State all stock and bond prices in dollars and cents.
Unit 14.1 Stocks
1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute 100% of the profits to stockholders. (T or F) False
2. If a corporation goes out of business, preferred stockholders are paid before creditors. (T or F) False. Preferred stock-holders are paid before common stockstock-holders but after creditors.
3. ABC corporation has 1,150,000 shares of common stock and 200,000 shares of cumulative preferred stock. The annual dividend on the preferred stock is $3 per share. The only dividends paid last year were to preferred stockholders in the amount of $1 per share. This year the board of directors decided to distribute $1,575,000 in dividends. If you own 75 shares of common stock, what is the amount of your annual dividend?
Total dividends $1,575,000
Dividends for preferred stock: $400,000 last year + $600,000 this year -1,000,000
Dividends available to common stockholders $ 575,000
Dividends per share of common stock: $575,000 ÷1,150,000 shares = $0.50 Your dividend: 75 shares ×$0.50 per share = $37.50
4. All stockbrokerage companies charge the same commission. (T or F) False. Commissions vary, depending on the ser-vices the stockbroker provides.
5. The largest stock exchange in the United States is the Dow Jones Stock Exchange. (T or F) False. The largest stock exchange in the United States is the New York Stock Exchange.
6. A “bear market” occurs when investors are pessimistic about the overall economy and the stock market. (T or F) True 7. Observe the following stock quote. What are (a)the highest price during the last 52 weeks, (b)the lowest price during
the last 52 weeks, (c) the last price this day, (d)the change in price this day, (e)the number of shares traded this day, and (f) the last dividend, assuming dividends are paid quarterly. Confirm (g)the Yld% and (h)the PE Ratio, assuming annual earnings per share of $3.21.
a. $92.13per share b. $78.25per share c. $86.56per share
d. Decreased $0.63per share
e. 35,200 shares(352 ×100 = 35,200) f. 35¢ per share(1.40 ÷4 quarters = 0.35)
g. 1.40 (amount in “Div” column) ÷86.56 (amount in “Close” column) ≈.016 ≈1.6% h.
For Problems 8–12, evaluate an investment in 100 shares of stock.
8. You buy the 100 shares at a price of 38.50 and incur brokerage fees totaling $80. What is your total cost? (100 shares ×$38.50) + $80 = $3,850 + $80 = $3,930
9. Four years later, you sell the stock at a price of 46.00 and incur brokerage fees totaling $120. What are your net proceeds? (100 shares ×$46) - $120 = $4,600 - $120 = $4,480
10. Assuming you received no dividends, calculate your rate of return on the investment.
Chapter Review Problems
52 weeks PE Vol Net
Hi Lo Stock Sym Div Yld% Ratio 100s Close Chg
92.13 78.25 Wrigley WWY 1.40 1.6 27 352 86.56 -0.63
PE =P=$86.56≈26.97 ≈27
11. Assume instead you received dividends of 75¢ per share at the end of each year; you received your fourth annual divi-dend immediately before selling the stock. Calculate your rate of return.
12. Assume you received no dividend the third year. Calculate your rate of return.
*Note: The final dividend occurred at the end of year 4, the same time as the sale, so we combine with the sales proceeds before entering.
13. Data for three companies is shown. Calculate the PE ratio for each. Use 1 decimal place in the ratio.
14. Refer to Problem 13. For Company A, what does the PE ratio of 8.0 mean? If we owned stock in Company A, our share of earnings would be $8.13 for each share of stock we owned. Someone willing to pay $65 for a share of stock would be paying about $8.00 for each $1 of annual earnings(assuming that annual earnings remain constant).
15. Refer to Problem 13. Based on the PE ratios (i.e., assume that future earnings will remain the same as recent earnings), which of the three stocks is the best buy? Company A. The price–earnings ratio for Company A is the lowest (8.0), indicating the investor pays the least per dollar of earnings.
16. Refer to Problem 13. What accounts for the high PE ratio for Company C? (short answer) Investors apparently feel Company C has a much better future than is indicated by current earnings.
Unit 14.2 Bonds
17. Corporate bonds are generally in denominations of $1,000. (T or F) True 18. Treasury bills are a form of zero-coupon bond. (T or F) True
19. All municipal bonds are tax-exempt. (T or F) False
20. Bonds that have a high degree of risk must provide a high interest rate to attract investors. (T or F) True
For Problems 21 and 22, assume you own a 30-year 8% bond that pays interest annually and matures in 24 years. You are thinking about selling the bond.
21. If the prevailing rate for similar bonds is 6%, your bond will be priced at (a)par, (b)a discount, or (c)a premium. (c) Premium.Investors would prefer to have your 8% bond rather than a new 6% bond, so they will pay a premium for your bond.
22. If the prevailing rate for similar bonds is 10%, your bond will be priced at (a)par, (b)a discount, or(c)a premium. (b) Discount.Investors would prefer to have a new 10% bond rather than your 8% bond, so they will buy your bond only if you sell at a discount.
N i PV PMT FV
↑ 5.15 ↑ 75 ↑
T I B A I I P L U S H P 1 0 B I I
_ C ALL 0.00
3,930 +/- CFj -3,930.00 75 CFj 2 __ Nj 2.00
0 CFj 0.00
75 + 4,480 = CFj 4,555.00*
__ IRR/YR 4.70
CF 2nd CLR WORK CFo=0.00 3,930 +/- ENTER CFo=-3,930.00 ↓ 75 ENTER ↓ 2 ENTER F01=2.00
↓ C02=0.00
↓ 1 ENTER F02=1.00
↓ 75 + 4,480 = ENTER C03=4,555.00*
IRR CPT 4.70
2nd QUIT 2nd
2nd
Company Price per share Earnings per share PE ratio
A $65.00 $8.13 8.0
B $65.00 $5.91 11.0
23. You purchased a newly issued 7% 40-year $1,000 bond 8 years ago at par. The bond pays interest each 6 months. You incur financial difficulties and are forced to sell the bond. You have just received the 16th semiannual interest payment. The prevailing rate on similar bonds is 9.25%. What is your $1,000 bond worth today?
*Note: The investor who buys your bond will own the bond until it matures in 32 years
**Note: Semiannual interest payment (that the investor will receive) = $1,000 face value ×3.5% periodic rate = $35
24. Refer to Problem 23. If the prevailing rate on similar bonds is 5.25%, what is your bond worth today?
25. A corporation issues 25-year $1,000 zero-coupon bonds. Calculate the price you must pay for one of these bonds based on a prevailing 13% annual rate.
26. Refer to Problem 25. Two years later, you decide to sell the bond. Calculate the value of your bond based on a pre-vailing 8.25% rate.
27. Refer to Problems 25 and 26. Assuming you had no brokerage fees, what is your annual rate of return?
For Problems 28–37, refer to the following bond quote.
28. What is the coupon rate? 85/
8% =8.625%
29. In what year does the bond mature? 2026 30. How many bonds were sold this day? 30 bonds
31. Based on a $1,000 face value, what was the price for the last bond traded? $1,000 ×1057/
8% = $1,000 ×105.875% =$1,058.75
32. Why do you suppose the bond is priced at a premium? Apparently, the prevailing rate for new bonds is less than the coupon rate for this bond; therefore, investors are willing to pay a premium for this bond. 33. What happened to the price this day? $1,000 ×1/
8% = $1,000 ×0.125% = $1.25;Price decreased $1.25 34. Confirm the “Cur Yld” quote.
35. If you bought the bond at the closing price in 2002, immediately after the annual interest has been paid, what is your TYM?
36. Refer to Problem 35. Why is your YTM less than the coupon rate? You purchased the bond at a premium; this
N i PV PMT FV
32 ×2 = 64* 9.25 ÷2 ≈4.63 -770.23 35** 1,000
N i PV PMT FV
↑ 5.25 ÷2 ≈2.63 -1,269.85 ↑ ↑
N i PV PMT FV
25 13 -47.10 1,000
N i PV PMT FV
23 8.25 -161.49 ↑
N i PV PMT FV
2 85.17 -47.10 161.49
Bond Cur Yld Vol Close Net Chg
ATT 85/
826 8.1 30 1057/8 - 1/8
Cur Yld = Coupon rate = 8.625 ≈.08146 ≈8.146% ≈8.1%
Close column value 105.875
N i PV PMT FV
37. Which is a better indicator of your rate of return—the YTM found in Problem 35 or the Cur Yld from Problem 34? The YTM (8.06%). The Cur Yld (8.146%) incorrectly assumes you will receive interest payments forever and never recover the face value of the bond.
38. You buy three $5,000 Treasury bonds at a price of 133:13. What is the total price? Price per bond: $5,000 ×133 13/32% = $5,000 ×133.40625% = $6,670.3125
Number of bonds 3
Total price $ 20,010.94
39. Suppose you buy a 7.5% $1,000 bond for $1,122.50 immediately after semiannual interest has been paid to the previous owner. Eight years later, you sell the bond for $987.52, immediately after you receive the semiannual interest check. What is your yield during ownership?
Unit 14.3 Mutual funds
40. For each fund, find the NAV.
41. With a closed-end mutual fund, no additional shares are sold by the company after the initial offering. (T or F) True 42. With a front-end load mutual fund, an investor pays a fee when the shares are purchased. (T or F) True
43. Suppose you buy 25 shares in a mutual fund at an NAV of $12.23. You elect to reinvest distributions and, as a result, own 38.214 shares in 5 years. You sell the shares at an NAV of $24.44. You pay a back-end load of $55. Calculate your annual rate of return.
*Note: (38.214 shares ×$24.44) - $55 = $933.95 - $55 = $878.95
44. Suppose you invest $40 each month (starting today) into a mutual fund. You reinvest distributions. At the end of 6 years, you sell all your shares and receive $2,522. Calculate your rate of return.
(You lost money on this investment: a negative4.45% return.)
Note: So you don’t forget, you may want to put your calculator back in “end” mode now.
Challenge problems
For Problems 45–50, tell whether the statement refers to stock, a bond, or both.
45. With this investment, you become an owner of a corporation. Stock
46. For this investment, you can calculate your rate of return beforeyou make the investment. Bond 47. For this investment, you may receive dividends. Stock
48. A quote in the financial section of a newspaper looks like this: StdOil 83/
822. Bond
N i PV PMT FV
8 ×2 = 16 2.73 ×2 ≈5.46 -1,122.50 37.50 987.52
Total of closing Shares
prices Liabilities outstanding NAV
$23,478,000 $4,122,000 800,000 $8,155,000 $1,050,000 450,000 $745,000,000 $192,000,000 5,820,000
$23,478,000 - $4,122,000 = $19,356,000 = $24.20 800,000 800,000
$8,155,000 - $1,050,000 = $7,105,000 = $15.79 450,000 450,000
$745,000,000 - $192,000,000 = $553,000,000 = $95.02 5,820,000 5,820,000
N i PV PMT FV
5 23.51 -305.75 878.95*
N i PV PMT FV
6 ×12 = 72 -0.37 ×12 ≈-4.45 -40 Begin 2,522
49. The value of this investment can change during ownership. Both 50. With this investment, you are a lender. Bond
51. Assuming a 31% tax rate, which bond, purchased at par, has the greater after-tax rate of return: (a)a corporate bond pay-ing 8.75% or (b) a tax-free municipal bond paying 6.25%?
a. Before-tax return 8.75
Portion to taxman: 8.75 ×31% ~~ -2.71
After-tax return 6.04
b. After-tax return 6.25 (The municipal bond has the greater after-tax return)
52. Which bond purchased at par provides the greater return: A 7.6% corporate bond paying interest annuallyor a 7.5% cor-porate bond paying interest semiannually?
Let’s find the annual percentage yield (APY)for the 7.5% bond. To do so, we will use an arbitrary $100 deposit:
7.5% compounded semiannually is equivalent to 7.64% compounded annually, so the bond paying 7.5% semiannually provides a greater return.
For Problems 53–55, evaluate the investments of Jerry and Rose.
53. Jerry purchased 200 shares of corporate stock 8 years ago for $38 a share plus brokerage fees totaling $140. He received quarterly dividends of 40¢ per share. He just sold the stock (immediately after receiving the 32nd quarterly dividend) for $56.88 per share less brokerage fees totaling $225. First, calculate Jerry’s rate of return, compounded quarterly. Then, determine the annual percentage yield (APY) using an arbitrary $100 deposit amount.
*Note: (200 shares ×$38) + $140 = $7,600 + $140 = $7,740 **Note: 200 shares ×$0.40 = $80
***Note: (200 shares ×$56.88) - $225 = $11,376 - $225 = $11,151
54. Nine years ago, Rose purchased eight 8.25% $1,000 corporate bonds for 1051/
2plus incidental brokerage fees totaling
$18. Rose received interest checks semiannually. Immediately after receiving her 18th interest check, she sold the bonds for 113 less brokerage fees totaling $165. Calculate Rose’s yield, compounded semiannually. Then, determine the annual percentage yield (APY) using an arbitrary $100 deposit amount.
*Note: 8($1,000 ×105.5%) + $18 = 8($1,055) + $18 = $8,440 + $18 = $8,458 **Note: 8($1,000 ×4.125% periodic rate) = 8($41.25) = $330
***Note: 8($1,000 ×113%) - $165 = 8($1,130) - $165 = $9,040 - $165 = $8,875
55. Who got the greater rate of return?
Jerry earned 8.10% compounded quarterly. Rose earned 8.18% compounded semiannually. However, both rates are equivalent to 8.35% compounded annually, so they got the same rate of return.
N i PV PMT FV
2 7.5 ÷2 = 3.75 -100 107.64
1 7.64 ↑ ↑
N i PV PMT FV
8 ×4 = 32 2.03 ×4 ≈8.10 -7,740* 80** 11,151***
4 ↑ -100 0 108.35
1 8.35 ↑ ↑ ↑
N i PV PMT FV
9 ×2 = 18 4.09 ×2 ≈8.18 -8,458* 330** 8,875***
2 ↑ -100 0 108.35
1. Refer to the following stock quote. Determine (a)the highest price during the last 52 weeks, (b)the number of shares traded this day, and (c)the last dividend, assuming dividends are paid quarterly.
a. $51.38per share b. 161,300 shares(1,613 ×100 = 161,300) c. 15¢ per share(.60 ÷4 quarters = .15)
2. Refer to the stock quote of Problem 1. Assume you buy 100 shares of stock at the closing price and incur brokerage fees of $120. You own the stock for 4 years and receive dividends of 15¢ per share at the end of each quarter.
Immediately after receiving the 16th quarterly dividend, you sell the stock at a price of 47.13 and incur brokerage fees of $145. Calculate your rate of return.
3. You purchased some stock 8 years ago for $4,000. You received annual dividends of $150 at the end of years 1 through 5, no dividend for years 6 and 7, and $200 at the end of year 8. Immediately after receiving the $200 divi-dend you sold the stock for $6,500. What is your rate of return?
*Note: The final dividend was at the end of year 8, the same time as the sale, so we combine these two amounts before entering.
4. A company reported annual earnings per share of $2.28. If the price is currently $86.75 per share, what is the PE ratio?
5. Refer to the following bond quote. Suppose you bought one of these $1,000 bonds at the closing price in the year 2002, immediately after annual interest was paid to the previous owner. What is your YTM?
*Note: The bond matures in the year 2018, so you will own the bond for 16 years. **Note: $1,000 ×1083/4% = $1,000 ×108.75% = $1,087.50
***Note: $1,000 face value ×83/8% = $1,000 ×8.375% = $83.75
Practice Test
52 weeks PE Vol Net
Hi Lo Stock Sym Div Yld% Ratio 100s Close Chg
51.38 38.25 Walgreen WAG .60 1.6 25 1613 44.94 -0.88
N i PV PMT FV
4 ×4 = 16 0.26 ×4 1.06~~ -4,614 15 4,568
T I B A I I P L U S H P 1 0 B I I
_ C ALL 0.00
4,000 +/- CFj -4,000.00 150 CFj 5 __ Nj 5.00 0 CFj 2 __ Nj 2.00 200 + 6,500 = CFj 6,700.00*
__ IRR/YR 8.80
CF 2nd CLR WORK CFo=0.00 4,000 +/- ENTER CFo=-4,000.00 ↓ 150 ENTER ↓ 5 ENTER F01=5.00
↓ C02=0.00
↓ 2 ENTER F02=2.00
↓ 200 + 6,500 = ENTER C03=6,700.00*
IRR CPT 8.80
2nd QUIT 2nd
2nd
PE =P=$86.75≈38.05 ≈38
E $2.28
Bond Cur Yld Vol Close Net Chg
K mart 83/
818 7.7 30 1083/4 + 11/4
N i PV PMT FV
6. You purchased a 6.5% bond 4 years ago at par. The bond matures in 16 years and pays interest at the end of each 6 months. Similar bonds are being issued that pay 8.25% interest. What is your $1,000 bond worth today?
*Note: $1,000 face value ×3.25% periodic rate = $32.50
7. A mutual fund has investments with closing prices totaling $12,742,000, liabilities of $3,450,000, and 900,000 shares outstanding. What is the NAV?
8. Suppose you invest $75 at the end of each month into a mutual fund. You reinvest distributions. At the end of 5 years, you sell all your shares and receive $5,872. Calculate your rate of return.
N i PV PMT FV
16 ×2 = 32 8.25 ÷2 4.13~~ -846.07 32.50* 1,000
N i PV PMT FV
5 ×12 = 60 0.87 ×12 ≈10.42 -75 5,872
NAV = $12,742,000 - $3,450,000 = $9,292,000 = $10.32
