60.
|
You just sold 600 shares of Wesley, Inc. stock at a price of $32.04 a share. Last year, you paid $30.92 a share to buy this stock. Over the course of the year, you received dividends totaling $1.20 per share. What is your total capital gain on this investment?
Capital gain = ($32.04 - $30.92) × 600 = $672
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Capital gain |
61.
|
Last year, you purchased 500 shares of Analog Devices, Inc. stock for $11.16 a share. You have received a total of $120 in dividends and $7,190 from selling the shares. What is your capital gains yield on this stock?
Capital gains yield = [($7,190/500) - $11.16]/$11.16 = 28.85 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Capital gains yield |
62.
|
Today, you sold 200 shares of Indian River Produce stock. Your total return on these shares is 6.2 percent. You purchased the shares one year ago at a price of $31.10 a share. You have received a total of $100 in dividends over the course of the year. What is your capital gains yield on this investment?
Capital gains yield = .062 - [($100/$200)/$31.10] = 4.59 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Capital gains yield |
63.
|
Four months ago, you purchased 1,500 shares of Lakeside Bank stock for $11.20 a share. You have received dividend payments equal to $0.25 a share. Today, you sold all of your shares for $8.60 a share. What is your total dollar return on this investment?
Total dollar return = ($8.60 - $11.20 + $0.25) × 1,500 = -$3,525
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Dollar returns |
64.
|
One year ago, you purchased 500 shares of Best Wings, Inc. stock at a price of $9.75 a share. The company pays an annual dividend of $0.10 per share. Today, you sold all of your shares for $15.60 a share. What is your total percentage return on this investment?
Total percentage return = ($15.60 - $9.75 + $0.10)/$9.75 = 61.03 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Percentage return |
65.
|
Last year, you purchased a stock at a price of $47.10 a share. Over the course of the year, you received $2.40 per share in dividends while inflation averaged 3.4 percent. Today, you sold your shares for $49.50 a share. What is your approximate real rate of return on this investment?
Nominal return = ($49.50 - $47.10 + $2.40)/$47.10 = 10.19 percent
Approximate real return = 0.1019 - 0.034 = 6.79 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Approximate real return |
66.
|
One year ago, you purchased 150 shares of a stock at a price of $54.18 a share. Today, you sold those shares for $40.25 a share. During the past year, you received total dividends of $182 while inflation averaged 4.2 percent. What is your approximate real rate of return on this investment?
Nominal return = [$40.25 - $54.18 + ($182/150)]/$54.18 = -0.2420
Approximate real return = -0.2420 - 0.042 = -28.40 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Approximate real return |
67.
|
What is the amount of the risk premium on a U.S. Treasury bill if the risk-free rate is 2.8 percent and the market rate of return is 8.35 percent?
There is no excess return, or risk premium, for a risk-free security such as the T-bill.
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Risk-free security |
68.
|
A stock had returns of 11 percent, -18 percent, -21 percent, 20 percent, and 34 percent over the past five years. What is the standard deviation of these returns?
Average return = (0.11 - 0.18 - 0.21 + 0.20 + 0.34)/5 = .052;
σ = √[1/(5 - 1)] [(0.11 - 0.052)2 + (-0.18 - 0.052)2 + (-0.21 -0.052)2 + (0.05 - 0.052)2 + (0.34 - 0.052)2] = 24.01 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.4 Topic: Standard deviation |
69.
|
The common stock of Air United, Inc., had annual returns of 15.6 percent, 2.4 percent, -11.8 percent, and 32.9 percent over the last four years, respectively. What is the standard deviation of these returns?
Average return = (0.156 + 0.024 - 0.118 + 0.329)/4 = 0.09775
σ = √[1/(4 - 1)] [(0.156 - 0.09775)2 + (0.024 - 0.09775)2 + (-0.118 - 0.09775)2 + (0.329 - 0.09775)2] = 19.05 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.4 Topic: Standard deviation |
70.
|
A stock had annual returns of 3.6 percent, -8.7 percent, 5.6 percent, and 12.5 percent over the past four years. Which one of the following best describes the probability that this stock will produce a return of 22 percent or more in a single year?
Average return = (0.036 - 0.087 + 0.056 + 0.125)/4 = 0.0325
∑ = √[1/(4 - 1)] [(0.036 - 0.0325)2 + (-0.087 - 0.0325)2 + (0.056 - 0.0325)2 + (0.125 - 0.0325)2] = 0.0883 Upper end of 95 percent range = 0.0325 + (2 × 0.0883) = 20.91 percent Upper end of 99 percent range = 0.0325 + (3 × 0.0883) = 29.75 percent A return of 22 percent or more in a single year has between a 1 percent and a 2.5 percent probability of occurring in any one year. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
71.
|
A stock has an expected rate of return of 13 percent and a standard deviation of 21 percent. Which one of the following best describes the probability that this stock will lose at least half of its value in any one given year?
Lower bound of 99 percent range = 0.13 - (3 × 0.21) = -50 percent
Probability of losing 50 percent or more in any one year is 0.5 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
72.
|
A stock has returns of 18 percent, 15 percent, -21 percent, and 6 percent for the past four years. Based on this information, what is the 95 percent probability range of returns for any one given year?
Average return = (0.18 + 0.15 - 0.21 + 0.06)/4 = 0.045
σ = (0.18 - 0.045)2 + (0.15 - 0.045)2 + (-0.21 - 0.045)2 + (0.06 - 0.045)2] = .177482 95% probability range = 0.045 ± (2 × 0.177482) percent = -31.00 to 40.00 percent |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
73.
|
Your friend is the owner of a stock which had returns of 25 percent, -36 percent, 1 percent, and 16 percent for the past four years. Your friend thinks the stock may be able to achieve a return of 50 percent or more in a single year. Based on these returns, what is the probability that your friend is correct?
Average return = (0.25 - 0.36 + 0.01 + 0.16)/4 = 0.015
σ = √[1/(4 - 1)] [(0.25 - 0.015)2 + (-0.36 - 0.015)2 + (0.01 - 0.015)2 + (0.16 - 0.015)2] = 0.2689 Upper end of 68 percent range = 0.015 + (1 × 0.2689) = 28.39 percent Upper end of 95 percent range = 0.015 + (2 × 0.2689) = 55.28 percent The probability of earning at least 50 percent in any one year is greater than 2.5 percent but less than 16 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
74.
|
A stock had returns of 15 percent, 8 percent, 12 percent, -15 percent, and -4 percent for the past five years. Based on these returns, what is the approximate probability that this stock will return at least 20 percent in any one given year?
Average return = (0.15 + 0.08 + 0.12 - 0.15 - 0.04)/5 = 0.032
σ = √[1/(5 - 1)] [(0.15 - 0.02)2 + (0.08 - 0.02)2 + (0.12 - 0.02)2 + (-0.15 - 0.02)2 + (-0.04 - 0.02)2] = 0.1248 Upper end of 68 percent range = 0.032 + 0.1248 = 15.68 percent Probability of earning at least 20 percent in any one year is less than 16 percent but greater than 2.5 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
75.
|
A stock had returns of 14 percent, 13 percent, -10 percent, and 7 percent for the past four years. Which one of the following best describes the probability that this stock will lose no more than 10 percent in any one year?
Average return = (0.14 + 0.13 - 0.10 + 0.07)/4 = 0.06
σ = √[1/(4 - 1)][(0.14 - 0.06)2 + (0.13 - 0.06)2 + (-0.10 - 0.06)2 + (0.07 - 0.06)2] = 0.11106 Lower bound of 68 percent range = 0.06 - (1 × 0.11106) = -5.11 percent Lower bound of 95 percent range = 0.06 - (2 × 0.11106) = -16.21 percent Probability of losing more than 10 percent in any given year is between 2.5 and 16 percent. Thus, the probability of NOT losing more than 10 percent is between 84 and 97.5 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
76.
|
Over the past five years, a stock produced returns of 11 percent, 14 percent, 4 percent, -9 percent, and 5 percent. What is the probability that an investor in this stock will not lose more than 10 percent in any one given year?
Average return = (0.11 + 0.14 + 0.02 - 0.09 + 0.05)/5 = 0.05
σ = √[1/(5 - 1)][(0.11 - 0.046)2 + (0.14 - 0.046)2 + (0.04 - 0.046)2 + (-0.09 - 0.046)2 + (0.05 - 0.046)2] = 0.0886 Lower bound of 68% probability range = 0.05 - (1 × 0.0886) = -3.86 percent Lower bound of 95% probability range = 0.05 - (2 × 0.0886) = -12.72 percent The probability of losing 10 percent or more is greater than 2.5 percent but less than 16 percent. Thus, the probability of NOT losing more than 10 percent is greater than 84 percent but less than 97.5 percent. |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability of occurrence |
77.
|
A stock has annual returns of 6 percent, 14 percent, -3 percent, and 2 percent for the past four years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.
Arithmetic average = (0.06 + 0.14 - 0.03 + 0.02)/4 = 4.75 percent
Geometric return = (1.06 × 1.14 × 0.97 × 1.02).25 - 1 = 4.57 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Arithmetic and geometric returns |
78.
|
A stock has annual returns of 5 percent, 21 percent, -12 percent, 7 percent, and -6 percent for the past five years. The arithmetic average of these returns is _____ percent while the geometric average return for the period is _____ percent.
Arithmetic average = (0.05 + 0.21- 0.12 + 0.07 - 0.06)/5 = 3.00 percent
Geometric return = (1.05 × 1.21 × 0.88 × 1.07 × 0.94).20 - 1 = 2.37 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Arithmetic and geometric returns |
79.
|
A stock had returns of 16 percent, 4 percent, 8 percent, 14 percent, -9 percent, and -5 percent over the past six years. What is the geometric average return for this time period?
Geometric average = (1.16 × 1.04 × 1.08 × 1.14 × 0.91 × 0.95)1/6 - 1 = 4.26 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Geometric return |
80.
|
A stock had the following prices and dividends. What is the geometric average return on this stock?
Return for year 2 = ($16.10 - $16.40 + $0.50)/$16.40 = 1.2195 percent
Return for year 3 = ($15.48 - $16.10 + $0.50)/$16.10 = -0.7453 percent Return for year 4 = ($9.15 - $15.48 + $0.75)/$15.48 = -36.0465 percent Geometric return = (1.012195 × 0.9925472 × 0.639535)1/3 - 1 = -13.71 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Geometric return |
81.
|
Over the past fifteen years, the common stock of The Flower Shoppe, Inc. has produced an arithmetic average return of 12.2 percent and a geometric average return of 11.5 percent. What is the projected return on this stock for the next five years according to Blume's formula?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Blume's formula |
82.
|
Based on past 23 years, Westerfield Industrial Supply's common stock has yielded an arithmetic average rate of return of 10.5 percent. The geometric average return for the same period was 8.57 percent. What is the estimated return on this stock for the next 4 years according to Blume's formula?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Blume's formula |
83.
|
A stock has a geometric average return of 14.6 percent and an arithmetic average return of 15.5 percent based on the last 33 years. What is the estimated average rate of return for the next 6 years based on Blume's formula?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Blume's formula |
84.
|
Suppose a stock had an initial price of $80 per share, paid a dividend of $1.35 per share during the year, and had an ending share price of $87. What was the capital gains yield?
Capital gains yield = ($87 - $80)/$80 = 8.75 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 12-2 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.1 Topic: Capital gains yield |
85.
|
Suppose you bought a 10 percent coupon bond one year ago for $950. The face value of the bond is $1,000. The bond sells for $985 today. If the inflation rate last year was 9 percent, what was your total real rate of return on this investment?
Nominal return = ($985 - $950 + $100)/$950 = 0.1421
Real return = [(1 + 0.1421)/(1 + 0.09)] - 1 = 4.78 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 12-4 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Nominal and real returns |
86.
|
Calculate the standard deviation of the following rates of return:
Average return = (0.07 + 0.25 + 0.14 - 0.15 + 0.16)/5 = 0.094
Standard deviation = √[1/(5 - 1)] [(0.07 - 0.094)2 + (0.25 - 0.094)2 +(0.14 - 0.094)2 +(-0.15 - 0.094)2 + (0.16 - 0.094)2] = 15.08 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 12-7 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.4 Topic: Standard deviation |
87.
|
You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 2 percent, -12 percent, 16 percent, 22 percent, and 18 percent. What is the variance of these returns?
Average = (0.02 - 0.12 + 0.16 + 0.22 + 0.18)/5 = 0.092
Variance = [1/(5 - 1)] [(0.02 - 0.092)2 + (-0.12 - 0.092)2 + (0.16 - 0.092)2 + (0.22 - 0.092)2 + (0.18 - 0.092)2] = 0.01972 |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 12-9 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.4 Topic: Variance |
88.
|
You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 3 percent, -10 percent, 24 percent, 22 percent, and 12 percent. Suppose the average inflation rate over this time period was 3.6 percent and the average T-bill rate was 4.8 percent. Based on this information, what was the average nominal risk premium?
Average return = (0.03 - 0.10 + 0.24 + 0.22 + 0.12)/5 = 0.102
Average nominal risk premium = 0.102 - 0.048 = 5.40 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 12-10 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Nominal risk premium |
89.
|
You bought one of Great White Shark Repellant Co.'s 10 percent coupon bonds one year ago for $815. These bonds pay annual payments, have a face value of $1,000, and mature 14 years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 14 percent. The inflation rate over the past year was 3.7 percent. What was your total real return on this investment?
Nominal return = ($759.92 - $815 + $100)/$815 = 0.0551 Real return = [(1 + 0.0551)/(1 + 0.037)] - 1 = 1.75 percent |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 12-13 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.3 Topic: Real return |
90.
|
You find a certain stock that had returns of 4 percent, -5 percent, -15 percent, and 16 percent for four of the last five years. The average return of the stock for the 5-year period was 13 percent. What is the standard deviation of the stock's returns for the five-year period?
Return for missing year: 0.04 - 0.05 - 0.15 + 0.16 + x = 0.13 × 5; x = 65 percent
Std dev = √[1/(5 - 1)] [(0.04 - 0.13)2 + (-0.05 - 0.13)2 + (-0.15 - 0.13)2 + (0.16 - 0.13)2 + (0.65 - 0.13)2 = 31.23 percent |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 12-14 Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Standard deviation |
91.
|
A stock had returns of 12 percent, 16 percent, 10 percent, 19 percent, 15 percent, and -6 percent over the last six years. What is the geometric average return on the stock for this period?
Geometric average = (1.12 × 1.16 × 1.10 × 1.19 × 1.15 × 0.94)1/6 - 1 = 10.68 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 12-15 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Geometric average return |
92.
|
Assume that the returns from an asset are normally distributed. The average annual return for the asset is 18.1 percent and the standard deviation of the returns is 32.5 percent. What is the approximate probability that your money will triple in value in a single year?
The upper tail of the 99 percent range = 0.181 + (3 × 0.325) = 1.156 = 115.6 percent, which is less than the 200 percent required to triple your money. Thus, the probability of occurrence is less than 0.5 percent.
|
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy EOC:12-17 Learning Objective: 12-03 The historical risks on various important types of investments. Section: 12.4 Topic: Probability ranges |
93.
|
Over a 30-year period an asset had an arithmetic return of 13 percent and a geometric return of 10.5 percent. Using Blume's formula, what is your best estimate of the future annual returns over the next 5 years?
|
AACSB: Analytic
Blooms: Apply Difficulty: 2 Medium EOC: 12-20 Learning Objective: 12-01 How to calculate the return on an investment. Section: 12.5 Topic: Blume's formula |
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