BUSI 683 - MONEY AND CAPITAL
MARKETS - Stock Valuation
Question Bank - Set 1
Liberty University
Question 1
Question
A company pays an annual dividend of 4.50pershare.Iftherequiredrateofreturnonthestockis10
Solution
Step 1: Calculate the Dividend Growth Rate Given that the annual dividend
grows at a constant rate of 5
Step 2: Calculate the Expected Dividend Next Year The dividend expected
next year can be calculated using the formula for constant growth dividends:
D1=D0×(1 + g)
D1= 4.50 ×(1 + 0.05)
D1= 4.50 ×1.05
D1= 4.725
Step 3: Calculate the Price of the Stock The price of the stock can be
calculated using the Gordon Growth Model formula:
P0=D1
r−g
Where: - P0is the current value of the stock - D1is the expected dividend next
year - ris the required rate of return - gis the dividend growth rate
Plugging in the values:
P0=4.725
0.10 −0.05
P0=4.725
0.05
P0= 94.50
Therefore, the current value of the stock is 94.50.
Question 2
Question
A company is expected to pay an annual dividend of 5.00pershareindefinitely.Iftherequiredrateofreturnis8%perannum, whatisthevalueofthestock?
Solution
Step 1: We can use the Gordon Growth Model to find the value of the stock.
The formula is given by:
P0=D0×(1 + g)
r−g
where: P0= Value of the stock, D0= Dividend per share, r= Required rate
of return, g= Growth rate of dividends.
Step 2: In this case, D0= 5.00, r= 0.08, and since the dividends are
expected to be paid indefinitely, we can assume a perpetual growth rate gthat
is equal to the rate of inflation. Assuming an inflation rate of 3%, we get
g= 0.03.
Step 3: Now we can substitute the values into the formula:
P0=5.00 ×(1 + 0.03)
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the value of the stock is 103pershare.
Question 3
Question
A company is expected to pay its first annual dividend of 2.50pershareoneyearfromnow.Dividendsareexpectedtogrowataconstantrateof6
Solution
Step 1: Calculate the expected dividend per share next year. Since the first divi-
dend will be 2.50pershareanddividendsareexpectedtogrowataconstantrateof 6D1=
D0×(1 + g)
D1= $2.50 ×(1 + 0.06) = $2.65
Step 2: Calculate the constant growth rate, g, as a decimal. The constant
growth rate is given as 6
g=6
100 = 0.06
2
Step 3: Calculate the price of the stock using the dividend discount model.
The price of the stock can be calculated using the formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= expected dividend per share
next year - r= required rate of return on the stock - g= constant growth rate
Substitute the values into the formula:
P0=$2.65
0.12 −0.06
P0=$2.65
0.06
P0= $44.17
Therefore, the current value of the stock is
$
44.17 per share.
Question 4
Question
A company just paid a dividend of 5pershare.T hedividendisexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend growth rate. Given: Dividend (D0) = 5pershareDividendgrowthrate(g) =
8
Thus, the expected dividend for next year (D1) is:
D1 = D0×(1 + g)
D1=5×(1 + 0.08)
D1=5×1.08 =
5.40
Step 2: Calculate the required rate of return. Given: Required rate of return
(r) = 15
Step 3: Calculate the stock price using the Gordon Growth Model formula:
P0 = D1
r−g
P0 = 5.40
0.15 −0.08
P0 = 5.40
0.07 =
77.14
Therefore, the current stock price is 77.14pershare.
3
Question 5
Question
A company is expected to pay an annual dividend of 3.00pershareindefinitely.Iftherequiredrateofreturnis7
Solution
Step 1: Identify the variables given in the question.
In this case, we have:
Annual dividend: D= $3.00
Required rate of return: r= 7% = 0.07
Step 2: Use the Gordon Growth Model formula to calculate the present value
of the stock.
The Gordon Growth Model is given by:
P0=D
r−g
Where: - P0= Present value of the stock - D= Annual dividend - r= Required
rate of return - g= Growth rate of dividends
Step 3: Calculate the present value of the stock.
Since the company is expected to pay an annual dividend indefinitely, we can as-
sume the dividends will grow at a constant rate, which means g= 0. Therefore,
the formula simplifies to:
P0=D
r=3.00
0.07 = $42.86
Step 4: State the final answer.
The present value of the stock is $42.86.
Question 6
Question
A company just paid a dividend of 5pershare.T herequiredrateof returnonthecompany′sstockis12
Solution
Step 1: Calculate the dividend growth rate. Given that the dividends are
expected to grow at a rate of 5
Dividend Growth Rate (g) = 0.05
4
Step 2: Use the Dividend Discount Model (DDM) formula to calculate the
price of the stock. The price of the stock using the DDM formula can be
calculated as follows:
Stock Price = Dividends Next Year
Required Rate of Return - Dividend Growth Rate
where
Dividends Next Year = Dividend ×(1 + Dividend Growth Rate)
Required Rate of Return = 0.12
Step 3: Substitute the values into the formula and calculate.
Dividends Next Year = $5 ×(1 + 0.05) = $5.25
Stock Price = $5.25
0.12 −0.05 =$5.25
0.07 ≈$75
Therefore, the current price of the stock is approximately
$
75.
Question 7
Question
A company is expected to pay a dividend of 3 dollars per share next year and
is expected to grow its dividends at a constant rate of 6% per year indefinitely.
If the required rate of return is 10%, what is the current price of the stock?
Solution
Step 1: Calculate the dividend in the second year.
Dividend in the second year = Dividend in the first year ×(1 + growth rate)
= 3 ×(1 + 0.06)
= 3 ×1.06
= 3.18
Step 2: Calculate the expected dividend and price of the stock using the
dividend discount model. The price of a stock is given by the formula:
P0=D1
r−g
where: - P0is the price of the stock now, - D1is the dividend expected next
year, - ris the required rate of return, - gis the growth rate of the dividends.
5
Plugging in the values, we get:
P0=3.18
0.10 −0.06
=3.18
0.04
= 79.50
Therefore, the current price of the stock is 79.50.
Question 8
Question
A company’s stock is currently trading at 90pershare.T hecompanyisexpectedtopayadividendof3
per share next year, and dividends are expected to grow at a constant rate of 5
Solution
Step 1: Calculate the dividend in the next year. The dividend paid next year
is given as D1 =3.
Step 2: Calculate the growth rate of dividends. The growth rate of dividends
is given as g = 5
Step 3: Calculate the required rate of return. The required rate of return is
given as 10
Step 4: Use the Gordon Growth Model to calculate the intrinsic value of the
stock. The Gordon Growth Model is:
P0=D1
r−g
Substitute the given values to find the intrinsic value of the stock:
P0=3
0.10 −0.05
P0=3
0.05
P0= 60
Therefore, the intrinsic value of the stock based on the dividend discount
model is 60pershare.
Question 9
Question
A company’s stock is currently priced at
$50 per share. The company pays a yearly dividend of
6
$2.50 per share, which is expected to grow at a constant rate of 6% per year.
If the required rate of return on the stock is 10%, what is the stock’s intrinsic
value?
Solution
Let’s denote the annual dividend as D(current dividend) and D1(dividend next
year), the growth rate as g, the required rate of return as r, and the intrinsic
value as V0. We can use the Gordon growth model to find the intrinsic value of
the stock:
V0=D1
r−g
Step 1: Find the dividend next year
The dividend next year, D1,is found by multiplying the current dividend by (1 + g) :
D1=D×(1 + g)=2.50 ×(1 + 0.06) = 2.50 ×1.06 = 2.65
Step 2: Calculate the intrinsic value of the stock
Now we can substitute the values into the Gordon growth model formula:
V0=D1
r−g=2.65
0.10 −0.06 =2.65
0.04 = 66.25
Therefore, the intrinsic value of the stock is
$66.25.
Question 10
Question
A company’s stock currently pays an annual dividend of 5.50pershare, anddividendsareexpectedtogrowatarateof 7
Solution
Let’s denote the current value of the stock as P0, the annual dividend as D0
(5.50), thegrowthrateofdividendsasg(7
Step 1: Calculate the dividend in the next period D1using the growth rate
formula:
D1=D0×(1 + g)
D1= 5.50 ×(1 + 0.07) = 5.50 ×1.07 = 5.885 (rounded to 3 decimal places)
Step 2: Calculate the price of the stock P1at the end of the first year using
the dividend discount model:
P1=D1
r−g
7
P1=5.885
0.12 −0.07 =5.885
0.05 = 117.70 (rounded to 2 decimal places)
Step 3: Calculate the current value of the stock P0using the price of the
stock at the end of the first year:
P0=D1
r+P1
(1 + r)
P0=5.885
0.12 +117.70
(1 + 0.12)
P0= 49.04 + 117.70
1.12 = 49.04 + 105.45 = 154.49 (rounded to 2 decimal places)
Therefore, the current value of the stock is
$
154.49.
Question 11
Question
A company is expected to pay a dividend of 3.50pershareoneyearf romnow.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the expected dividend in year 2 using the growth rate:
D2=D1×(1 + g)
D2= 3.50 ×(1 + 0.05)
D2= 3.50 ×1.05 = 3.675
Step 2: Calculate the constant growth rate dividend discount model (Gordon
growth model) formula to find the current stock price:
P0=D1
r−g
Where: - P0= current price of the stock - D1= expected dividend next year -
r= required rate of return - g= growth rate
Substitute the given values into the formula:
P0=3.50
0.10 −0.05
P0=3.50
0.05
P0= 70
Therefore, the current value of the stock is 70.
8
Question 12
Question
A company pays an annual dividend of 3.50pershare.Iftherequiredrateofreturnis8
Solution
Step 1: Calculate the growth rate of dividends using the dividend growth model
formula P0=D1
r−g, where P0is the current stock price, D1is the next year’s
dividend, ris the required rate of return, and gis the growth rate of dividends.
Step 2: Given that D1= $3.50, r= 0.08, and solving for g, we have:
P0=3.50
0.08 −g
Step 3: Assume the company’s dividends are expected to grow at a constant
rate. Hence, we can express D1in terms of the current dividend D0and the
growth rate g:D1=D0×(1 + g).
Step 4: Since we know D0= $3.50, D1= 3.50 ×(1 + g)=3.50 + 3.50g.
Step 5: Substituting 3.50 + 3.50gfor D1in the initial formula, we have:
P0=3.50 + 3.50g
0.08 −g
Step 6: Simplifying the equation, we get:
P0=3.50(1 + g)
0.08 −g
Step 7: Now, substitute D0= $3.50 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 8: Substitute r= 0.08 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 9: Equate the equation to the current stock price:
P0=3.50(1 + g)
0.08 −g
Therefore, the current stock price can be calculated using this formula.
Question 13
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
9
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock based on the expected dividend for next year and the required rate of
return.
Step 1: The expected dividend for next year is calculated using the formula:
D1 = D0×(1 + g)
where: D1 = Expected dividend for next year, D0 = Current dividend, g=
Growth rate.
Plugging in the values:
D1=3.50 ×(1 + 0.05)
D1=3.50 ×1.05
D1 = 3.675
Therefore, the expected dividend for next year is 3.675pershare.
Step 2: The Gordon Growth Model formula is:
P0 = D1
r−g
where: P0 = Current value of the stock, D1 = Expected dividend for next year,
r= Required rate of return, g= Growth rate.
Plugging in the values:
P0 = 3.675
0.10 −0.05
P0 = 3.675
0.05
P0 = 73.50
Therefore, the current value of the stock is 73.50pershare.
Question 14
Question
Company XYZ just paid a dividend of 3.50pershare.T hedividendisexpectedtogrowataconstantrateof 4
10
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Calculate the dividend in year 1. The dividend in year 1 (D1) can
be calculated using the formula for constant growth dividends:
D1 = D0×(1 + g)
D1=3.50 ×(1 + 0.04)
D1=3.50 ×1.04
D1=3.64
Step 3: Calculate the price of the stock. The price of the stock (P0) can be
calculated using the Gordon Growth Model formula:
P0 = D1
r−g
where: - D1 = 3.64 (dividend in year 1) - r= 0.10 (required rate of return) -
g= 0.04 (dividend growth rate)
P0 = 3.64
0.10 −0.04
P0 = 3.64
0.06
P0 = 60.67
Therefore, the current stock price of Company XYZ is 60.67pershare.
Question 15
Question
A company’s stock is currently priced at $80 per share. The company is expected
to pay a dividend of $4 per share in one year. If the dividends are expected to
grow at a rate of 7% per year indefinitely, what is the expected rate of return
for an investor who buys the stock at the current price?
Solution
Step 1: Calculate the expected dividend in two years Given that the dividend
is expected to grow at a rate of 7% per year, the dividend in two years will be:
$4 ×(1 + 0.07) = $4.28
11
Step 2: Calculate the dividend yield The dividend yield is the expected
dividend in one year divided by the current stock price:
Dividend Yield = $4
$80 = 0.05
Step 3: Calculate the expected capital gains yield The capital gains yield is
the growth rate of dividends:
Capital Gains Yield = 0.07
Step 4: Calculate the total expected rate of return The total expected rate
of return is the sum of the dividend yield and the capital gains yield:
Expected Rate of Return = Dividend Yield+Capital Gains Yield = 0.05+0.07 = 0.12
Therefore, the expected rate of return for an investor who buys the stock at the
current price is 12%.
Question 16
Question
A company pays a dividend of
$
3 per share annually and is expected to grow
at a constant rate of 6
Solution
Let’s denote the current value of the stock as P0, the dividend per share as D0,
the growth rate as g, and the required rate of return as r.
Step 1: Calculate the dividend next year, D1, using the growth rate formula:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.06)
D1= 3 ×1.06 = 3.18
Step 2: Calculate the price of the stock, P1, at the end of the year using
the dividend discount model formula:
P1=D1
r−g
P1=3.18
0.10 −0.06
P1=3.18
0.04 = 79.50
12
Step 3: Use the formula for the current value of the stock as the present
value of next year’s stock price:
P0=P1
1 + r
P0=79.50
1+0.10
P0=79.50
1.10 = 72.27
Therefore, the current value of the stock is
$
72.27.
Question 17
Question
A company pays a dividend of 8.50pershareannuallyandthedividendisexpectedtogrowataconstantrateof5
Solution
Let’s denote the current stock price as P0, the dividend paid per share as D0
(which is 8.50), thegrowthrateofdividendsasg (which is 5
Step 1: Calculate the expected dividend next year, D1, using the dividend
growth rate formula:
D1=D0×(1 + g)
D1= 8.50 ×(1 + 0.05)
D1= 8.50 ×1.05
D1= 8.925
Step 2: Calculate the dividend yield, D1/P0, which should be equal to the
required rate of return: D1
P0
=r
8.925
P0
= 0.12
P0=8.925
0.12
P0= 74.375
Therefore, the current stock price is 74.38pershare.
Question 18
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
13
Solution
Step 1: Calculate the dividend in year 2.
D2=D1×(1 + Growth Rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Calculate the required rate of return as a percentage.
r= 10%
Step 3: Use the Gordon Growth Model to find the stock price.
P0=D1
r−g=$3.50
0.10 −0.05 = $70.00
Therefore, the current value of the stock is
$
70.00 per share.
Question 19
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend expected in the second year. Step 2: Calculate
the stock price using the Gordon Growth Model.
Step 1: Given: Dividend in the first year, D1 = 3.50Dividendgrowthrate, g =
5
The dividend in the second year, D2, can be calculated using the formula:
D2 = D1×(1 + g)
D2 = $3.50 ×(1 + 0.05)
D2 = $3.50 ×1.05
D2 = $3.675
Step 2: The stock price, P0, can be calculated using the Gordon Growth
Model:
P0 = D1×(1 + g)
r−g
where r is the required rate of return.
Given: D1 = 3.50g= 5r= 10
Substitute the values into the formula:
P0 = $3.50 ×(1 + 0.05)
0.10 −0.05
14
P0 = $3.50 ×1.05
0.05
P0 = $3.675
0.05
P0 = $73.50
Therefore, the current price of the stock is 73.50pershare.
Question 20
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
Solution
Step 1: Determine the dividend in the next year using the growth rate.
D1=D0×(1 + g)=3.50 ×(1 + 0.05) = 3.675
Step 2: Calculate the dividend yield using the required rate of return.
D1=D1
r−g
3.675 = 3.675
0.10 −0.05
3.675 = 3.675
0.05
3.675 = 73.50
Therefore, the current stock price for Company XYZ is 73.50.
Question 21
Question
ABC Company is expected to pay a dividend of 3.00persharenextyear, andthedividendsareexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the constant growth rate (g). Since the dividends are expected
to grow at a constant rate of 5
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock. The Gordon Growth Model is given by:
P0=D1
r−g
15
where: - P0is the current value of the stock, - D1is the dividend expected to be
paid next year, - ris the required rate of return on the stock, - gis the constant
growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
P0=3.00
0.10 −0.05
Step 4: Calculate the current value of the stock.
P0=3.00
0.05 = 60.00
Therefore, the current value of the stock is 60.00.
Question 22
Question
A company paid a dividend of $2.50 per share last year, and is expected to
increase its dividend by 5
Solution
Step 1: Calculate the next dividend payment. Given that the company is in-
creasing its dividend by 5
D1 = $2.50 ×1.05 = $2.625
Step 2: Determine the dividend growth rate. The dividend growth rate (g)
is 5
Step 3: Calculate the required rate of return. The required rate of return
(r) is 10
Step 4: Apply the Gordon Growth Model formula to find the current value
of the stock:
P0=D1
r−g
P0=$2.625
0.10 −0.05
P0=$2.625
0.05
P0= $52.50
Therefore, the current value of the stock is $52.50.
16
Question 23
Question
A company’s stock is expected to pay a dividend of 3.50 dollars next year, and
dividends are expected to grow at a constant rate of 5% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Step 1: Calculate the dividend in the second year using the growth rate. Step
2: Calculate the current value of the stock using the dividend discount model.
Step 1: The dividend in the second year will be:
D2=D1×(1 + growth rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: The current value of the stock can be calculated using the dividend
discount model formula:
P0=D1
r−g
where: - P0is the current value of the stock, - D1is the dividend next year
(
$
3.50), - ris the required rate of return (10%), and - gis the growth rate of
dividends (5%).
Substitute the values into the formula:
P0=$3.50
0.10 −0.05 =$3.50
0.05 = $70
Therefore, the current value of the stock is
$
70.
Question 24
Question
A company’s stock is expected to have dividends of $2, $2.50, and $3 in the
next three years. After that, the dividends are expected to grow at a constant
rate of 5% per year indefinitely. If the required rate of return on the stock is
10%, what is the current value of the stock?
Solution
Step 1: Calculate the present value of the dividends for the next three years.
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
17
where D1, D2, D3are the dividends for the next three years and ris the required
rate of return. Substitute the given values:
P V =2
(1 + 0.10)1+2.50
(1 + 0.10)2+3
(1 + 0.10)3
P V =2
1.10 +2.50
1.102+3
1.103
P V ≈1.8182 + 2.0661 + 2.3136
P V ≈6.1979
Step 2: Calculate the expected dividend at year 4 and the price of the stock
using the Gordon Growth Model. The formula for the Gordon Growth Model
is:
P4=D4
r−g
where D4is the dividend at year 4, ris the required rate of return, and gis the
growth rate of dividends. Substitute the given values:
P4=3×(1 + 0.05)
0.10 −0.05
P4=3×1.05
0.05
P4=3.15
0.05
P4= 63
Step 3: Calculate the present value of the stock. The current value of the
stock is the sum of the present value of the dividends for the next three years
and the price of the stock at year 4.
Current V alue =P V +P4
Current V alue = 6.1979 + 63
Current V alue ≈69.1979
Therefore, the current value of the stock is approximately $69.20.
Question 25
Question
A company pays an annual dividend of 3pershareandexpectsthedividendstogrowatarateof 5
18
Solution
Step 1: Calculate the dividend in the next year using the growth rate. Step 2:
Use the dividend discount model to find the current value of the stock.
Step 1: The dividend in the next year can be calculated using the formula
for the dividend growth rate:
D1=D0×(1 + g)
where: - D1is the dividend in the next year, - D0is the current dividend, and
-gis the growth rate.
Plugging in the values:
D1= 3 ×(1 + 0.05) = 3.15
Step 2: The current value of the stock can be calculated using the dividend
discount model:
P0=D1
r−g
where: - P0is the current value of the stock, - ris the required rate of return,
and - gis the growth rate.
Plugging in the values:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 26
Question
A company is expected to pay an annual dividend of 4.50pershareindefinitely.Iftherequiredrateofreturnforinvestorsis10
Solution
Step 1: Calculate the fair value of the stock using the Gordon Growth Model
formula:
Fair Value = Dividends per Share
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend indefinitely,
the growth rate can be assumed to be equal to the nominal growth rate of the
economy. Let’s assume a nominal growth rate of 5
Step 3: Substitute the values into the formula:
Fair Value = 4.50
0.10 −0.05
19
Fair Value = 4.50
0.05
Fair Value = 90
Therefore, the fair value of the stock is 90pershare.
Question 27
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay a dividend of $5 per share at the end of the year. Dividends
are expected to grow at a constant rate of 5% per year. If the required rate of
return on the stock is 10%, what is the stock’s value?
Solution
Step 1: Calculate the expected dividend in the next year.
Expected Dividend in the next year = $5 ×(1 + 0.05) = $5.25
Step 2: Since the dividends are expected to grow at a constant rate, we can
use the Gordon Growth Model to find the stock’s value.
Stock Value = Expected Dividend in the next year
Required Rate of Return −Growth Rate of Dividends
Stock Value = $5.25
0.10 −0.05 =$5.25
0.05 = $105
Therefore, the stock’s value is $105.□
Question 28
Question
A company is expected to pay a dividend of 2.50 per share at the end of the
year. Dividends are expected to grow at a rate of 5% per year indefinitely. If
the required rate of return is 10%, what is the stock’s current price?
Solution
Step 1: Calculate the dividend one year from now using the growth rate. Step
2: Calculate the price of the stock using the dividend discount model. Step 3:
Substitute the given values into the formula to find the stock’s current price.
Step 1: Calculate the dividend one year from now. The dividend next year
is given by:
D1=D0×(1 + g)
20
where: - D0= current dividend per share = 2.50 - g= growth rate = 5% = 0.05
D1= 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Therefore, the dividend one year from now is 2.625.
Step 2: Calculate the price of the stock using the dividend discount model.
The price of the stock is given by:
P0=D1
r−g
where: - D1= dividend one year from now - r= required rate of return =
10% = 0.10 - g= growth rate = 5% = 0.05
Step 3: Substitute the values into the formula.
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the stock’s current price is 52.50.
Question 29
Question
A company expects to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof8
Solution
Step 1: Calculate the expected dividend in year 2. Step 2: Determine the
expected stock price in year 1. Step 3: Calculate the present value of the stock
price in year 1 to find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated using the formula
for the dividend in any future year:
D1=D0×(1 + g)
where: D1= Dividend in year 1 = 5.00D0= Dividend in the current year g=
Growth rate of dividends = 8
Therefore, the expected dividend in year 2 is:
D1=
5.00 ×(1 + 0.08) =5.40
Step 2: The expected stock price in year 1 can be calculated using the
dividend discount model formula:
P1=D1
r−g
21
where: P1= Stock price in year 1 D1= Dividend in year 1 r= Required rate
of return = 12g= Growth rate of dividends = 8
Substitute the known values into the formula:
P1=
5.400.12−0.08= 5.40 0.04= 135
Step 3: The present value of the stock price in year 1 (current value of the
stock) can be calculated by discounting the stock price in year 1 back to the
present value using the formula:
P V =P1
(1 + r)1
where: P V = Present value of the stock P1= Stock price in year 1 r= Required
rate of return = 12
Substitute the known values into the formula:
P V =
135(1+0.12)1=135 1.12≈120.54
Therefore, the current value of the stock is approximately 120.54.
Question 30
Question
A company is expected to pay a dividend of 5.00persharenextyear, anddividendsareexpectedtogrowatarateof8
Solution
Let’s denote the current price of the stock as P0, the dividend next year as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the expected dividend next year using the growth rate.
Given that D0=
$
5.00 is the dividend this year, the expected dividend next year
D1is
D1=D0×(1 + g) = $5.00 ×(1 + 0.08) = $5.40
Step 2: Use the dividend discount model to calculate the current price of
the stock. The dividend discount model states that the current price of the
stock is the sum of all future dividends discounted back to present value.
P0=D1
r−g
22
Question 2
Question
A company is expected to pay an annual dividend of 5.00pershareindefinitely.Iftherequiredrateofreturnis8%perannum, whatisthevalueofthestock?
Solution
Step 1: We can use the Gordon Growth Model to find the value of the stock.
The formula is given by:
P0=D0×(1 + g)
r−g
where: P0= Value of the stock, D0= Dividend per share, r= Required rate
of return, g= Growth rate of dividends.
Step 2: In this case, D0= 5.00, r= 0.08, and since the dividends are
expected to be paid indefinitely, we can assume a perpetual growth rate gthat
is equal to the rate of inflation. Assuming an inflation rate of 3%, we get
g= 0.03.
Step 3: Now we can substitute the values into the formula:
P0=5.00 ×(1 + 0.03)
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the value of the stock is 103pershare.
Question 3
Question
A company is expected to pay its first annual dividend of 2.50pershareoneyearfromnow.Dividendsareexpectedtogrowataconstantrateof6
Solution
Step 1: Calculate the expected dividend per share next year. Since the first divi-
dend will be 2.50pershareanddividendsareexpectedtogrowataconstantrateof 6D1=
D0×(1 + g)
D1= $2.50 ×(1 + 0.06) = $2.65
Step 2: Calculate the constant growth rate, g, as a decimal. The constant
growth rate is given as 6
g=6
100 = 0.06
2
Step 3: Calculate the price of the stock using the dividend discount model.
The price of the stock can be calculated using the formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= expected dividend per share
next year - r= required rate of return on the stock - g= constant growth rate
Substitute the values into the formula:
P0=$2.65
0.12 −0.06
P0=$2.65
0.06
P0= $44.17
Therefore, the current value of the stock is
$
44.17 per share.
Question 4
Question
A company just paid a dividend of 5pershare.T hedividendisexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend growth rate. Given: Dividend (D0) = 5pershareDividendgrowthrate(g) =
8
Thus, the expected dividend for next year (D1) is:
D1 = D0×(1 + g)
D1=5×(1 + 0.08)
D1=5×1.08 =
5.40
Step 2: Calculate the required rate of return. Given: Required rate of return
(r) = 15
Step 3: Calculate the stock price using the Gordon Growth Model formula:
P0 = D1
r−g
P0 = 5.40
0.15 −0.08
P0 = 5.40
0.07 =
77.14
Therefore, the current stock price is 77.14pershare.
3
Question 5
Question
A company is expected to pay an annual dividend of 3.00pershareindefinitely.Iftherequiredrateofreturnis7
Solution
Step 1: Identify the variables given in the question.
In this case, we have:
Annual dividend: D= $3.00
Required rate of return: r= 7% = 0.07
Step 2: Use the Gordon Growth Model formula to calculate the present value
of the stock.
The Gordon Growth Model is given by:
P0=D
r−g
Where: - P0= Present value of the stock - D= Annual dividend - r= Required
rate of return - g= Growth rate of dividends
Step 3: Calculate the present value of the stock.
Since the company is expected to pay an annual dividend indefinitely, we can as-
sume the dividends will grow at a constant rate, which means g= 0. Therefore,
the formula simplifies to:
P0=D
r=3.00
0.07 = $42.86
Step 4: State the final answer.
The present value of the stock is $42.86.
Question 6
Question
A company just paid a dividend of 5pershare.T herequiredrateof returnonthecompany′sstockis12
Solution
Step 1: Calculate the dividend growth rate. Given that the dividends are
expected to grow at a rate of 5
Dividend Growth Rate (g) = 0.05
4
Step 2: Use the Dividend Discount Model (DDM) formula to calculate the
price of the stock. The price of the stock using the DDM formula can be
calculated as follows:
Stock Price = Dividends Next Year
Required Rate of Return - Dividend Growth Rate
where
Dividends Next Year = Dividend ×(1 + Dividend Growth Rate)
Required Rate of Return = 0.12
Step 3: Substitute the values into the formula and calculate.
Dividends Next Year = $5 ×(1 + 0.05) = $5.25
Stock Price = $5.25
0.12 −0.05 =$5.25
0.07 ≈$75
Therefore, the current price of the stock is approximately
$
75.
Question 7
Question
A company is expected to pay a dividend of 3 dollars per share next year and
is expected to grow its dividends at a constant rate of 6% per year indefinitely.
If the required rate of return is 10%, what is the current price of the stock?
Solution
Step 1: Calculate the dividend in the second year.
Dividend in the second year = Dividend in the first year ×(1 + growth rate)
= 3 ×(1 + 0.06)
= 3 ×1.06
= 3.18
Step 2: Calculate the expected dividend and price of the stock using the
dividend discount model. The price of a stock is given by the formula:
P0=D1
r−g
where: - P0is the price of the stock now, - D1is the dividend expected next
year, - ris the required rate of return, - gis the growth rate of the dividends.
5
Plugging in the values, we get:
P0=3.18
0.10 −0.06
=3.18
0.04
= 79.50
Therefore, the current price of the stock is 79.50.
Question 8
Question
A company’s stock is currently trading at 90pershare.T hecompanyisexpectedtopayadividendof3
per share next year, and dividends are expected to grow at a constant rate of 5
Solution
Step 1: Calculate the dividend in the next year. The dividend paid next year
is given as D1 =3.
Step 2: Calculate the growth rate of dividends. The growth rate of dividends
is given as g = 5
Step 3: Calculate the required rate of return. The required rate of return is
given as 10
Step 4: Use the Gordon Growth Model to calculate the intrinsic value of the
stock. The Gordon Growth Model is:
P0=D1
r−g
Substitute the given values to find the intrinsic value of the stock:
P0=3
0.10 −0.05
P0=3
0.05
P0= 60
Therefore, the intrinsic value of the stock based on the dividend discount
model is 60pershare.
Question 9
Question
A company’s stock is currently priced at
$50 per share. The company pays a yearly dividend of
6
$2.50 per share, which is expected to grow at a constant rate of 6% per year.
If the required rate of return on the stock is 10%, what is the stock’s intrinsic
value?
Solution
Let’s denote the annual dividend as D(current dividend) and D1(dividend next
year), the growth rate as g, the required rate of return as r, and the intrinsic
value as V0. We can use the Gordon growth model to find the intrinsic value of
the stock:
V0=D1
r−g
Step 1: Find the dividend next year
The dividend next year, D1,is found by multiplying the current dividend by (1 + g) :
D1=D×(1 + g)=2.50 ×(1 + 0.06) = 2.50 ×1.06 = 2.65
Step 2: Calculate the intrinsic value of the stock
Now we can substitute the values into the Gordon growth model formula:
V0=D1
r−g=2.65
0.10 −0.06 =2.65
0.04 = 66.25
Therefore, the intrinsic value of the stock is
$66.25.
Question 10
Question
A company’s stock currently pays an annual dividend of 5.50pershare, anddividendsareexpectedtogrowatarateof 7
Solution
Let’s denote the current value of the stock as P0, the annual dividend as D0
(5.50), thegrowthrateofdividendsasg(7
Step 1: Calculate the dividend in the next period D1using the growth rate
formula:
D1=D0×(1 + g)
D1= 5.50 ×(1 + 0.07) = 5.50 ×1.07 = 5.885 (rounded to 3 decimal places)
Step 2: Calculate the price of the stock P1at the end of the first year using
the dividend discount model:
P1=D1
r−g
7
P1=5.885
0.12 −0.07 =5.885
0.05 = 117.70 (rounded to 2 decimal places)
Step 3: Calculate the current value of the stock P0using the price of the
stock at the end of the first year:
P0=D1
r+P1
(1 + r)
P0=5.885
0.12 +117.70
(1 + 0.12)
P0= 49.04 + 117.70
1.12 = 49.04 + 105.45 = 154.49 (rounded to 2 decimal places)
Therefore, the current value of the stock is
$
154.49.
Question 11
Question
A company is expected to pay a dividend of 3.50pershareoneyearf romnow.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the expected dividend in year 2 using the growth rate:
D2=D1×(1 + g)
D2= 3.50 ×(1 + 0.05)
D2= 3.50 ×1.05 = 3.675
Step 2: Calculate the constant growth rate dividend discount model (Gordon
growth model) formula to find the current stock price:
P0=D1
r−g
Where: - P0= current price of the stock - D1= expected dividend next year -
r= required rate of return - g= growth rate
Substitute the given values into the formula:
P0=3.50
0.10 −0.05
P0=3.50
0.05
P0= 70
Therefore, the current value of the stock is 70.
8
Question 12
Question
A company pays an annual dividend of 3.50pershare.Iftherequiredrateofreturnis8
Solution
Step 1: Calculate the growth rate of dividends using the dividend growth model
formula P0=D1
r−g, where P0is the current stock price, D1is the next year’s
dividend, ris the required rate of return, and gis the growth rate of dividends.
Step 2: Given that D1= $3.50, r= 0.08, and solving for g, we have:
P0=3.50
0.08 −g
Step 3: Assume the company’s dividends are expected to grow at a constant
rate. Hence, we can express D1in terms of the current dividend D0and the
growth rate g:D1=D0×(1 + g).
Step 4: Since we know D0= $3.50, D1= 3.50 ×(1 + g)=3.50 + 3.50g.
Step 5: Substituting 3.50 + 3.50gfor D1in the initial formula, we have:
P0=3.50 + 3.50g
0.08 −g
Step 6: Simplifying the equation, we get:
P0=3.50(1 + g)
0.08 −g
Step 7: Now, substitute D0= $3.50 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 8: Substitute r= 0.08 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 9: Equate the equation to the current stock price:
P0=3.50(1 + g)
0.08 −g
Therefore, the current stock price can be calculated using this formula.
Question 13
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
9
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock based on the expected dividend for next year and the required rate of
return.
Step 1: The expected dividend for next year is calculated using the formula:
D1 = D0×(1 + g)
where: D1 = Expected dividend for next year, D0 = Current dividend, g=
Growth rate.
Plugging in the values:
D1=3.50 ×(1 + 0.05)
D1=3.50 ×1.05
D1 = 3.675
Therefore, the expected dividend for next year is 3.675pershare.
Step 2: The Gordon Growth Model formula is:
P0 = D1
r−g
where: P0 = Current value of the stock, D1 = Expected dividend for next year,
r= Required rate of return, g= Growth rate.
Plugging in the values:
P0 = 3.675
0.10 −0.05
P0 = 3.675
0.05
P0 = 73.50
Therefore, the current value of the stock is 73.50pershare.
Question 14
Question
Company XYZ just paid a dividend of 3.50pershare.T hedividendisexpectedtogrowataconstantrateof 4
10
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Calculate the dividend in year 1. The dividend in year 1 (D1) can
be calculated using the formula for constant growth dividends:
D1 = D0×(1 + g)
D1=3.50 ×(1 + 0.04)
D1=3.50 ×1.04
D1=3.64
Step 3: Calculate the price of the stock. The price of the stock (P0) can be
calculated using the Gordon Growth Model formula:
P0 = D1
r−g
where: - D1 = 3.64 (dividend in year 1) - r= 0.10 (required rate of return) -
g= 0.04 (dividend growth rate)
P0 = 3.64
0.10 −0.04
P0 = 3.64
0.06
P0 = 60.67
Therefore, the current stock price of Company XYZ is 60.67pershare.
Question 15
Question
A company’s stock is currently priced at $80 per share. The company is expected
to pay a dividend of $4 per share in one year. If the dividends are expected to
grow at a rate of 7% per year indefinitely, what is the expected rate of return
for an investor who buys the stock at the current price?
Solution
Step 1: Calculate the expected dividend in two years Given that the dividend
is expected to grow at a rate of 7% per year, the dividend in two years will be:
$4 ×(1 + 0.07) = $4.28
11
Step 2: Calculate the dividend yield The dividend yield is the expected
dividend in one year divided by the current stock price:
Dividend Yield = $4
$80 = 0.05
Step 3: Calculate the expected capital gains yield The capital gains yield is
the growth rate of dividends:
Capital Gains Yield = 0.07
Step 4: Calculate the total expected rate of return The total expected rate
of return is the sum of the dividend yield and the capital gains yield:
Expected Rate of Return = Dividend Yield+Capital Gains Yield = 0.05+0.07 = 0.12
Therefore, the expected rate of return for an investor who buys the stock at the
current price is 12%.
Question 16
Question
A company pays a dividend of
$
3 per share annually and is expected to grow
at a constant rate of 6
Solution
Let’s denote the current value of the stock as P0, the dividend per share as D0,
the growth rate as g, and the required rate of return as r.
Step 1: Calculate the dividend next year, D1, using the growth rate formula:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.06)
D1= 3 ×1.06 = 3.18
Step 2: Calculate the price of the stock, P1, at the end of the year using
the dividend discount model formula:
P1=D1
r−g
P1=3.18
0.10 −0.06
P1=3.18
0.04 = 79.50
12
Step 3: Use the formula for the current value of the stock as the present
value of next year’s stock price:
P0=P1
1 + r
P0=79.50
1+0.10
P0=79.50
1.10 = 72.27
Therefore, the current value of the stock is
$
72.27.
Question 17
Question
A company pays a dividend of 8.50pershareannuallyandthedividendisexpectedtogrowataconstantrateof5
Solution
Let’s denote the current stock price as P0, the dividend paid per share as D0
(which is 8.50), thegrowthrateofdividendsasg (which is 5
Step 1: Calculate the expected dividend next year, D1, using the dividend
growth rate formula:
D1=D0×(1 + g)
D1= 8.50 ×(1 + 0.05)
D1= 8.50 ×1.05
D1= 8.925
Step 2: Calculate the dividend yield, D1/P0, which should be equal to the
required rate of return: D1
P0
=r
8.925
P0
= 0.12
P0=8.925
0.12
P0= 74.375
Therefore, the current stock price is 74.38pershare.
Question 18
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
13
Solution
Step 1: Calculate the dividend in year 2.
D2=D1×(1 + Growth Rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Calculate the required rate of return as a percentage.
r= 10%
Step 3: Use the Gordon Growth Model to find the stock price.
P0=D1
r−g=$3.50
0.10 −0.05 = $70.00
Therefore, the current value of the stock is
$
70.00 per share.
Question 19
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend expected in the second year. Step 2: Calculate
the stock price using the Gordon Growth Model.
Step 1: Given: Dividend in the first year, D1 = 3.50Dividendgrowthrate, g =
5
The dividend in the second year, D2, can be calculated using the formula:
D2 = D1×(1 + g)
D2 = $3.50 ×(1 + 0.05)
D2 = $3.50 ×1.05
D2 = $3.675
Step 2: The stock price, P0, can be calculated using the Gordon Growth
Model:
P0 = D1×(1 + g)
r−g
where r is the required rate of return.
Given: D1 = 3.50g= 5r= 10
Substitute the values into the formula:
P0 = $3.50 ×(1 + 0.05)
0.10 −0.05
14
P0 = $3.50 ×1.05
0.05
P0 = $3.675
0.05
P0 = $73.50
Therefore, the current price of the stock is 73.50pershare.
Question 20
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
Solution
Step 1: Determine the dividend in the next year using the growth rate.
D1=D0×(1 + g)=3.50 ×(1 + 0.05) = 3.675
Step 2: Calculate the dividend yield using the required rate of return.
D1=D1
r−g
3.675 = 3.675
0.10 −0.05
3.675 = 3.675
0.05
3.675 = 73.50
Therefore, the current stock price for Company XYZ is 73.50.
Question 21
Question
ABC Company is expected to pay a dividend of 3.00persharenextyear, andthedividendsareexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the constant growth rate (g). Since the dividends are expected
to grow at a constant rate of 5
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock. The Gordon Growth Model is given by:
P0=D1
r−g
15
where: - P0is the current value of the stock, - D1is the dividend expected to be
paid next year, - ris the required rate of return on the stock, - gis the constant
growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
P0=3.00
0.10 −0.05
Step 4: Calculate the current value of the stock.
P0=3.00
0.05 = 60.00
Therefore, the current value of the stock is 60.00.
Question 22
Question
A company paid a dividend of $2.50 per share last year, and is expected to
increase its dividend by 5
Solution
Step 1: Calculate the next dividend payment. Given that the company is in-
creasing its dividend by 5
D1 = $2.50 ×1.05 = $2.625
Step 2: Determine the dividend growth rate. The dividend growth rate (g)
is 5
Step 3: Calculate the required rate of return. The required rate of return
(r) is 10
Step 4: Apply the Gordon Growth Model formula to find the current value
of the stock:
P0=D1
r−g
P0=$2.625
0.10 −0.05
P0=$2.625
0.05
P0= $52.50
Therefore, the current value of the stock is $52.50.
16
Question 23
Question
A company’s stock is expected to pay a dividend of 3.50 dollars next year, and
dividends are expected to grow at a constant rate of 5% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Step 1: Calculate the dividend in the second year using the growth rate. Step
2: Calculate the current value of the stock using the dividend discount model.
Step 1: The dividend in the second year will be:
D2=D1×(1 + growth rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: The current value of the stock can be calculated using the dividend
discount model formula:
P0=D1
r−g
where: - P0is the current value of the stock, - D1is the dividend next year
(
$
3.50), - ris the required rate of return (10%), and - gis the growth rate of
dividends (5%).
Substitute the values into the formula:
P0=$3.50
0.10 −0.05 =$3.50
0.05 = $70
Therefore, the current value of the stock is
$
70.
Question 24
Question
A company’s stock is expected to have dividends of $2, $2.50, and $3 in the
next three years. After that, the dividends are expected to grow at a constant
rate of 5% per year indefinitely. If the required rate of return on the stock is
10%, what is the current value of the stock?
Solution
Step 1: Calculate the present value of the dividends for the next three years.
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
17
where D1, D2, D3are the dividends for the next three years and ris the required
rate of return. Substitute the given values:
P V =2
(1 + 0.10)1+2.50
(1 + 0.10)2+3
(1 + 0.10)3
P V =2
1.10 +2.50
1.102+3
1.103
P V ≈1.8182 + 2.0661 + 2.3136
P V ≈6.1979
Step 2: Calculate the expected dividend at year 4 and the price of the stock
using the Gordon Growth Model. The formula for the Gordon Growth Model
is:
P4=D4
r−g
where D4is the dividend at year 4, ris the required rate of return, and gis the
growth rate of dividends. Substitute the given values:
P4=3×(1 + 0.05)
0.10 −0.05
P4=3×1.05
0.05
P4=3.15
0.05
P4= 63
Step 3: Calculate the present value of the stock. The current value of the
stock is the sum of the present value of the dividends for the next three years
and the price of the stock at year 4.
Current V alue =P V +P4
Current V alue = 6.1979 + 63
Current V alue ≈69.1979
Therefore, the current value of the stock is approximately $69.20.
Question 25
Question
A company pays an annual dividend of 3pershareandexpectsthedividendstogrowatarateof 5
18
Solution
Step 1: Calculate the dividend in the next year using the growth rate. Step 2:
Use the dividend discount model to find the current value of the stock.
Step 1: The dividend in the next year can be calculated using the formula
for the dividend growth rate:
D1=D0×(1 + g)
where: - D1is the dividend in the next year, - D0is the current dividend, and
-gis the growth rate.
Plugging in the values:
D1= 3 ×(1 + 0.05) = 3.15
Step 2: The current value of the stock can be calculated using the dividend
discount model:
P0=D1
r−g
where: - P0is the current value of the stock, - ris the required rate of return,
and - gis the growth rate.
Plugging in the values:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 26
Question
A company is expected to pay an annual dividend of 4.50pershareindefinitely.Iftherequiredrateofreturnforinvestorsis10
Solution
Step 1: Calculate the fair value of the stock using the Gordon Growth Model
formula:
Fair Value = Dividends per Share
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend indefinitely,
the growth rate can be assumed to be equal to the nominal growth rate of the
economy. Let’s assume a nominal growth rate of 5
Step 3: Substitute the values into the formula:
Fair Value = 4.50
0.10 −0.05
19
Fair Value = 4.50
0.05
Fair Value = 90
Therefore, the fair value of the stock is 90pershare.
Question 27
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay a dividend of $5 per share at the end of the year. Dividends
are expected to grow at a constant rate of 5% per year. If the required rate of
return on the stock is 10%, what is the stock’s value?
Solution
Step 1: Calculate the expected dividend in the next year.
Expected Dividend in the next year = $5 ×(1 + 0.05) = $5.25
Step 2: Since the dividends are expected to grow at a constant rate, we can
use the Gordon Growth Model to find the stock’s value.
Stock Value = Expected Dividend in the next year
Required Rate of Return −Growth Rate of Dividends
Stock Value = $5.25
0.10 −0.05 =$5.25
0.05 = $105
Therefore, the stock’s value is $105.□
Question 28
Question
A company is expected to pay a dividend of 2.50 per share at the end of the
year. Dividends are expected to grow at a rate of 5% per year indefinitely. If
the required rate of return is 10%, what is the stock’s current price?
Solution
Step 1: Calculate the dividend one year from now using the growth rate. Step
2: Calculate the price of the stock using the dividend discount model. Step 3:
Substitute the given values into the formula to find the stock’s current price.
Step 1: Calculate the dividend one year from now. The dividend next year
is given by:
D1=D0×(1 + g)
20
where: - D0= current dividend per share = 2.50 - g= growth rate = 5% = 0.05
D1= 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Therefore, the dividend one year from now is 2.625.
Step 2: Calculate the price of the stock using the dividend discount model.
The price of the stock is given by:
P0=D1
r−g
where: - D1= dividend one year from now - r= required rate of return =
10% = 0.10 - g= growth rate = 5% = 0.05
Step 3: Substitute the values into the formula.
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the stock’s current price is 52.50.
Question 29
Question
A company expects to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof8
Solution
Step 1: Calculate the expected dividend in year 2. Step 2: Determine the
expected stock price in year 1. Step 3: Calculate the present value of the stock
price in year 1 to find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated using the formula
for the dividend in any future year:
D1=D0×(1 + g)
where: D1= Dividend in year 1 = 5.00D0= Dividend in the current year g=
Growth rate of dividends = 8
Therefore, the expected dividend in year 2 is:
D1=
5.00 ×(1 + 0.08) =5.40
Step 2: The expected stock price in year 1 can be calculated using the
dividend discount model formula:
P1=D1
r−g
21
where: P1= Stock price in year 1 D1= Dividend in year 1 r= Required rate
of return = 12g= Growth rate of dividends = 8
Substitute the known values into the formula:
P1=
5.400.12−0.08= 5.40 0.04= 135
Step 3: The present value of the stock price in year 1 (current value of the
stock) can be calculated by discounting the stock price in year 1 back to the
present value using the formula:
P V =P1
(1 + r)1
where: P V = Present value of the stock P1= Stock price in year 1 r= Required
rate of return = 12
Substitute the known values into the formula:
P V =
135(1+0.12)1=135 1.12≈120.54
Therefore, the current value of the stock is approximately 120.54.
Question 30
Question
A company is expected to pay a dividend of 5.00persharenextyear, anddividendsareexpectedtogrowatarateof8
Solution
Let’s denote the current price of the stock as P0, the dividend next year as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the expected dividend next year using the growth rate.
Given that D0=
$
5.00 is the dividend this year, the expected dividend next year
D1is
D1=D0×(1 + g) = $5.00 ×(1 + 0.08) = $5.40
Step 2: Use the dividend discount model to calculate the current price of
the stock. The dividend discount model states that the current price of the
stock is the sum of all future dividends discounted back to present value.
P0=D1
r−g
22
Question 2
Question
A company is expected to pay an annual dividend of 5.00pershareindefinitely.Iftherequiredrateofreturnis8%perannum, whatisthevalueofthestock?
Solution
Step 1: We can use the Gordon Growth Model to find the value of the stock.
The formula is given by:
P0=D0×(1 + g)
r−g
where: P0= Value of the stock, D0= Dividend per share, r= Required rate
of return, g= Growth rate of dividends.
Step 2: In this case, D0= 5.00, r= 0.08, and since the dividends are
expected to be paid indefinitely, we can assume a perpetual growth rate gthat
is equal to the rate of inflation. Assuming an inflation rate of 3%, we get
g= 0.03.
Step 3: Now we can substitute the values into the formula:
P0=5.00 ×(1 + 0.03)
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the value of the stock is 103pershare.
Question 3
Question
A company is expected to pay its first annual dividend of 2.50pershareoneyearfromnow.Dividendsareexpectedtogrowataconstantrateof6
Solution
Step 1: Calculate the expected dividend per share next year. Since the first divi-
dend will be 2.50pershareanddividendsareexpectedtogrowataconstantrateof 6D1=
D0×(1 + g)
D1= $2.50 ×(1 + 0.06) = $2.65
Step 2: Calculate the constant growth rate, g, as a decimal. The constant
growth rate is given as 6
g=6
100 = 0.06
2
Step 3: Calculate the price of the stock using the dividend discount model.
The price of the stock can be calculated using the formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= expected dividend per share
next year - r= required rate of return on the stock - g= constant growth rate
Substitute the values into the formula:
P0=$2.65
0.12 −0.06
P0=$2.65
0.06
P0= $44.17
Therefore, the current value of the stock is
$
44.17 per share.
Question 4
Question
A company just paid a dividend of 5pershare.T hedividendisexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend growth rate. Given: Dividend (D0) = 5pershareDividendgrowthrate(g) =
8
Thus, the expected dividend for next year (D1) is:
D1 = D0×(1 + g)
D1=5×(1 + 0.08)
D1=5×1.08 =
5.40
Step 2: Calculate the required rate of return. Given: Required rate of return
(r) = 15
Step 3: Calculate the stock price using the Gordon Growth Model formula:
P0 = D1
r−g
P0 = 5.40
0.15 −0.08
P0 = 5.40
0.07 =
77.14
Therefore, the current stock price is 77.14pershare.
3
Question 5
Question
A company is expected to pay an annual dividend of 3.00pershareindefinitely.Iftherequiredrateofreturnis7
Solution
Step 1: Identify the variables given in the question.
In this case, we have:
Annual dividend: D= $3.00
Required rate of return: r= 7% = 0.07
Step 2: Use the Gordon Growth Model formula to calculate the present value
of the stock.
The Gordon Growth Model is given by:
P0=D
r−g
Where: - P0= Present value of the stock - D= Annual dividend - r= Required
rate of return - g= Growth rate of dividends
Step 3: Calculate the present value of the stock.
Since the company is expected to pay an annual dividend indefinitely, we can as-
sume the dividends will grow at a constant rate, which means g= 0. Therefore,
the formula simplifies to:
P0=D
r=3.00
0.07 = $42.86
Step 4: State the final answer.
The present value of the stock is $42.86.
Question 6
Question
A company just paid a dividend of 5pershare.T herequiredrateof returnonthecompany′sstockis12
Solution
Step 1: Calculate the dividend growth rate. Given that the dividends are
expected to grow at a rate of 5
Dividend Growth Rate (g) = 0.05
4
Step 2: Use the Dividend Discount Model (DDM) formula to calculate the
price of the stock. The price of the stock using the DDM formula can be
calculated as follows:
Stock Price = Dividends Next Year
Required Rate of Return - Dividend Growth Rate
where
Dividends Next Year = Dividend ×(1 + Dividend Growth Rate)
Required Rate of Return = 0.12
Step 3: Substitute the values into the formula and calculate.
Dividends Next Year = $5 ×(1 + 0.05) = $5.25
Stock Price = $5.25
0.12 −0.05 =$5.25
0.07 ≈$75
Therefore, the current price of the stock is approximately
$
75.
Question 7
Question
A company is expected to pay a dividend of 3 dollars per share next year and
is expected to grow its dividends at a constant rate of 6% per year indefinitely.
If the required rate of return is 10%, what is the current price of the stock?
Solution
Step 1: Calculate the dividend in the second year.
Dividend in the second year = Dividend in the first year ×(1 + growth rate)
= 3 ×(1 + 0.06)
= 3 ×1.06
= 3.18
Step 2: Calculate the expected dividend and price of the stock using the
dividend discount model. The price of a stock is given by the formula:
P0=D1
r−g
where: - P0is the price of the stock now, - D1is the dividend expected next
year, - ris the required rate of return, - gis the growth rate of the dividends.
5
Plugging in the values, we get:
P0=3.18
0.10 −0.06
=3.18
0.04
= 79.50
Therefore, the current price of the stock is 79.50.
Question 8
Question
A company’s stock is currently trading at 90pershare.T hecompanyisexpectedtopayadividendof3
per share next year, and dividends are expected to grow at a constant rate of 5
Solution
Step 1: Calculate the dividend in the next year. The dividend paid next year
is given as D1 =3.
Step 2: Calculate the growth rate of dividends. The growth rate of dividends
is given as g = 5
Step 3: Calculate the required rate of return. The required rate of return is
given as 10
Step 4: Use the Gordon Growth Model to calculate the intrinsic value of the
stock. The Gordon Growth Model is:
P0=D1
r−g
Substitute the given values to find the intrinsic value of the stock:
P0=3
0.10 −0.05
P0=3
0.05
P0= 60
Therefore, the intrinsic value of the stock based on the dividend discount
model is 60pershare.
Question 9
Question
A company’s stock is currently priced at
$50 per share. The company pays a yearly dividend of
6
$2.50 per share, which is expected to grow at a constant rate of 6% per year.
If the required rate of return on the stock is 10%, what is the stock’s intrinsic
value?
Solution
Let’s denote the annual dividend as D(current dividend) and D1(dividend next
year), the growth rate as g, the required rate of return as r, and the intrinsic
value as V0. We can use the Gordon growth model to find the intrinsic value of
the stock:
V0=D1
r−g
Step 1: Find the dividend next year
The dividend next year, D1,is found by multiplying the current dividend by (1 + g) :
D1=D×(1 + g)=2.50 ×(1 + 0.06) = 2.50 ×1.06 = 2.65
Step 2: Calculate the intrinsic value of the stock
Now we can substitute the values into the Gordon growth model formula:
V0=D1
r−g=2.65
0.10 −0.06 =2.65
0.04 = 66.25
Therefore, the intrinsic value of the stock is
$66.25.
Question 10
Question
A company’s stock currently pays an annual dividend of 5.50pershare, anddividendsareexpectedtogrowatarateof 7
Solution
Let’s denote the current value of the stock as P0, the annual dividend as D0
(5.50), thegrowthrateofdividendsasg(7
Step 1: Calculate the dividend in the next period D1using the growth rate
formula:
D1=D0×(1 + g)
D1= 5.50 ×(1 + 0.07) = 5.50 ×1.07 = 5.885 (rounded to 3 decimal places)
Step 2: Calculate the price of the stock P1at the end of the first year using
the dividend discount model:
P1=D1
r−g
7
P1=5.885
0.12 −0.07 =5.885
0.05 = 117.70 (rounded to 2 decimal places)
Step 3: Calculate the current value of the stock P0using the price of the
stock at the end of the first year:
P0=D1
r+P1
(1 + r)
P0=5.885
0.12 +117.70
(1 + 0.12)
P0= 49.04 + 117.70
1.12 = 49.04 + 105.45 = 154.49 (rounded to 2 decimal places)
Therefore, the current value of the stock is
$
154.49.
Question 11
Question
A company is expected to pay a dividend of 3.50pershareoneyearf romnow.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the expected dividend in year 2 using the growth rate:
D2=D1×(1 + g)
D2= 3.50 ×(1 + 0.05)
D2= 3.50 ×1.05 = 3.675
Step 2: Calculate the constant growth rate dividend discount model (Gordon
growth model) formula to find the current stock price:
P0=D1
r−g
Where: - P0= current price of the stock - D1= expected dividend next year -
r= required rate of return - g= growth rate
Substitute the given values into the formula:
P0=3.50
0.10 −0.05
P0=3.50
0.05
P0= 70
Therefore, the current value of the stock is 70.
8
Question 12
Question
A company pays an annual dividend of 3.50pershare.Iftherequiredrateofreturnis8
Solution
Step 1: Calculate the growth rate of dividends using the dividend growth model
formula P0=D1
r−g, where P0is the current stock price, D1is the next year’s
dividend, ris the required rate of return, and gis the growth rate of dividends.
Step 2: Given that D1= $3.50, r= 0.08, and solving for g, we have:
P0=3.50
0.08 −g
Step 3: Assume the company’s dividends are expected to grow at a constant
rate. Hence, we can express D1in terms of the current dividend D0and the
growth rate g:D1=D0×(1 + g).
Step 4: Since we know D0= $3.50, D1= 3.50 ×(1 + g)=3.50 + 3.50g.
Step 5: Substituting 3.50 + 3.50gfor D1in the initial formula, we have:
P0=3.50 + 3.50g
0.08 −g
Step 6: Simplifying the equation, we get:
P0=3.50(1 + g)
0.08 −g
Step 7: Now, substitute D0= $3.50 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 8: Substitute r= 0.08 into the equation:
P0=3.50(1 + g)
0.08 −g
Step 9: Equate the equation to the current stock price:
P0=3.50(1 + g)
0.08 −g
Therefore, the current stock price can be calculated using this formula.
Question 13
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
9
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock based on the expected dividend for next year and the required rate of
return.
Step 1: The expected dividend for next year is calculated using the formula:
D1 = D0×(1 + g)
where: D1 = Expected dividend for next year, D0 = Current dividend, g=
Growth rate.
Plugging in the values:
D1=3.50 ×(1 + 0.05)
D1=3.50 ×1.05
D1 = 3.675
Therefore, the expected dividend for next year is 3.675pershare.
Step 2: The Gordon Growth Model formula is:
P0 = D1
r−g
where: P0 = Current value of the stock, D1 = Expected dividend for next year,
r= Required rate of return, g= Growth rate.
Plugging in the values:
P0 = 3.675
0.10 −0.05
P0 = 3.675
0.05
P0 = 73.50
Therefore, the current value of the stock is 73.50pershare.
Question 14
Question
Company XYZ just paid a dividend of 3.50pershare.T hedividendisexpectedtogrowataconstantrateof 4
10
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Calculate the dividend in year 1. The dividend in year 1 (D1) can
be calculated using the formula for constant growth dividends:
D1 = D0×(1 + g)
D1=3.50 ×(1 + 0.04)
D1=3.50 ×1.04
D1=3.64
Step 3: Calculate the price of the stock. The price of the stock (P0) can be
calculated using the Gordon Growth Model formula:
P0 = D1
r−g
where: - D1 = 3.64 (dividend in year 1) - r= 0.10 (required rate of return) -
g= 0.04 (dividend growth rate)
P0 = 3.64
0.10 −0.04
P0 = 3.64
0.06
P0 = 60.67
Therefore, the current stock price of Company XYZ is 60.67pershare.
Question 15
Question
A company’s stock is currently priced at $80 per share. The company is expected
to pay a dividend of $4 per share in one year. If the dividends are expected to
grow at a rate of 7% per year indefinitely, what is the expected rate of return
for an investor who buys the stock at the current price?
Solution
Step 1: Calculate the expected dividend in two years Given that the dividend
is expected to grow at a rate of 7% per year, the dividend in two years will be:
$4 ×(1 + 0.07) = $4.28
11
Step 2: Calculate the dividend yield The dividend yield is the expected
dividend in one year divided by the current stock price:
Dividend Yield = $4
$80 = 0.05
Step 3: Calculate the expected capital gains yield The capital gains yield is
the growth rate of dividends:
Capital Gains Yield = 0.07
Step 4: Calculate the total expected rate of return The total expected rate
of return is the sum of the dividend yield and the capital gains yield:
Expected Rate of Return = Dividend Yield+Capital Gains Yield = 0.05+0.07 = 0.12
Therefore, the expected rate of return for an investor who buys the stock at the
current price is 12%.
Question 16
Question
A company pays a dividend of
$
3 per share annually and is expected to grow
at a constant rate of 6
Solution
Let’s denote the current value of the stock as P0, the dividend per share as D0,
the growth rate as g, and the required rate of return as r.
Step 1: Calculate the dividend next year, D1, using the growth rate formula:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.06)
D1= 3 ×1.06 = 3.18
Step 2: Calculate the price of the stock, P1, at the end of the year using
the dividend discount model formula:
P1=D1
r−g
P1=3.18
0.10 −0.06
P1=3.18
0.04 = 79.50
12
Step 3: Use the formula for the current value of the stock as the present
value of next year’s stock price:
P0=P1
1 + r
P0=79.50
1+0.10
P0=79.50
1.10 = 72.27
Therefore, the current value of the stock is
$
72.27.
Question 17
Question
A company pays a dividend of 8.50pershareannuallyandthedividendisexpectedtogrowataconstantrateof5
Solution
Let’s denote the current stock price as P0, the dividend paid per share as D0
(which is 8.50), thegrowthrateofdividendsasg (which is 5
Step 1: Calculate the expected dividend next year, D1, using the dividend
growth rate formula:
D1=D0×(1 + g)
D1= 8.50 ×(1 + 0.05)
D1= 8.50 ×1.05
D1= 8.925
Step 2: Calculate the dividend yield, D1/P0, which should be equal to the
required rate of return: D1
P0
=r
8.925
P0
= 0.12
P0=8.925
0.12
P0= 74.375
Therefore, the current stock price is 74.38pershare.
Question 18
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
13
Solution
Step 1: Calculate the dividend in year 2.
D2=D1×(1 + Growth Rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Calculate the required rate of return as a percentage.
r= 10%
Step 3: Use the Gordon Growth Model to find the stock price.
P0=D1
r−g=$3.50
0.10 −0.05 = $70.00
Therefore, the current value of the stock is
$
70.00 per share.
Question 19
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend expected in the second year. Step 2: Calculate
the stock price using the Gordon Growth Model.
Step 1: Given: Dividend in the first year, D1 = 3.50Dividendgrowthrate, g =
5
The dividend in the second year, D2, can be calculated using the formula:
D2 = D1×(1 + g)
D2 = $3.50 ×(1 + 0.05)
D2 = $3.50 ×1.05
D2 = $3.675
Step 2: The stock price, P0, can be calculated using the Gordon Growth
Model:
P0 = D1×(1 + g)
r−g
where r is the required rate of return.
Given: D1 = 3.50g= 5r= 10
Substitute the values into the formula:
P0 = $3.50 ×(1 + 0.05)
0.10 −0.05
14
P0 = $3.50 ×1.05
0.05
P0 = $3.675
0.05
P0 = $73.50
Therefore, the current price of the stock is 73.50pershare.
Question 20
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof5
Solution
Step 1: Determine the dividend in the next year using the growth rate.
D1=D0×(1 + g)=3.50 ×(1 + 0.05) = 3.675
Step 2: Calculate the dividend yield using the required rate of return.
D1=D1
r−g
3.675 = 3.675
0.10 −0.05
3.675 = 3.675
0.05
3.675 = 73.50
Therefore, the current stock price for Company XYZ is 73.50.
Question 21
Question
ABC Company is expected to pay a dividend of 3.00persharenextyear, andthedividendsareexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the constant growth rate (g). Since the dividends are expected
to grow at a constant rate of 5
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock. The Gordon Growth Model is given by:
P0=D1
r−g
15
where: - P0is the current value of the stock, - D1is the dividend expected to be
paid next year, - ris the required rate of return on the stock, - gis the constant
growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
P0=3.00
0.10 −0.05
Step 4: Calculate the current value of the stock.
P0=3.00
0.05 = 60.00
Therefore, the current value of the stock is 60.00.
Question 22
Question
A company paid a dividend of $2.50 per share last year, and is expected to
increase its dividend by 5
Solution
Step 1: Calculate the next dividend payment. Given that the company is in-
creasing its dividend by 5
D1 = $2.50 ×1.05 = $2.625
Step 2: Determine the dividend growth rate. The dividend growth rate (g)
is 5
Step 3: Calculate the required rate of return. The required rate of return
(r) is 10
Step 4: Apply the Gordon Growth Model formula to find the current value
of the stock:
P0=D1
r−g
P0=$2.625
0.10 −0.05
P0=$2.625
0.05
P0= $52.50
Therefore, the current value of the stock is $52.50.
16
Question 23
Question
A company’s stock is expected to pay a dividend of 3.50 dollars next year, and
dividends are expected to grow at a constant rate of 5% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Step 1: Calculate the dividend in the second year using the growth rate. Step
2: Calculate the current value of the stock using the dividend discount model.
Step 1: The dividend in the second year will be:
D2=D1×(1 + growth rate) = $3.50 ×(1 + 0.05) = $3.675
Step 2: The current value of the stock can be calculated using the dividend
discount model formula:
P0=D1
r−g
where: - P0is the current value of the stock, - D1is the dividend next year
(
$
3.50), - ris the required rate of return (10%), and - gis the growth rate of
dividends (5%).
Substitute the values into the formula:
P0=$3.50
0.10 −0.05 =$3.50
0.05 = $70
Therefore, the current value of the stock is
$
70.
Question 24
Question
A company’s stock is expected to have dividends of $2, $2.50, and $3 in the
next three years. After that, the dividends are expected to grow at a constant
rate of 5% per year indefinitely. If the required rate of return on the stock is
10%, what is the current value of the stock?
Solution
Step 1: Calculate the present value of the dividends for the next three years.
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
17
where D1, D2, D3are the dividends for the next three years and ris the required
rate of return. Substitute the given values:
P V =2
(1 + 0.10)1+2.50
(1 + 0.10)2+3
(1 + 0.10)3
P V =2
1.10 +2.50
1.102+3
1.103
P V ≈1.8182 + 2.0661 + 2.3136
P V ≈6.1979
Step 2: Calculate the expected dividend at year 4 and the price of the stock
using the Gordon Growth Model. The formula for the Gordon Growth Model
is:
P4=D4
r−g
where D4is the dividend at year 4, ris the required rate of return, and gis the
growth rate of dividends. Substitute the given values:
P4=3×(1 + 0.05)
0.10 −0.05
P4=3×1.05
0.05
P4=3.15
0.05
P4= 63
Step 3: Calculate the present value of the stock. The current value of the
stock is the sum of the present value of the dividends for the next three years
and the price of the stock at year 4.
Current V alue =P V +P4
Current V alue = 6.1979 + 63
Current V alue ≈69.1979
Therefore, the current value of the stock is approximately $69.20.
Question 25
Question
A company pays an annual dividend of 3pershareandexpectsthedividendstogrowatarateof 5
18
Solution
Step 1: Calculate the dividend in the next year using the growth rate. Step 2:
Use the dividend discount model to find the current value of the stock.
Step 1: The dividend in the next year can be calculated using the formula
for the dividend growth rate:
D1=D0×(1 + g)
where: - D1is the dividend in the next year, - D0is the current dividend, and
-gis the growth rate.
Plugging in the values:
D1= 3 ×(1 + 0.05) = 3.15
Step 2: The current value of the stock can be calculated using the dividend
discount model:
P0=D1
r−g
where: - P0is the current value of the stock, - ris the required rate of return,
and - gis the growth rate.
Plugging in the values:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 26
Question
A company is expected to pay an annual dividend of 4.50pershareindefinitely.Iftherequiredrateofreturnforinvestorsis10
Solution
Step 1: Calculate the fair value of the stock using the Gordon Growth Model
formula:
Fair Value = Dividends per Share
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend indefinitely,
the growth rate can be assumed to be equal to the nominal growth rate of the
economy. Let’s assume a nominal growth rate of 5
Step 3: Substitute the values into the formula:
Fair Value = 4.50
0.10 −0.05
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Fair Value = 4.50
0.05
Fair Value = 90
Therefore, the fair value of the stock is 90pershare.
Question 27
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay a dividend of $5 per share at the end of the year. Dividends
are expected to grow at a constant rate of 5% per year. If the required rate of
return on the stock is 10%, what is the stock’s value?
Solution
Step 1: Calculate the expected dividend in the next year.
Expected Dividend in the next year = $5 ×(1 + 0.05) = $5.25
Step 2: Since the dividends are expected to grow at a constant rate, we can
use the Gordon Growth Model to find the stock’s value.
Stock Value = Expected Dividend in the next year
Required Rate of Return −Growth Rate of Dividends
Stock Value = $5.25
0.10 −0.05 =$5.25
0.05 = $105
Therefore, the stock’s value is $105.□
Question 28
Question
A company is expected to pay a dividend of 2.50 per share at the end of the
year. Dividends are expected to grow at a rate of 5% per year indefinitely. If
the required rate of return is 10%, what is the stock’s current price?
Solution
Step 1: Calculate the dividend one year from now using the growth rate. Step
2: Calculate the price of the stock using the dividend discount model. Step 3:
Substitute the given values into the formula to find the stock’s current price.
Step 1: Calculate the dividend one year from now. The dividend next year
is given by:
D1=D0×(1 + g)
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where: - D0= current dividend per share = 2.50 - g= growth rate = 5% = 0.05
D1= 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Therefore, the dividend one year from now is 2.625.
Step 2: Calculate the price of the stock using the dividend discount model.
The price of the stock is given by:
P0=D1
r−g
where: - D1= dividend one year from now - r= required rate of return =
10% = 0.10 - g= growth rate = 5% = 0.05
Step 3: Substitute the values into the formula.
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the stock’s current price is 52.50.
Question 29
Question
A company expects to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof8
Solution
Step 1: Calculate the expected dividend in year 2. Step 2: Determine the
expected stock price in year 1. Step 3: Calculate the present value of the stock
price in year 1 to find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated using the formula
for the dividend in any future year:
D1=D0×(1 + g)
where: D1= Dividend in year 1 = 5.00D0= Dividend in the current year g=
Growth rate of dividends = 8
Therefore, the expected dividend in year 2 is:
D1=
5.00 ×(1 + 0.08) =5.40
Step 2: The expected stock price in year 1 can be calculated using the
dividend discount model formula:
P1=D1
r−g
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where: P1= Stock price in year 1 D1= Dividend in year 1 r= Required rate
of return = 12g= Growth rate of dividends = 8
Substitute the known values into the formula:
P1=
5.400.12−0.08= 5.40 0.04= 135
Step 3: The present value of the stock price in year 1 (current value of the
stock) can be calculated by discounting the stock price in year 1 back to the
present value using the formula:
P V =P1
(1 + r)1
where: P V = Present value of the stock P1= Stock price in year 1 r= Required
rate of return = 12
Substitute the known values into the formula:
P V =
135(1+0.12)1=135 1.12≈120.54
Therefore, the current value of the stock is approximately 120.54.
Question 30
Question
A company is expected to pay a dividend of 5.00persharenextyear, anddividendsareexpectedtogrowatarateof8
Solution
Let’s denote the current price of the stock as P0, the dividend next year as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the expected dividend next year using the growth rate.
Given that D0=
$
5.00 is the dividend this year, the expected dividend next year
D1is
D1=D0×(1 + g) = $5.00 ×(1 + 0.08) = $5.40
Step 2: Use the dividend discount model to calculate the current price of
the stock. The dividend discount model states that the current price of the
stock is the sum of all future dividends discounted back to present value.
P0=D1
r−g
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Substitute D1= $5.40, r= 0.12, and g= 0.08 into the formula:
P0=$5.40
0.12 −0.08 =$5.40
0.04 = $135.00
Therefore, the current price of the stock is
$
135.00.
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