Valuation Problems:  Stocks, Bonds, and Other Investments

1.  What is the value of the two investments:  

a.      Stock in which you expect a dividend of $300 a year indefinitely.  You feel you should obtain a 10% return based on the risk you are taking

 Solution:  $3,000

b.  Painting that you expect to sell for $300,000 in 5 years.  You feel you should obtain a 20% return.

 Solution:  $120,563

c.      Let’s say that you know you have a major art gallery interested in buying your painting at the beginning of next year (one year from now).  You have been offered $130,000.  You trust the art gallery manager.  In matter of fact, the manager is willing to sign a contract.  Would you place a different required return?  Using your own discount rate, would you sell the painting to the art gallery or try to sell it in 5 years?

 Solution:  $120,370 using 8%- answers will vary depending on the required return used

2.     Cemex, a large cement provider, issued a 10 percent coupon interest rate, 10-year bond with a $1,000 par value.  The market rate for a bond like this (risk level of company and maturity rate) is 11 percent.  The company is selling 100,000 of these bonds.  How much should these bonds sell for in the marketplace?  Excluding transaction costs, how much will Cemex collect?

 Solution:  $941.92 Market Value; $94,192,000 collected

3.     You decide to buy IBM bonds that are selling in the open market for $950.  The coupon rate is 8 percent.  The bonds mature in 10 years.  What is the Yield-to-Maturity of these bonds?

Solution:  8.77% PV = -$950, n = 10, pmt = $80, FV = $1,000, CPT = I/Y

4.     You just bought IBM bonds that mature in twenty years.  You paid $1,000 (par value).  The bonds have a coupon rate of 8 percent.  If interest rates fall and the required return on your bond is now 6 percent, what is the value of your bond?

Solution:  $1,229 

5.     You also own an IBM bond that matures in two years.  Let’s assume it is selling for $1,000 on the open market and has a coupon rate of 8 percent.  If interest rates fall and the required return on your bond is now 6 percent, what is the value of your bond (in reality, 4 and 5 would not occur at the same time)? 

 Solution:  $1,037

6.     Look at the new value of the bonds in problems 4 and 5.  The same change in interest rates occurred.  Did the value of the bonds change the same amount?  Can you make sense of this?

Required Return:  A specified return required by investors for a given level of risk

Expected Return:  The return that is expected to be earned

(These two definitions can be confusing because they can casually be used interchangeably.)

7.     You are analyzing Microsoft ($110 per share) and the external environment (competition, legal proceedings, global economic environment, technological advances, etc.).  You are looking to make a quick profit—planning to hold for 1 year.  You figure there is a 50%, 25%, and 25%, probability that the stock will go up or down 40%, 10%, or -40%, respectively.  The risk-free rate is now 5 percent, the beta of Microsoft is 1.1, and the market return rate is 10 percent (5 percent premium over the risk free rate).  What is the expected return of Microsoft?  Using CAPM, what is the required return of Microsoft?  Based on the risk-level as calculated by CAPM, should you invest in Microsoft?

 Solution:  E(R) = 12.5%; Required Return = 10.5% Yes

8.     Assume Microsoft is selling for $100.  Due to all the legal proceedings, Microsoft has been more volatile than in the past.  Therefore, the Beta of Microsoft has changed to 1.3.  You figure Microsoft will be selling for $130 by the end of this year.  Based on the level of risk (using CAPM), is Microsoft worth buying?

 Solution:  $111.50, Yes

9.     Using the Gordon Model, calculate the value of the following stock.  Use CAPM to determine the required rate of return (Risk free = 5%, Market Return = 10%, Beta = .9).  The dividend growth rate = 7%.  The dividend one period out is $2.76.

Solution:  $110.40-- $2.76/(.095-.07)

10. Assume in the above problem that the company has just landed a major account in Asia.  Assume the risk level of the company hasn’t changed but the expected growth in dividends is expected to grow at 9 percent.  Dividends one period out = $2.81.  What is the value of the stock using the Gordon Growth Model?

 Solution:  $562.00

11. What are the limitations of the Gordon Growth Model?

12. Assume in problem 9 that the company landing the major account in Asia has increased its earnings volatility.  Therefore, the stock is expected to be more volatile.  You decide to adjust the Beta to 1.0 to evaluate the value of the stock.  Using the Gordon Model and the dividend growth rate of 7%, what is the value of the stock?  Using the Gordon Model, dividends of $2.81 one period out, and the dividend growth rate of 9%, what is the value of the stock?

 Solutions:  $92.00 and $281.00

13. Using the above problems, explain how taking on a new project (e.g., Asia) can increase or decrease the value of a stock.

14. Alligators R Us is contemplating expansion through the issuance of debt/bonds.  Your broker calls you and suggests that you buy 10 bonds—price $1,150 for each bond, 11 percent coupon rate, $1,000 par value, interest paid  annually.  The bonds mature in 12 years.  Calculate the Yield-to-Maturity (YTM).  Are the bonds selling at a discount or premium?

Solution:  8.91%, premium

15. You are considering buying a “high-flying” stock.  The company started last year in the basement of the president’s house.  The company consults with companies that do business on the web.  It specializes in security issues on the web.  The company made $200,000 last year.  The company will not pay dividends in the foreseeable future.  The company has no assets.  The company has one employee—the president.  He is a genius with computers but otherwise mentally retarded.  The company has major clients—Lucent, IBM, Microsoft, and IBM just to name a few.  The mother has cancer and is concerned about her son.  She wants you to buy the company.  The only agreement is that you hire someone trustworthy to take care of the president and that the president’s basic necessities are cared for.  All other earnings are yours.  How much would you pay for this company?  Or, how would you go about determining the value of this company?

 Solution:  Good Luck!

16. Michael Jackson is issuing $1,000 par-value bonds with a 12 percent coupon interest rate.  The bonds will mature in 16 years. 

a.      If bonds of similar risk are currently earning a 10 percent rate of return (YTM), how much should the Michael Jackson bonds sell for today?

Solution:  $1,156.47

b.     Why might similar-risk bonds earn a return (YTM) below the coupon rate of Michael Jackson’s bonds?  

Last Updated:  October 29, 2001