CHAPTER 5—VALUATION CONCEPTS
1. When considering stock and bond valuation models, we implicitly assume that the marginal investor is risk
averse, which means that he or she requires a higher rate of return for a given level of risk than a risk neutral
individual, other things held constant.
2. A 20-year original maturity bond with 1 year left to maturity has more interest rate price risk than a 10-year
original maturity bond with 1 year left to maturity. (Assume that the bonds have equal default risk and equal
3. The constant growth model used for evaluating the price of a share of common stock can also be used to find the
price of perpetual preferred stock or any other perpetuity.
4. A bond's value will increase as interest rates rise over time.
5. A bond with a $100 annual interest payment with five years to maturity (not expected to default) would sell for a
premium if interest rates were below 9% and would sell for a discount if interest rates were greater than 11%.
6. Other things held constant, P/E ratios are higher for firms with high growth prospects. At the same time, P/E's are
lower for riskier firms, other things held constant. These two factors, growth prospects and riskiness, may either
be offsetting or reinforcing as P/E determinants.
7. If the yield to maturity (the market rate of return) of a bond is less than its coupon rate, the bond should be selling
at a discount; i.e., the bond's market price should be less than its face (maturity) value.
8. If the prices of investment reflect existing information and adjust very quickly when new information becomes
available, then the financial markets have achieved informational efficiency.
9. The longer the maturity of a bond, the more its price will change in response to a given change in interest rates;
this is called interest rate price risk.
10. Assuming g will remain constant, the dividend yield is a good measure of the required return on a common stock
under which of the following circumstances?
a. g = 0
b. g > 0
c. g < 0
d. Under no circumstances.
e. Answers a and b are both correct.
11. If the expected rate of return on a stock exceeds the required rate,
a. The stock is experiencing supernormal growth.
b. The stock should be sold.
c. The company is probably not trying to maximize price per share.
d. The stock is a good buy.
e. Dividends are not being declared.
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12. If the stock market is semi-strong efficient, which of the following statements is correct?
a. All stocks should have the same expected returns; however, they may have different
b. In equilibrium, stocks and bonds should have the same expected returns.
c. Investors can outperform the market if they have access to information which has not yet
been publicly revealed.
d. if the stock market has been performing strongly over the past several months, stock prices
are more likely to decline than increase over the next several months.
e. None of the above statements is correct.
13. Bonds issued by BB&C Communications that have a coupon rate of interest equal to 10.65 percent currently have
a yield to maturity (YTM) equal to 15.25 percent. Based on this information, BB&C's bonds must currently be
selling at __________ in the financial markets.
a. par value
b. a discount
c. a premium
d. Not enough information is given to answer this question.
e. None of the above is a correct answer.
14. According to the efficient markets hypothesis (EMH), which form of market efficiency states that all publicly
available information, past and present, is already included in the price of financial assets?
a. weak form
b. semi-strong form
c. strong form
d. None of the above, because the financial markets cannot be efficient.
15. If the yield to maturity (the market rate of return) of a bond is less than its coupon rate, the bond should be
a. selling at a discount; i.e., the bond's market price should be less than its face (maturity)
b. selling at a premium; i.e., the bond's market price should be greater than its face value.
c. selling at par; i.e., the bond's market price should be the same as its face value.
d. purchased because it is a good deal.
16. If you buy a bond that is selling for less than its face, or maturity, value what will happen to the price (value) of
the bond as the maturity date nears if market interest rates do not change during the life of the bond?
a. Because interest rates remain constant, nothing happens to the market value of the bond.
b. The price of the bond should decrease even further below the bond's face value because
the rates in the market are too high.
c. The price of the bond will increase as the bond gets closer to its maturity because the
bond's value has to equal its face value at maturity.
d. This question cannot be answered without additional information.
e. None of the above is a correct answer.
17. Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual
interest payments of $40. If you require a 10 percent simple yield to maturity on this investment, what is the
maximum price you should be willing to pay for the bond?
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18. A $1,000 par value bond pays interest of $35 each quarter and will mature in 10 years. If your simple annual
required rate of return is 12 percent with quarterly compounding, how much should you be willing to pay for this
19. A share of perpetual preferred stock pays an annual dividend of $6 per share. If investors require a 12 percent rate
of return, what should be the price of this preferred stock?
20. A share of preferred stock pays a quarterly dividend of $2.50. If the price of this preferred stock is currently $50,
what is the simple annual rate of return?
21. A share of preferred stock pays a dividend of $0.50 each quarter. If you are willing to pay $20.00 for this
preferred stock, what is your simple (not effective) annual rate of return?
22. The last dividend paid by Klein Company was $1.00. Klein's growth rate is expected to be a constant 5 percent for
2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein's required rate of return
on equity (ks) is 12 percent. What is the current price of Klein's common stock?
23. Assume that a 15-year, $1,000 face value bond pays interest of $37.50 every 3 months. If you require a simple
annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this
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24. In order to accurately assess the capital structure of a firm, it is necessary to convert its balance sheet figures to a
market value basis. KJM Corporation's balance sheet as of January 1, 2001, is as follows:
Long-term debt (bonds, at par) $10,000,000
Preferred stock 2,000,000
Common stock ($10 par) 10,000,000
Retained earnings 4,000,000
Total debt and equity $26,000,000
The bonds have a 4 percent coupon rate, payable semiannually, and a par value of $1,000. They mature on
January 1, 2011. The yield to maturity is 12 percent, so the bonds now sell below par. What is the current market
value of the firm's debt?
25. You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual
coupon payment of $80, and a par value of $1,000. Unfortunately, Euler is on the brink of bankruptcy. The
creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next
interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be
made as scheduled. The postponed payments will accrue interest at an annual rate of 6 percent, and they will then
be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their
substantial risk, is now 28 percent. What is the present value of each bond?
26. You are contemplating the purchase of a 20-year bond that pays $50 in interest each six months. You plan to hold
this bond for only 10 years, at which time you will sell it in the marketplace. You require a 12 percent annual
return, but you believe the market will require only an 8 percent return when you sell the bond 10 years hence.
Assuming you are a rational investor, how much should you be willing to pay for the bond today?
27. JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six
months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional
financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000,
and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue
to raise $2,000,000 cash?
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28. Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six
months and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then to
sell it in the market. You (and other investors) currently require a simple annual rate of 16 percent, but you expect
the market to require a rate of only 12 percent when you sell the bond due to a general decline in interest rates.
How much should you be willing to pay for this bond?
29. The current price of a 10-year, $1,000 par value bond is $1,158.91. Interest on this bond is paid every six months,
and the simple annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond?
30. A firm expects to pay dividends at the end of each of the next four years of $2.00, $1.50, $2.50, and $3.50. If
growth is then expected to level off at 8 percent, and if you require a 14 percent rate of return, how much should
you be willing to pay for this stock?
31. Eastern Auto Parts' last dividend was D0 = $0.50, and the company expects to experience no growth for the next 2
years. However, Eastern will grow at an annual rate of 5 percent in the third and fourth years, and, beginning with
the fifth year, it should attain a 10 percent growth rate which it should sustain thereafter. Eastern has a required
rate of return of 12 percent. What should be the present price per share of Eastern common stock?
32. The Satellite Building Company has fallen on hard times. Its management expects to pay no dividends for the
next 2 years. However, the dividend for Year 3, D3, will be $1.00 per share, and the dividend is expected to grow
at a rate of 3 percent in Year 4, 6 percent in Year 5, and 10 percent in Year 6 and thereafter. If the required return
for Satellite is 20 percent, what is the current equilibrium price of the stock?
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33. You are considering the purchase of a common stock that just paid a dividend of $2.00. You expect this stock to
have a growth rate of 30 percent for the next 3 years, then to have a long-run normal growth rate of 10 percent
thereafter. If you require a 15 percent rate of return, how much should you be willing to pay for this stock?
34. You have a chance to purchase a perpetual security that has a stated annual payment (cash flow) of $50. However,
this is an unusual security in that the payment will increase at an annual rate of 5 percent per year; this increase is
designed to help you keep up with inflation. The next payment to be received (your first payment, due in 1 year)
will be $52.50. If your required rate of return is 15 percent, how much should you be willing to pay for this
35. Suppose you are willing to pay $30 today for a share of stock which you expect to sell at the end of one year for
$32. If you require an annual rate of return of 12 percent, what must be the amount of the annual dividend which
you expect to receive at the end of Year 1?
36. Carlson Products, a constant growth company, has a current market (and equilibrium) stock price of $20.00.
Carlson's next dividend, D1, is forecasted to be $2.00, and Carlson is growing at an annual rate of 6 percent.
Carlson has a beta coefficient of 1.2, and a required rate of return on the market is 15 percent. As Carlson's
financial manager, you have access to insider information concerning a switch in product lines which would not
change the growth rate, but would cut Carlson's beta coefficient in half. If you buy the stock at the current market
price, what is your expected percentage capital gain?
e. There would be a capital loss.
37. Over the past few years, Swanson Company has retained, on the average, 70 percent of its earnings in the
business. The future retention rate is expected to remain at 70 percent of earnings, and long-run earnings growth
is expected to be 10 percent. If the risk-free rate, kRF, is 8 percent, the expected return on the market, kM, is 12
percent, Swanson's beta is 2.0, and the most recent dividend, D0, was $1.50, what is the most likely market price
and P/E ratio (P0/E1) for Swanson's stock today?
a. $27.50; 5.0x
b. $33.00; 6.0x
c. $25.00; 5.0x
d. $22.50; 4.5x
e. $45.00; 4.5x
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38. The probability distribution for kM for the coming year is as follows:
If kRF = 6.05% and Stock X has a beta of 2.0, an expected constant growth rate of 7 percent, and D0 = $2, what
market price gives the investor a return consistent with the stock's risk?
39. Rick bought a bond when it was issued by Macroflex Corporation 14 years ago. The bond, which has a $1,000
face value and a coupon rate equal to 10 percent, matures in six years. Interest is paid every six months; the next
interest payment is scheduled for six months from today. If the yield on similar risk investments is 14 percent,
what is the current market value (price) of the bond?
40. Tony's Pizzeria plans to issue bonds with a par value of $1,000 and 10 years to maturity. These bonds will pay
$45 interest every 6 months. Current market conditions are such that the bonds will be sold to net $937.79. What
is the YTM of the issue as a broker would quote it to an investor?
41. The current market price of Smith Corporation's 10 percent, 10-year bonds is $1,297.58. A 10 percent coupon
interest rate is paid semiannually, and the par value is equal to $1,000. What is the YTM (stated on a simple, or
annual, basis) if the bonds mature 10 years from today?
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42. Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent
the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent
thereafter. The required rate of return on equity (ks) is 10 percent. What is the current price of the common stock?
43. A $1,000 par value bond sells for $1,216. It matures in 20 years, has a 14 percent coupon, pays interest
semiannually, and can be called in 5 years at a price of $1,100. What is the bond's YTM?
44. You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually,
and interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more
interest payments you will receive, but the party selling the bond cannot remember. Can you determine how many
interest payments remain?
45. Garcia Inc. has a current dividend of $3.00 per share (D0 = $3.00). Analysts expect that the dividend will grow at
a rate of 25 percent a year for the next three years, and thereafter it will grow at a constant rate of 10 percent a
year. The company's cost of equity capital is estimated to be 15 percent. What is the current stock price of Garcia
46. Assume that the average firm in your company's industry is expected to grow at a constant rate of 5 percent, and
its dividend yield is 4 percent. You company is about as risky as the average firm in the industry, but it has just
developed a line of innovative new products which leads you to expect that its earnings and dividends will grow
at a rate of 40 percent. ( = D0 ((1 + g) = D0 (1.40)) this year and 25 percent the following year, after which growth
should match the 5 percent industry average rate. The last dividend paid (D0) was $2. What is the value per share
of your firm's stock?
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22. ANS: D
CHAPTER 5—VALUATION CONCEPTS 23. ANS: B
24. ANS: A
TRUE/FALSE 25. ANS: D
1. ANS: T 26. ANS: D
2. ANS: F 27. ANS: B
3. ANS: T 28. ANS: D
4. ANS: F 29. ANS: D
5. ANS: T 30. ANS: E
6. ANS: T 31. ANS: D
7. ANS: F 32. ANS: C
8. ANS: T 33. ANS: A
9. ANS: T 34. ANS: C
MULTIPLE CHOICE 35. ANS: C
10. ANS: A 36. ANS: C
11. ANS: D 37. ANS: A
12. ANS: C 38. ANS: D
13. ANS: B 39. ANS: A
14. ANS: B 40. ANS: B
15. ANS: B 41. ANS: B
16. ANS: C 42. ANS: D
17. ANS: D 43. ANS: E
18. ANS: C 44. ANS: B
19. ANS: B 45. ANS: C
20. ANS: C 46. ANS: B
21. ANS: A