2004, such that the yield to maturity is 13.5%. What price should you offer?

5. You currently have a 30-year fixed-rate mortgage financed at 7.25% on a $200,000 home. There are 25 years remaining on the mortgage. Your banker friend tells you that for a small fee (2% of the principal borrowed), you can refinance the remaining balance of your mortgage at a fixed rate of 5.75% for 25 years. What is the present value of the benefit (savings) to refinancing?

6. Your business partner offers you a position that should pay-off $5,000 per year for 8 years, followed by $1000 per year forever. In order to earn a rate of return equal to 16.5%, how much should you pay to get into the position?

7. You purchase a small business that costs $25,000. At the end of the first year, it returns profit to you of $5000. At the end of the second and third years, respectively, it returns profit to you of $7000 and $12000. Then, after 4 years, you sell the business for $30,000. What is your rate of return on this investment?

8. A share of stock paid its annual dividend of $1.20 exactly 4 years ago and you expect that next year's dividend will equal $1.70. Your analyst tells you the stock's expected total return is 17.5%, and that the stock's current price is $65.12. According to the constant dividend growth model, what is the stock's intrinsic value and, more importantly, should you buy the stock?

9. You are interested in purchasing some shares in a company that you believe will experience tremendous growth over the next few years. Specifically you expect that no dividends will be paid for the next two years. However, in year three, you expect that a dividend of $.75 will be paid. Further more, in years four through six, you expect the dividend to increase by 25% each year. After which, the company growth rate will slow to 8% annually. If the required return on this

investment is 15%, what would the intrinsic value of this stock be?

10. Consider the following possible scenarios for VLK corp:

Economy Return

Excellent 22%

Good 14%

Fair 8%

Poor 4%

a. What is the expected return for an investment in VLK?

b. What is the standard deviation of the above returns?

11. You have observed the following returns over time:

Year AMK Market

1990 10% 13%

1991 14% 18%

1992 -12% -13%

1993 6% 10%

1994 8% 11%

a. Given the above information, what is the beta for AMK?

b. Is AMK more or less risky than an average stock?

For 12 & 13:

12. How much is the payment on a $175,000 loan given an interest rate of 7%, and 72 monthly payments?

13. How much of the eighth payment is principal repayment?

14. Why is beta a more appropriate measure of risk than a stock's standard deviation of possible returns?

15. What interest rate, compounded monthly will yield the same rare of return as 6% compounded daily?

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#### Solution Summary

Answers questions on Time Value of Money, Bond & Stock Valuation, Risk & Return dealing with yield to maturity, price of a bond, present value, rate of return on investment, constant dividend growth model, stock's intrinsic value, expected return and standard deviation of return, beta of stock, amortization, time value of money.