2. Labrador has issued bonds, common stock, and preferred stock. The YTM for the bonds is 14% and the expected annual return for the preferred stock is
... [Show More] 19%. Which of the following assertions about the expected annual return for the common stock issued by Labrador is most likely to be true?
A. The expected annual return for the common stock is 9%
B. The expected annual return for the common stock is 14%
C. The expected annual return for the common stock is 16%
D. The expected annual return for the common stock is 19%
E. The expected annual return for the common stock is 21%
(Spring 2010, test 3, question 8)
(Fall 2010, test 3, question 1)
(Fall 2011, final, question 10)
(Fall 2012, final, question 10)
(Spring 2013, final, question 12)
Answer: E. The expected annual return for the common stock is 21%
Labrador common stock is most likely to be the riskiest, Labrador bonds are most likely to be the least risky, and Labrador preferred stock is most likely to be in the middle.
Therefore, Labrador common stock should have the highest expected return, Labrador bonds should have the lowest expected return as measured by YTM, and Labrador preferred stock should have an expected return between the expected return of common stock and the YTM of bonds.
Since Labrador’s preferred stock has an expected return of 19%, its common stock should have a return greater than 19%, and 21% is the only alternative that is greater than 19%.
3. Retriever has issued bonds, common stock, and preferred stock. The YTM for the bonds is 12% and the expected annual return for the common stock is 17%. Which of the following assertions about the expected annual return for the preferred stock issued by Retriever is most likely to be true?
A. The expected annual return for the preferred stock is 4%
B. The expected annual return for the preferred stock is 12%
C. The expected annual return for the preferred stock is 14%
D. The expected annual return for the preferred stock is 17%
E. The expected annual return for the preferred stock is 21%
(Spring 2015, test 2, question 6)
(Fall 2015, final, question 7)
Answer: C. The expected annual return for the preferred stock is 14%
Retriever common stock is most likely to be the riskiest, Retriever bonds are most likely to be the least risky, and Retriever preferred stock is most likely to be in the middle.
Therefore, Retriever common stock should have the highest expected return, Retriever bonds should have the lowest expected return as measured by YTM, and Retriever preferred stock should have an expected return between the expected return of common stock and the YTM of bonds.
Since Retriever’s bonds have YTM of 12% and its common stock has an expected return of 17%, its preferred stock should have a return between 12% and 17%, and 14% is the only alternative that is between 12% and 17%.
4. Today, you sold 1 share of Mega stock. The percentage return over the past quarter (from 3 months ago to today) for these shares was 10.42 percent. You purchased the shares 3 months ago at a price of $30.53 per share. You just received $1.87 in dividends. What was the price of the stock when you sold it?
Percentage return = total dollar return ÷ initial value
Total dollar return = cash flow from investment + capital gain
Capital gain = ending value – initial value
Initial value = $30.53 per share
Cash flow from investment = dividends = $1.87
Percentage return = .1042
Percentage return over the past quarter = (cash flow from investment + capital gain) ÷ initial value
= (cash flow from investment + ending price – initial price) ÷ initial value
.1042 = ($1.87 + ending price – $30.53) / $30.53
.1042 × $30.53 = $3.18 = $1.87 + ending price – $30.53
$3.18 – $1.87 + $30.53 = ending price = $31.84
Confirm that the price per share at the end of the quarter is $31.84
Percentage return over the past quarter
= (cash flow from investment + capital gain) ÷ initial value
= (cash flow from investment + ending value – initial value) ÷ initial value
= ($1.87 + $31.84 – $30.53) ÷ $30.53
= ($1.87 + $1.31) ÷ $30.53
= $3.18 ÷ $30.53
= 10.42 percent = percentage return that is given ☺
5. One year ago, Dan purchased 1 share of Buy-Mart stock. A share of Buy-Mart is currently priced at $47.56. Buy-Mart just paid an annual dividend of $1.83 per share. If the stock’s percentage return was -1.45% over the past year (from one year ago to today), what was the price of the Buy-Mart share when Dan bought it?
(Spring 2012, test 3, question 2)
Percentage return = total dollar return ÷ initial value
Total dollar return = cash flow from investment + capital gain
Capital gain = ending value – initial value = ending price – initial price
Cash flow from investment = dividends = $1.83
Capital gain = $47.56 – initial price per share
Percentage return = -1.45% = -0.0145
Percentage return over the past year
= (cash flow from investment + capital gain) ÷ initial price
= (cash flow from investment + ending price – initial price) ÷ initial price
-0.0145 = (1.83 + $47.56 – initial price) ÷ initial price
-0.0145 × initial price = 1.83 + $47.56 – initial price
-0.0145 × initial price = $49.39 – initial price
(-0.0145 × initial price) + initial price = $49.39
(-0.0145 × initial price) + (1 × initial price) = $49.39
(-0.0145 + 1) × initial price = $49.39
0.9855 × initial price = $49.39
initial price = $49.39 / .9855 = $50.12
6. Bentley stock has an expected annual return of 14.60 percent. The stock is currently priced at $60.43 per share and has an expected dividend yield of 5.20 percent. What is the price of the stock expected to be in 1 year?
(Spring 2014, test 3, question 1)
(Fall 2016, test 2, question 9)
Approach to solve
1) Find expected capital appreciation yield
2) Use expected capital appreciation yield to find price expected in 1 year
1) Find expected capital appreciation yield
Expected return = expected dividend yield + expected capital appreciation yield
.1460 = .0520 + expected capital appreciation yield
So expected capital appreciation yield = .1460 – .0520
= .0940
2) Use expected capital appreciation yield to find price expected in 1 year
Expected capital appreciation yield = expected capital gain / initial value
= (expected ending value – expected initial value) / expected initial value
Expected initial value = today’s stock price = $60.43
Expected ending value = expected stock price in 1 year
So .0940 = (expected ending value – 60.43) / 60.43
.0940 × 60.43 = 5.68 = expected ending value – 60.43
expected ending value = 5.68 + 60.43
= $66.11
Confirm
Expected return = expected dividend yield + expected capital appreciation yield
= .0520 + (5.68/60.43)
= .0520 + .0940 = .1460
Another approach to solve
1) Find expected dividend
2) Use expected dividend to find price expected in 1 year
1) Find expected dividend
Expected dividend yield = expected dividends / expected initial value
.0520 = expected dividends / $60.43
Expected dividends = .0520 × $60.43 = $3.14
2) Use expected dividend to find price expected in 1 year
P0 = (D1 + P1) ÷ (1 + R)
60.43 = (3.14 + P1) ÷ (1.1460)
60.43 × 1.1460 = (3.14 + P1)
69.25 = (3.14 + P1)
P1 = 69.25 – 3.14
= $66.11
7. Wheel Source stock has an expected annual return of 17.40 percent. The stock is expected to be priced at $72.37 per share in 1 year and the stock currently has an expected dividend yield of 5.30 percent. What is the current price of the stock?
(Fall 2011, test 3, question 2)
(Spring 2013, test 3, question 2)
(Fall 2013, final, question 9)
(Spring 2017, test 3, question 1)
(Fall 2018, test 2, question 7)
Approach to solve
1) Find expected capital appreciation yield
2) Use expected capital appreciation yield to find current stock price
1) Find expected capital appreciation yield
Expected return = expected dividend yield + expected capital appreciation yield
.174 = .053 + expected capital appreciation yield
So expected capital appreciation yield = .1740 – .0530 = .1210
2) Use expected capital appreciation yield to find current stock price
Expected capital appreciation yield = expected capital gain / initial value
= (expected ending value – expected initial value) / expected initial value
Expected ending value = expected stock price in 1 year = $72.37
Expected initial value = today’s stock price
So .1210 = (72.37 – expected initial value) / expected initial value
.1210 × expected initial value = 72.37 – expected initial value
(.1210 × expected initial value) + expected initial value = 72.37
(.1210 × expected initial value) + (1 × expected initial value) = 72.37
(.1210 + 1) × expected initial value = 72.37
1.1210 × expected initial value = 72.37
expected initial value = 72.37 / 1.1210 = $64.56 = today’s stock price
Confirm
Expected return = expected dividend yield + expected capital appreciation yield
= expected dividend yield + (expected capital gain / expected initial value)
= expected dividend yield + [(expected ending value – expected initial value) / expected initial value]
= .0530 + [(72.37 – 64.56) / 64.56]
= .0530 + [7.81 / 64.56]
= .0530 + .1210
= .1740 ☺
8. What is the price of PBJ stock expected to be in 2 years if it has an annual expected return of 9.83 percent, is expected to be priced at $29.65 in 1 year, and is expected to pay an annual dividend of $1.59 in 3 years and be priced at $34.72 in 3 years? The stock is expected to pay annual dividends forever.
Set up time line with what we know and don’t know
Time 0 1 2 3
Time 0 1 year 2 years 3 years
Variable P1 P2 D3 and P3
Expected Amount $29.65 ? D3 = 1.59; P3= 34.72
Expected annual return = .0983
Pt = (Dt+1 + Pt+1) ÷ (1 + R)
In this case, we can set t = 2 to find P2 as the sum of D3 and P3 discounted by (1+R)
R is the annual return expected on the stock divided by the number of possible dividends per year = 9.83% ÷ 1 = 9.83% = .0983
If t = 2, P2 = (D3 + P3) ÷ (1 + R)
= (1.59 + 34.72) / (1.0983) = 36.31 / 1.0983 = $33.06
The stock is expected to be priced at $33.06 in 2 years
Note that the expected price in 1 year of $29.65 is irrelevant to solving the problem. If we knew D2, we could use P1 and D2 to solve for P2.
Note that the fact that the stock is expected to pay annual dividends forever is not relevant to the solution. Nothing is mentioned about the amount of these dividends that could be useful (such as whether they are fixed or grow at a constant rate forever).
9. What is the price of PBJ stock expected to be in 3 years if it has an annual expected return of 11.81 percent, is expected to pay an annual dividend of $2.39 in 2 years and an annual dividend of $1.72 in 3 years, and is expected to be priced at $38.42 in 2 years? The stock is expected to pay annual dividends forever.
Set up time line with what we know and don’t know
Time 0 1 2 3
Time 0 1 year 2 years 3 years
Variable D2 and P2 D3 and P3
Expected Amount D2 = 2.39; P2= 38.42 D3 = 1.72; P3 = ?
Expected annual return = .1181
Pt = (Dt+1 + Pt+1) ÷ (1 + R)
In this case, we can set t = 2 to find P3 from the fact that P2 is the sum of D3 and P3 discounted by (1+R)
R is the annual return expected on the stock divided by the number of possible dividends per year = 11.81% ÷ 1 = 11.81% = .1181
If t = 2, P2 = (D3 + P3) ÷ (1 + R)
So 38.42 = (1.72 + P3) / (1.1181)
So 38.42 × 1.1181 = 42.96 = (1.72 + P3)
So P3 = 42.96 – 1.72 = $41.24
The stock is expected to be priced at $41.24 in 3 years
Note that in this case, with the information that’s given, the expected dividend in 2 years is not relevant to finding the expected price of the stock in 2 years. Setting up timelines is very useful for determining what information is irrelevant, what information is relevant, and how to use the relevant information effectively.
Note that the fact that the stock is expected to pay annual dividends forever is not relevant to the solution. Nothing is mentioned about the amount of these dividends that could be useful (such as whether they are fixed or grow at a constant rate forever).
10. Electric Blue stock is expected to pay a dividend of $3.61 in 1 year and a dividend of $4.03 in 2 years. The stock is expected to be priced at $40.81 in 1 year and at $41.78 in 2 years. What is the current price of Electric Blue stock? The stock’s dividend is paid annually and the next dividend is expected in 1 year.
(Fall 2012, test 3, question 3)
(Fall 2013, test 3, question 3)
(Fall 2014, final question 10)
(Fall 2018, test 2, question 8)
We want to determine the value of P0 and we know that P0 = (D1 + P1) / (1 + R)
We are given D1 and P1, but do not know R
However, we can get R from P1 = (D2 + P2) / (1 + R), because we are given P1, P2, and D2
Approach:
1) Find R
2) Find P0
1) Find R
P1 = (D2 + P2) / (1 + R)
P1 = 40.81
P2 = 41.78
D2 = 4.03
40.81 = (4.03 + 41.78) / (1 + R)
= (45.81) / (1 + R)
So 40.81 × (1 + R) = 45.81
So 1 + R = 45.81 / 40.81 = 1.1225
So R = 1.1225 – 1 = 0.1225 = 12.25%
2) Find P0
P0 = (D1 + P1) / (1 + R)
D1 = 3.61
P1 = 40.81
R = .1225
P0 = (3.61 + 40.81) / 1.1225
= 44.42 / 1.1225
= $39.57
P0 = $39.57
11. Electric Yellow stock is expected to pay a dividend of $2.71 in 1 year and a dividend of $3.06 in 2 years. The stock is currently priced at $38.60 and is expected to be priced at $38.04 in 1 year. What is the price of Electric Yellow stock expected to be in 2 years? The stock’s dividend is paid annually and the next dividend is expected in 1 year.
(Spring 2012, test 3, question 3)
(Fall 2017, test 2, question 8)
We want to determine the value of P2 and we know that P1 = (D2 + P2) / (1 + R)
We are given P1 and D2, but do not know R
However, we can get R from P0 = (D1 + P1) / (1 + R), because we are given P0, P1, and D1
Approach:
1) Find R
2) Find P2
1) Find R
P0 = (D1 + P1) / (1 + R)
P0 = 38.60
P1 = 38.04
D1 = 2.71
38.60 = (2.71 + 38.04) / (1 + R)
= (40.75) / (1 + R)
So 38.60 × (1 + R) = 40.75
So 1 + R = 40.75 / 38.60 = 1.0557
So R = 1.0557 – 1 = 0.0557 = 5.57%
2) Find P2
P1 = (D2 + P2) / (1 + R)
P1 = 38.04
D2 = 3.06
R = 0.0557
38.04 = (3.06 + P2) / 1.0557
38.04 × 1.0557 = (3.06 + P2)
P2 = (38.04 × 1.0557) – 3.06
= $37.10
Answers may differ slightly due to rounding
12. Electric Pink stock is expected to pay a dividend of $1.36 in 1 year. The stock is currently priced at $22.50, is expected to be priced at $25.26 in 1 year, and is expected to be priced at $27.84 in 2 years. What is the dividend in 2 years expected to be for Electric Pink stock? The stock’s dividend is paid annually and the next dividend is expected in 1 year.
(Spring 2013, test 3, question 3)
(Spring 2015, final, question 12)
We want to determine the value of D2 and we know that P1 = (D2 + P2) / (1 + R)
We are given P1 and P2, but do not know R
However, we can get R from P0 = (D1 + P1) / (1 + R), because we are given P0, P1, and D1
Approach:
1) Find R
2) Find D2
1) Find R
P0 = (D1 + P1) / (1 + R)
P0 = 22.50
P1 = 25.26
D1 = 1.36
22.50 = (1.36 + 25.26) / (1 + R)
= (26.62) / (1 + R)
So 22.50 × (1 + R) = 26.62
So 1 + R = 26.62 / 22.50 = 1.1831
So R = 1.1831 – 1 = 0.1831 = 18.31%
2) Find D2
P1 = (D2 + P2) / (1 + R)
P1 = 25.26
P2 = 27.84
R = 0.1831
25.26 = (D2 + 27.84) / 1.1831
25.26 × 1.1831 = (D2 + 27.84)
D2 = (25.26 × 1.1831) – 27.84
= $2.05
Answers may differ slightly due to rounding
13. Electric Green stock is expected to pay a dividend of $1.14 in 2 years. The stock is currently priced at $22.60, is expected to be priced at $25.20 in 1 year, and is expected to be priced at $27.82 in 2 years. What is the dividend in 1 year expected to be for Electric Green stock? The stock’s dividend is paid annually and the next dividend is expected in 1 year.
(Spring 2016, test 3, question 1)
We want to determine the value of D1 and we know that P0 = (D1 + P1) / (1 + R)
We are given P0 and P1, but do not know R
However, we can get R from P1 = (D2 + P2) / (1 + R), because we are given P1, P2, and D2
Approach:
1) Find R
2) Find D1
1) Find R
P1 = (D2 + P2) / (1 + R)
P1 = 25.20
P2 = 27.82
D2 = 1.14
25.20 = (1.14 + 27.82) / (1 + R)
= (28.96) / (1 + R)
So 25.20 × (1 + R) = 28.96
So 1 + R = 28.96 / 25.20 = 1.1492
So R = 1.1492 – 1 = 0.1492 = 14.92%
2) Find D1
P0 = (D1 + P1) / (1 + R)
22.60 = (D1 + 25.20) / 1.1492
22.60 × 1.1492 = (D1 + 25.20)
D1 = (22.60 × 1.1492) – 25.20
= $0.77
D1 = $0.77
14. Aldon owns 1 share of stock A and 1 share of stock B. In 1 year from today, the total value of his holdings is expected to be $118. Stock A is currently priced at $45.87, has an expected return of 10.90%, and is expected to pay a dividend of $2.71 in 1 year from today. Stock B has an expected return of 15.32% and is expected to pay a dividend of $8.37 in 1 year from today. What is the price of stock B today?
(Spring 2018, test 2, question 9)
Approach to solve
1) Find the expected price of stock A in 1 year
2) Find the expected price of stock B in 1 year
3) Find the price of stock B today
1) Find the expected price of stock A in 1 year
P0 = (D1 + P1) / (1 + expected return) = (D1 + P1) / (1 + R)
R = .1090
P0 = 45.87
D1 = 2.71
45.87 = (2.71 + P1) / 1.1090
45.87 × 1.1090 = (2.71 + P1)
50.87 = (2.71 + P1)
P1 = 50.87 – 2.71 = $48.16
2) Find the expected price of stock B in 1 year
We know that the expected price of stock A in 1 year + the expected price of stock B in 1 year
= $118.00
Therefore, the expected price of stock B in 1 year
= $118.00 – expected price of stock A in 1 year
= $118.00 – $48.16 = $69.84
3) Find the price of stock B today
P0 = (D1 + P1) / (1 + expected return) = (D1 + P1) / (1 + R)
R = .1532
D1 = 8.37
P1 = 69.84
P0 = (8.37 + 69.84) / 1.1532
= 78.21 / 1.1532
= 67.82
15. Alvie owns 1 share of stock A and 1 share of stock B. In 1 year from today, the total value of his holdings is expected to be $143. Stock A is currently priced at $53.74, has an expected return of 9.70%, and is expected to pay a dividend of $5.11 in 1 year from today. Stock B is currently priced at $77.49 and is expected to pay a dividend of $1.77 in 1 year from today. What is the expected return for stock B?
(Fall 2014, test 3, question 2)
Approach to solve
1) Find the expected price of stock A in 1 year
2) Find the expected price of stock B in 1 year
3) Find the expected return for stock B
1) Find the expected price of stock A in 1 year
P0 = (D1 + P1) / (1 + expected return) = (D1 + P1) / (1 + R)
R = .0970
P0 = 53.74
D1 = 5.11
53.74 = (5.11 + P1) / 1.0970
53.74 × 1.0970 = (5.11 + P1)
58.95 = (5.11 + P1)
P1 = 58.95 – 5.11 = $53.84
2) Find the expected price of stock B in 1 year
We know that the expected price of stock A in 1 year + the expected price of stock B in 1 year
= $143.00
Therefore, the expected price of stock B in 1 year
= $143.00 – expected price of stock A in 1 year
= $143.00 – $53.84 = $89.16
3) Find the expected return for stock B
P0 = (D1 + P1) / (1 + expected return) = (D1 + P1) / (1 + R)
P0 = 77.49
D1 = 1.77
P1 = 89.16
77.49 = (1.77 + 89.16) / (1+R)
77.49 = 90.93 / (1+R)
So 1 + R = 90.93 / 77.49
= 1.1734
So R = .1734 = 17.34% [Show Less]