BUSI 683 - MONEY AND CAPITAL
MARKETS - Stock Valuation
Question Bank - Set 2
Liberty University
Question 1
Question
ABC Company just paid a dividend of 5.00pershare.Dividendsareexpectedtogrowatarateof8
Solution
Let D0be the current dividend, gbe the growth rate of dividends, rbe the
required rate of return, and P0be the current price of the stock.
Step 1: Calculate the next dividend D1using the formula for constant
growth dividends:
D1=D0×(1 + g)
D1= $5.00 ×(1 + 0.08) = $5.40
Step 2: Calculate the price of the stock using the dividend discount model:
P0=D1
r−g
P0=$5.40
0.12 −0.08 = $135
Therefore, the current value of the stock is
$
135.
Question 2
Question
A company just paid a dividend of 3pershare.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the constant growth
dividend valuation model to determine the current value of the stock.
Step 1: The dividend growth rate (g) is given as 5
Step 2: The constant growth dividend valuation model is given by:
P0=D1
r−g
Where: - P0= current value of the stock - D1= expected dividend per share
next year - r= required rate of return - g= dividend growth rate
Given D0= 3, g= 5%, r = 10%, Calculate D1:
D1=D0×(1 + g)=3×(1 + 0.05) = 3.15
Substitute the values into the formula:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 3
Question
A company’s stock is expected to pay a dividend of 20persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the second year. Given that the dividends
are expected to grow at a rate of 5
D2=D1×(1 + g) = $20 ×(1 + 0.05) = $21
Step 2: Calculate the price of the stock using the Gordon Growth Model.
The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= Price of the stock today D1= Dividend expected next year r=
Required rate of return g= Growth rate of dividends
Substitute the known values into the equation:
P0=$20
0.10 −0.05 =$20
0.05 = $400
Therefore, the current price of the stock is
$
400 per share.
2
Question 4
Question
A company’s stock pays an annual dividend of 3.50.Iftherequiredrateof returnf orthisstockis10
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to find the current price of the stock.
Step 1:
The dividend growth rate (g) is given as 4
Step 2:
The Gordon Growth Model formula is:
P0=D0×(1 + g)
r−g
where: - P0= current price of the stock - D0= most recent dividend payment
= 3.50 −r= required rate of return = 10- g= dividend growth rate = 4
Plugging in the values, we get:
P0=3.50 ×(1 + 0.04)
0.10 −0.04
P0=3.50 ×1.04
0.06
P0=3.64
0.06
P0= 60.67
Therefore, the current price of the stock is 60.67.
Question 5
Question
A company is expected to pay an annual dividend of 4pershareindef initely.If therequiredrateofreturnis10
Solution
Step 1: Calculate the value of the stock using the dividend discount model
formula:
Stock Value = Dividend per share
Required rate of return
Step 2: Substitute the given values into the formula:
Stock Value = $4
0.10 = $40
Step 3: Therefore, the value of the stock is
$
40 per share.
3
Question 6
Question
A company’s stock currently has a dividend yield of 3
Solution
Step 1: Let’s denote the current stock price as P0, the dividend yield as D0=
0.03P0, the growth rate of dividends as g= 0.05, and the required rate of return
as r= 0.10.
Step 2: According to the dividend discount model, the stock price can be
calculated using the formula:
P0=D1
r−g
where D1is the dividend expected in the next year.
Step 3: We know that the dividend in the next year (D1) can be calculated
as:
D1=D0×(1 + g)
D1= 0.03P0×(1 + 0.05)
D1= 0.03P0×1.05
D1= 0.0315P0
Step 4: Now substitute D1= 0.0315P0,r= 0.10, and g= 0.05 into the
stock price formula from Step 2:
P0=0.0315P0
0.10 −0.05
Step 5: Simplify the equation:
P0=0.0315P0
0.05
P0= 0.63P0
Step 6: Divide both sides by P0to solve for P0:
1=0.63
P0=1
0.63
P0≈1.5873
Step 7: Therefore, the current stock price is approximately 1.5873.
4
Question 7
Question
A company pays an annual dividend of 5pershare, whichisexpectedtogrowataconstantrateof4
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model is given by:
P=D0×(1 + g)
R−g
where: P= Stock price D0= Dividend per share today = 5g= Dividend growth
rate = 0.04 R= Required rate of return = 8
Step 3: Substitute the given values into the formula.
P=5×(1 + 0.04)
0.08 −0.04
Step 4: Simplify the expression.
P=5×1.04
0.04
P=5.2
0.04
P= 130
Therefore, the stock price is 130pershare.
Question 8
Question
You are considering investing in a company that is expected to pay a dividend
of 5persharenextyear.T hedividendsareexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend in year 2. The dividend in year 2 can be calcu-
lated using the formula for dividend growth:
D2=D1×(1 + g)
5
where D1is the dividend in year 1, gis the growth rate, and D2is the dividend
in year 2. Plugging in the values, we get:
D2= 5 ×(1 + 0.08) = 5.4
Step 2: Calculate the dividend yield. The dividend yield can be calculated
using the formula:
Dividend yield =D2
R
where D2is the dividend in year 2 and Ris the required rate of return. Plugging
in the values, we get:
Dividend yield =5.4
0.12 = 45
Step 3: Calculate the stock price. The current value of the stock can be
calculated using the formula for a perpetuity:
P0=D1
R−g
where P0is the current value of the stock, D1is the dividend in year 1, Ris
the required rate of return, and gis the growth rate. Plugging in the values, we
get:
P0=5
0.12 −0.08 =5
0.04 = 125
Therefore, the current value of the stock is 125pershare.
Question 9
Question
A company is expected to pay an annual dividend of 3.00pershareindef initely.If therequiredrateofreturnis8%, whatisthevalueof thestock?
Solution
Step 1: Calculate the value of the stock using the Gordon Growth Model for-
mula:
P=D
r−g
where: P= Price of the stock D= Dividend per share r= Required rate of
return g= Growth rate of dividends
Step 2: Given data: D= $3.00 per share r= 8% = 0.08
Step 3: To calculate the growth rate (g), we can use the formula for the
Dividend Payout Ratio:
Dividend Payout Ratio = D
E
6
where: E= Earnings per share
Step 4: Since the dividend is paid out in full, the Dividend Payout Ratio is
equal to 1, and we can rearrange the formula to solve for E:
E=D
Dividend Payout Ratio =D
Step 5: The Gordon Growth Model formula can be rearranged to solve for
g:
g=r−D
P
Step 6: Substitute the known values into the formula:
g= 0.08 −3.00
P
Step 7: Since this is an indefinitely growing dividend, the growth rate g
should be less than the required rate of return r, so we can rewrite the formula
as:
0.08 >0.08 −3.00
P
Step 8: Solve for P:
0>−3.00
P
0>−3.00
This is true for all positive values of P, so the value of the stock is infinite
according to the Gordon Growth Model.
Question 10
Question
Company XYZ is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the expected dividend for the second year. Step 2: Use the
formula for the present value of a growing perpetuity to find the current stock
price.
Step 1: The dividend for the second year (D2) can be calculated using the
formula for a growing dividend:
D2=D1×(1 + g)
where D1= $5.00 (dividend for the first year), g= 8% = 0.08 (growth rate).
Substitute the given values:
D2= $5.00 ×(1 + 0.08) = $5.00 ×1.08 = $5.40
7
Therefore, the dividend for the second year is
$
5.40 per share.
Step 2: The present value of a growing perpetuity formula is given by:
P V =D
r−g
where D= $5.40 (dividend for the second year), r= 12% = 0.12 (required rate
of return), g= 8% = 0.08 (growth rate).
Substitute the values into the formula:
P V =$5.40
0.12 −0.08 =$5.40
0.04 = $135
Therefore, the current value of Company XYZ’s stock is
$
135 per share.
Question 11
Question
A company’s stock currently pays a dividend of 2.50pershare.Dividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the dividend growth rate. The dividend growth rate is given
as 5
Step 2: Calculate the dividend next year, D1.
D1=D0×(1 + growth rate) = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 3: Calculate the required rate of return, r. The required rate of return,
r, is given as 10
Step 4: Use the Gordon Growth Model formula to calculate the current value
of the stock, P0. The Gordon Growth Model formula is:
P0=D1
r−growth rate
Substitute the values into the formula:
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is 52.50pershare.
Question 12
Question
A company is expected to pay an annual dividend of 5pershareindef initely.If therequiredrateofreturnis10
8
Solution
Step 1: Calculate the stock price using the dividend discount model formula:
Stock Price = Dividend
Required Rate of Return
Step 2: Substitute the given values into the formula:
Stock Price = 5
0.10
Step 3: Perform the calculation:
Stock Price = $50
Step 4: Therefore, the value of the stock is
$
50 per share.
Question 13
Question
A company is expected to pay an annual dividend of 3.50pershareindef initely.If therequiredrateofreturnis8%, whatisthecurrentvalueof thestock?
Solution
Step 1: Calculate the present value of the perpetual annual dividend using the
Gordon Growth Model formula:
Present Value of Stock = Dividend
Required Rate of Return −Growth Rate
Step 2: Substitute the given values into the formula:
Present Value of Stock = 3.50
0.08 −0=3.50
0.08 = 43.75
Step 3: The current value of the stock is
$
43.75 per share.
Question 14
Question
A company’s stock is currently trading at $100 per share. The company is
expected to pay a dividend of $2 per share this year, and dividends are expected
to grow at a rate of 5% annually. If the required rate of return for this stock is
8%, what is the stock’s expected price in 5 years?
9
Solution
Step 1: Calculate the dividend in 5 years. Given that the dividend is expected
to grow at a rate of 5% annually, the dividend in 5 years will be:
D= $2 ×(1 + 0.05)5= $2 ×1.2763 = $2.5526.
Step 2: Calculate the expected price of the stock in 5 years using the Gordon
Growth Model. The Gordon Growth Model formula is:
P=D
r−g,
where: - Pis the expected price of the stock, - Dis the dividend in 5 years
(
$
2.5526), - ris the required rate of return (8- gis the growth rate of dividends
(5
Substitute the values into the formula:
P=$2.5526
0.08 −0.05 =$2.5526
0.03 = $85.087.
Therefore, the stock’s expected price in 5 years is $85.087.
Question 15
Question
A company’s stock is currently trading at $100 per share. It is expected to pay
a dividend of $5.00 per share at the end of the year. The expected growth rate
of the company’s dividends is 8% per year forever. If the required rate of return
is 12%, what is the value of the stock?
Solution
Step 1: Calculate the dividend expected at the end of the year using the growth
rate.
Dividend at the end of the year = Current dividend ×(1 + Growth rate)
= $5.00 ×(1 + 0.08)
= $5.40
Step 2: Use the Gordon Growth Model to find the value of the stock. The
Gordon Growth Model is given by:
Stock Value = Dividend at the end of the year
Required rate of return −Growth rate
10
Plugging in the values:
Stock Value = $5.40
0.12 −0.08
=$5.40
0.04
= $135.00
Therefore, the value of the stock is $135.00.
Question 16
Question
A company’s stock is expected to pay a dividend of $5 next year. The dividends
are expected to grow indefinitely at a constant rate of 4
Solution
Step 1: Calculate the dividend in the following year using the growth rate. Step
2: Calculate the price of the stock using the formula for the present value of a
perpetuity.
Step 1: The dividend expected to be paid next year is D1= $5. The growth
rate is 4
D2=D1×(1 + growth rate) = $5 ×(1 + 0.04) = $5.20
Step 2: To find the current value of the stock (P0), we can use the formula
for the present value of a perpetuity:
P0=D1
r−g
where: D1= expected dividend next year =
$
5, r= required rate of return =
10g= growth rate = 4
Plugging in the values, we get:
P0=5
0.10 −0.04 =5
0.06 = $83.33
Therefore, the current value of the stock is
$
83.33.
Question 17
Question
Company XYZ is expected to pay an annual dividend of 4.50pershareindef initely.If therequiredrateofreturnis10
11
Solution
Step 1: Calculate the stock price using the Gordon Growth Model formula:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend of 4.50pershareindefinitely, thegrowthratecanbeassumedtobezero(dividendsarenotexpectedtogrow).Stock Price =
4.50
0.10−0
Stock Price = 4.50
0.10
Step 3: Calculate the stock price:
Stock Price = 45
Therefore, the stock price of Company XYZ is 45pershare.
Question 18
Question
A company’s stock currently pays an annual dividend of 5pershare.Iftherequiredrateof returnforthisstockis10
Solution
Step 1: Calculate the dividend growth rate using the formula g=D1
D0−1, where
D1 is the next year’s dividend and D0 is the current dividend.
g=5(1 + 0.04)
5−1
= 0.04
Step 2: Calculate the dividend expected one year from now using the formula
D1 = D0(1 + g).
D1 = 5(1 + 0.04) = 5.2
Step 3: Calculate the stock price using the Gordon Growth Model formula
P0 = D1
r−g, where ris the required rate of return.
P0 = 5.2
0.10 −0.04
=5.2
0.06
= 86.67
Therefore, the current stock price is 86.67pershare.
12
Question 19
Question
A company is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividends for the next 5 years using the dividend growth
rate formula:
Dn=D0×(1 + g)n
where: - Dn= Dividend in year n-D0= Dividend in the first year - g=
Growth rate - n= Number of years
Given D0= 5.00, g= 8% = 0.08, and n= 1,2,3,4,5, we can calculate: -
D1= 5.00 ×(1 + 0.08)1-D2= 5.00 ×(1 + 0.08)2-D3= 5.00 ×(1 + 0.08)3-
D4= 5.00 ×(1 + 0.08)4-D5= 5.00 ×(1 + 0.08)5
Step 2: Calculate the dividend in year 6 which grows at a constant rate of 3
D6=D5×(1 + g)
Step 3: Find the present value of all future dividends using the formula for
the present value of a growing perpetuity:
P V =D1
(1 + r)1+D2
(1 + r)2+... +D5
(1 + r)5+D6
(1 + r)6
where: - P V = Present value - r= Required rate of return
Given r= 10% = 0.10, compute the present value.
Step 4: Calculate the stock price by subtracting the present value of all
future dividends from the present value of a growing perpetuity:
Stock P rice =P V −D6
r−g
Compute the stock price.
Question 20
Question
A company is expected to pay a dividend of 3.00persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in year 2.
Dividend in year 2 = Dividend in year 1 ×(1 + growth rate)
13
Dividend in year 2 = $3.00 ×(1 + 0.05)
Dividend in year 2 = $3.00 ×1.05 = $3.15
Step 2: Calculate the dividend discount model value of the stock.
P0=D1
r−g
where: P0= price of the stock today D1= dividend in year 1 r= required rate
of return g= growth rate
Substitute the given values:
P0=$3.00
0.10 −0.05
P0=$3.00
0.05
P0= $60.00
Therefore, the current value of the stock is
$
60.00.
Question 21
Question
A company is expected to pay a dividend of 5persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividend one year from now. The dividend one year from
now (D1) can be calculated using the formula:
D1=D0×(1 + growth rate)
where - D0= dividend this year = 5 −Growthrate = 8
Therefore,
D1= 5 ×(1 + 0.08) = 5 ×1.08 = 5.40
Step 2: Calculate the current price of the stock using the constant growth
dividend valuation model formula. The price of the stock (P0) can be calculated
using the formula:
P0=D1
r−g
where - D1= dividend one year from now = 5.40−r= requiredrateof return =
12−g= growthrate = 8
Therefore,
P0=5.40
0.12 −0.08 =5.40
0.04 = 135
Hence, the current value of the stock is 135pershare.
14
Question 22
Question
A company’s stock is expected to pay a dividend of 3.50 next year and dividends
are expected to grow at a rate of 5% per year indefinitely. If the required rate
of return is 10%, what is the current value of the stock?
Solution
Step 1: Calculate the expected dividend for the second year. Given that divi-
dends are expected to grow at a rate of 5% per year, the expected dividend for
the second year can be calculated as follows:
Expected Dividend for Year 2 = Expected Dividend for Year 1×(1+Growth Rate)
Expected Dividend for Year 2 = 3.50 ×(1 + 0.05) = 3.50 ×1.05 = 3.675
Step 2: Determine the dividend discount model. The stock price can be
calculated using the dividend discount model, which is represented as:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 3: Calculate the current value of the stock. Substitute the given values
into the formula:
Stock Price = 3.50
0.10 −0.05 =3.50
0.05 = 70
Therefore, the current value of the stock is 70.
Question 23
Question
A company’s stock is currently priced at $100 per share. The company is ex-
pected to pay a dividend of $5 per share next year. If dividends are expected
to grow at a rate of 8
Solution
Let’s denote the required rate of return by r, the dividend next year by D1,
and the dividend growth rate by g. We can use the Dividend Discount Model
(DDM) to find the required rate of return:
P0=D1
r−g
15
Step 1: Find D1Given that the company is expected to pay a dividend of
$5 per share next year, D1= $5.
Step 2: Plug in the given values into the DDM formula We can plug
in the given values into the DDM formula:
100 = 5
r−0.08
Step 3: Solve for rSolving for r:
100 = 5
r−0.08
100r−8=5
100r= 13
r=13
100 = 0.13 = 13%
So, the stock’s required rate of return is 13
Question 24
Question
A company’s stock is currently trading at $50 per share. The company is ex-
pected to pay a dividend of $2 per share next year, with dividends expected to
grow at a rate of 5% per year indefinitely. If the required rate of return is 10%,
what is the intrinsic value of the stock?
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Expected Dividend for Next Year = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the expected dividend for the following year.
Expected Dividend in 2 Years = $2.10 ×(1 + 0.05) = $2.205
Step 3: Calculate the dividend yield, which is the expected dividend divided
by the current stock price.
Dividend Yield = $2.205
$50 = 0.0441
Step 4: Calculate the capital gains yield, which is the growth rate of divi-
dends.
Capital Gains Yield = 0.05 = 0.05
16
Step 5: Determine the total rate of return on the stock.
Total Rate of Return = Dividend Yield+Capital Gains Yield = 0.0441+0.05 = 0.0941
Step 6: Use the Gordon Growth Model to calculate the intrinsic value of the
stock.
V0=D1
r−g
V0=$2.10
0.10 −0.05
V0=$2.10
0.05
V0= $42
Therefore, the intrinsic value of the stock is $42.
Question 25
Question
A company’s dividends are expected to grow at a rate of 6
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = Previous dividend ×(1 + Growth rate)
Next dividend = $2.50 ×(1 + 0.06)
Next dividend = $2.50 ×1.06
Next dividend = $2.65
Step 2: Calculate the price of the stock using the dividend discount model.
Price = Next dividend
Required rate of return - Growth rate
Price = $2.65
0.10 −0.06
Price = $2.65
0.04
Price = $66.25
Therefore, the current price of the stock is
$
66.25.
17
Question 26
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowindef initelyataconstantrateof4
Solution
Step 1: Calculate the dividend in the following year using the growth rate:
Let D0be the dividend this year, D1be the dividend next year, and gbe the
growth rate. From the information provided, we have: D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.04) D1= 3.50 ×1.04 D1= 3.64
Step 2: Calculate the price of the stock using the Gordon Growth Model
formula: The Gordon Growth Model is given by: P0=D1
r−gwhere P0is the
current price of the stock, D1is the dividend next year, ris the required rate of
return, and gis the growth rate. Substitute the known values into the formula:
P0=3.64
0.10−0.04 P0=3.64
0.06 P0= 60.67
Therefore, the current price of the stock is 60.67pershare.
Question 27
Question
A company’s stock is expected to pay dividends of 2,2.50, and 3forthenextthreeyears.Af terthat, thedividendsareexpectedtogrowataconstantrateof 6
Solution
Step 1: Calculate the present value of the dividends for the first three years.
Given:
D1=
$
2
D2=
$
2.50
D3=
$
3
r= 10%
The present value of the first three dividends is calculated as follows:
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
P V =2
1.101+2.50
1.102+3
1.103
P V =2
1.10 +2.50
1.21 +3
1.331
P V ≈$5.37
18
Step 2: Calculate the present value of all future dividends. To find the value
of all future dividends after 3 years, we can use the Gordon Growth Model
formula:
P V =D3×(1 + g)
r−g
Where:
D3= 3
g= 6% = 0.06
r= 10% = 0.10
Substitute these values into the formula:
P V =3×(1 + 0.06)
0.10 −0.06
P V =3×1.06
0.04
P V =3.18
0.04
P V = $79.50
Step 3: Calculate the current value of the stock. The current value of the
stock is the sum of the present value of the first three dividends and the present
value of all future dividends:
Stock Value = $5.37 + $79.50
Stock Value = $84.87
Question 28
Question
You are considering investing in a company which is expected to pay an annual
dividend of 3.50pershareindefinitely.Iftherequiredrateof returnis10
Solution
Step 1: Calculate the price of the stock using the Gordon Growth Model. The
formula for the Gordon Growth Model is:
P=D
r−g
where: - P= Price of the stock - D= Annual dividend per share - r= Required
rate of return - g= Growth rate of dividends
19
Step 2: Substitute the given values into the formula:
P=3.50
0.10 −0
P=3.50
0.10
P= 35
Step 3: Therefore, the current value of the stock is 35pershare.
Question 29
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay an annual dividend of $5 per share indefinitely. If the required
rate of return for this stock is 10%, what is the estimated value of the stock
using the Gordon Growth Model?
Solution
Step 1: Calculate the growth rate using the dividend and required rate of return.
Dividend Growth Rate = Dividend per Share
Current Price per Share
Step 2: Plug in the values into the Gordon Growth Model formula.
P0=D0·(1 + g)
r−g
where: - P0= Estimated value of the stock - D0= Dividend per share - g=
Growth rate - r= Required rate of return
Step 3: Substitute the given values into the formula.
P0=$5 ·(1 + g)
0.10 −g
Step 4: Substitute the growth rate calculated in Step 1 into the formula
from Step 3.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate
Step 5: Solve for the estimated value of the stock P0by substituting the
given values.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate =?
20
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the constant growth
dividend valuation model to determine the current value of the stock.
Step 1: The dividend growth rate (g) is given as 5
Step 2: The constant growth dividend valuation model is given by:
P0=D1
r−g
Where: - P0= current value of the stock - D1= expected dividend per share
next year - r= required rate of return - g= dividend growth rate
Given D0= 3, g= 5%, r = 10%, Calculate D1:
D1=D0×(1 + g)=3×(1 + 0.05) = 3.15
Substitute the values into the formula:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 3
Question
A company’s stock is expected to pay a dividend of 20persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the second year. Given that the dividends
are expected to grow at a rate of 5
D2=D1×(1 + g) = $20 ×(1 + 0.05) = $21
Step 2: Calculate the price of the stock using the Gordon Growth Model.
The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= Price of the stock today D1= Dividend expected next year r=
Required rate of return g= Growth rate of dividends
Substitute the known values into the equation:
P0=$20
0.10 −0.05 =$20
0.05 = $400
Therefore, the current price of the stock is
$
400 per share.
2
Question 4
Question
A company’s stock pays an annual dividend of 3.50.Iftherequiredrateof returnf orthisstockis10
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to find the current price of the stock.
Step 1:
The dividend growth rate (g) is given as 4
Step 2:
The Gordon Growth Model formula is:
P0=D0×(1 + g)
r−g
where: - P0= current price of the stock - D0= most recent dividend payment
= 3.50 −r= required rate of return = 10- g= dividend growth rate = 4
Plugging in the values, we get:
P0=3.50 ×(1 + 0.04)
0.10 −0.04
P0=3.50 ×1.04
0.06
P0=3.64
0.06
P0= 60.67
Therefore, the current price of the stock is 60.67.
Question 5
Question
A company is expected to pay an annual dividend of 4pershareindef initely.If therequiredrateofreturnis10
Solution
Step 1: Calculate the value of the stock using the dividend discount model
formula:
Stock Value = Dividend per share
Required rate of return
Step 2: Substitute the given values into the formula:
Stock Value = $4
0.10 = $40
Step 3: Therefore, the value of the stock is
$
40 per share.
3
Question 6
Question
A company’s stock currently has a dividend yield of 3
Solution
Step 1: Let’s denote the current stock price as P0, the dividend yield as D0=
0.03P0, the growth rate of dividends as g= 0.05, and the required rate of return
as r= 0.10.
Step 2: According to the dividend discount model, the stock price can be
calculated using the formula:
P0=D1
r−g
where D1is the dividend expected in the next year.
Step 3: We know that the dividend in the next year (D1) can be calculated
as:
D1=D0×(1 + g)
D1= 0.03P0×(1 + 0.05)
D1= 0.03P0×1.05
D1= 0.0315P0
Step 4: Now substitute D1= 0.0315P0,r= 0.10, and g= 0.05 into the
stock price formula from Step 2:
P0=0.0315P0
0.10 −0.05
Step 5: Simplify the equation:
P0=0.0315P0
0.05
P0= 0.63P0
Step 6: Divide both sides by P0to solve for P0:
1=0.63
P0=1
0.63
P0≈1.5873
Step 7: Therefore, the current stock price is approximately 1.5873.
4
Question 7
Question
A company pays an annual dividend of 5pershare, whichisexpectedtogrowataconstantrateof4
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model is given by:
P=D0×(1 + g)
R−g
where: P= Stock price D0= Dividend per share today = 5g= Dividend growth
rate = 0.04 R= Required rate of return = 8
Step 3: Substitute the given values into the formula.
P=5×(1 + 0.04)
0.08 −0.04
Step 4: Simplify the expression.
P=5×1.04
0.04
P=5.2
0.04
P= 130
Therefore, the stock price is 130pershare.
Question 8
Question
You are considering investing in a company that is expected to pay a dividend
of 5persharenextyear.T hedividendsareexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend in year 2. The dividend in year 2 can be calcu-
lated using the formula for dividend growth:
D2=D1×(1 + g)
5
where D1is the dividend in year 1, gis the growth rate, and D2is the dividend
in year 2. Plugging in the values, we get:
D2= 5 ×(1 + 0.08) = 5.4
Step 2: Calculate the dividend yield. The dividend yield can be calculated
using the formula:
Dividend yield =D2
R
where D2is the dividend in year 2 and Ris the required rate of return. Plugging
in the values, we get:
Dividend yield =5.4
0.12 = 45
Step 3: Calculate the stock price. The current value of the stock can be
calculated using the formula for a perpetuity:
P0=D1
R−g
where P0is the current value of the stock, D1is the dividend in year 1, Ris
the required rate of return, and gis the growth rate. Plugging in the values, we
get:
P0=5
0.12 −0.08 =5
0.04 = 125
Therefore, the current value of the stock is 125pershare.
Question 9
Question
A company is expected to pay an annual dividend of 3.00pershareindef initely.If therequiredrateofreturnis8%, whatisthevalueof thestock?
Solution
Step 1: Calculate the value of the stock using the Gordon Growth Model for-
mula:
P=D
r−g
where: P= Price of the stock D= Dividend per share r= Required rate of
return g= Growth rate of dividends
Step 2: Given data: D= $3.00 per share r= 8% = 0.08
Step 3: To calculate the growth rate (g), we can use the formula for the
Dividend Payout Ratio:
Dividend Payout Ratio = D
E
6
where: E= Earnings per share
Step 4: Since the dividend is paid out in full, the Dividend Payout Ratio is
equal to 1, and we can rearrange the formula to solve for E:
E=D
Dividend Payout Ratio =D
Step 5: The Gordon Growth Model formula can be rearranged to solve for
g:
g=r−D
P
Step 6: Substitute the known values into the formula:
g= 0.08 −3.00
P
Step 7: Since this is an indefinitely growing dividend, the growth rate g
should be less than the required rate of return r, so we can rewrite the formula
as:
0.08 >0.08 −3.00
P
Step 8: Solve for P:
0>−3.00
P
0>−3.00
This is true for all positive values of P, so the value of the stock is infinite
according to the Gordon Growth Model.
Question 10
Question
Company XYZ is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the expected dividend for the second year. Step 2: Use the
formula for the present value of a growing perpetuity to find the current stock
price.
Step 1: The dividend for the second year (D2) can be calculated using the
formula for a growing dividend:
D2=D1×(1 + g)
where D1= $5.00 (dividend for the first year), g= 8% = 0.08 (growth rate).
Substitute the given values:
D2= $5.00 ×(1 + 0.08) = $5.00 ×1.08 = $5.40
7
Therefore, the dividend for the second year is
$
5.40 per share.
Step 2: The present value of a growing perpetuity formula is given by:
P V =D
r−g
where D= $5.40 (dividend for the second year), r= 12% = 0.12 (required rate
of return), g= 8% = 0.08 (growth rate).
Substitute the values into the formula:
P V =$5.40
0.12 −0.08 =$5.40
0.04 = $135
Therefore, the current value of Company XYZ’s stock is
$
135 per share.
Question 11
Question
A company’s stock currently pays a dividend of 2.50pershare.Dividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the dividend growth rate. The dividend growth rate is given
as 5
Step 2: Calculate the dividend next year, D1.
D1=D0×(1 + growth rate) = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 3: Calculate the required rate of return, r. The required rate of return,
r, is given as 10
Step 4: Use the Gordon Growth Model formula to calculate the current value
of the stock, P0. The Gordon Growth Model formula is:
P0=D1
r−growth rate
Substitute the values into the formula:
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is 52.50pershare.
Question 12
Question
A company is expected to pay an annual dividend of 5pershareindef initely.If therequiredrateofreturnis10
8
Solution
Step 1: Calculate the stock price using the dividend discount model formula:
Stock Price = Dividend
Required Rate of Return
Step 2: Substitute the given values into the formula:
Stock Price = 5
0.10
Step 3: Perform the calculation:
Stock Price = $50
Step 4: Therefore, the value of the stock is
$
50 per share.
Question 13
Question
A company is expected to pay an annual dividend of 3.50pershareindef initely.If therequiredrateofreturnis8%, whatisthecurrentvalueof thestock?
Solution
Step 1: Calculate the present value of the perpetual annual dividend using the
Gordon Growth Model formula:
Present Value of Stock = Dividend
Required Rate of Return −Growth Rate
Step 2: Substitute the given values into the formula:
Present Value of Stock = 3.50
0.08 −0=3.50
0.08 = 43.75
Step 3: The current value of the stock is
$
43.75 per share.
Question 14
Question
A company’s stock is currently trading at $100 per share. The company is
expected to pay a dividend of $2 per share this year, and dividends are expected
to grow at a rate of 5% annually. If the required rate of return for this stock is
8%, what is the stock’s expected price in 5 years?
9
Solution
Step 1: Calculate the dividend in 5 years. Given that the dividend is expected
to grow at a rate of 5% annually, the dividend in 5 years will be:
D= $2 ×(1 + 0.05)5= $2 ×1.2763 = $2.5526.
Step 2: Calculate the expected price of the stock in 5 years using the Gordon
Growth Model. The Gordon Growth Model formula is:
P=D
r−g,
where: - Pis the expected price of the stock, - Dis the dividend in 5 years
(
$
2.5526), - ris the required rate of return (8- gis the growth rate of dividends
(5
Substitute the values into the formula:
P=$2.5526
0.08 −0.05 =$2.5526
0.03 = $85.087.
Therefore, the stock’s expected price in 5 years is $85.087.
Question 15
Question
A company’s stock is currently trading at $100 per share. It is expected to pay
a dividend of $5.00 per share at the end of the year. The expected growth rate
of the company’s dividends is 8% per year forever. If the required rate of return
is 12%, what is the value of the stock?
Solution
Step 1: Calculate the dividend expected at the end of the year using the growth
rate.
Dividend at the end of the year = Current dividend ×(1 + Growth rate)
= $5.00 ×(1 + 0.08)
= $5.40
Step 2: Use the Gordon Growth Model to find the value of the stock. The
Gordon Growth Model is given by:
Stock Value = Dividend at the end of the year
Required rate of return −Growth rate
10
Plugging in the values:
Stock Value = $5.40
0.12 −0.08
=$5.40
0.04
= $135.00
Therefore, the value of the stock is $135.00.
Question 16
Question
A company’s stock is expected to pay a dividend of $5 next year. The dividends
are expected to grow indefinitely at a constant rate of 4
Solution
Step 1: Calculate the dividend in the following year using the growth rate. Step
2: Calculate the price of the stock using the formula for the present value of a
perpetuity.
Step 1: The dividend expected to be paid next year is D1= $5. The growth
rate is 4
D2=D1×(1 + growth rate) = $5 ×(1 + 0.04) = $5.20
Step 2: To find the current value of the stock (P0), we can use the formula
for the present value of a perpetuity:
P0=D1
r−g
where: D1= expected dividend next year =
$
5, r= required rate of return =
10g= growth rate = 4
Plugging in the values, we get:
P0=5
0.10 −0.04 =5
0.06 = $83.33
Therefore, the current value of the stock is
$
83.33.
Question 17
Question
Company XYZ is expected to pay an annual dividend of 4.50pershareindef initely.If therequiredrateofreturnis10
11
Solution
Step 1: Calculate the stock price using the Gordon Growth Model formula:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend of 4.50pershareindefinitely, thegrowthratecanbeassumedtobezero(dividendsarenotexpectedtogrow).Stock Price =
4.50
0.10−0
Stock Price = 4.50
0.10
Step 3: Calculate the stock price:
Stock Price = 45
Therefore, the stock price of Company XYZ is 45pershare.
Question 18
Question
A company’s stock currently pays an annual dividend of 5pershare.Iftherequiredrateof returnforthisstockis10
Solution
Step 1: Calculate the dividend growth rate using the formula g=D1
D0−1, where
D1 is the next year’s dividend and D0 is the current dividend.
g=5(1 + 0.04)
5−1
= 0.04
Step 2: Calculate the dividend expected one year from now using the formula
D1 = D0(1 + g).
D1 = 5(1 + 0.04) = 5.2
Step 3: Calculate the stock price using the Gordon Growth Model formula
P0 = D1
r−g, where ris the required rate of return.
P0 = 5.2
0.10 −0.04
=5.2
0.06
= 86.67
Therefore, the current stock price is 86.67pershare.
12
Question 19
Question
A company is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividends for the next 5 years using the dividend growth
rate formula:
Dn=D0×(1 + g)n
where: - Dn= Dividend in year n-D0= Dividend in the first year - g=
Growth rate - n= Number of years
Given D0= 5.00, g= 8% = 0.08, and n= 1,2,3,4,5, we can calculate: -
D1= 5.00 ×(1 + 0.08)1-D2= 5.00 ×(1 + 0.08)2-D3= 5.00 ×(1 + 0.08)3-
D4= 5.00 ×(1 + 0.08)4-D5= 5.00 ×(1 + 0.08)5
Step 2: Calculate the dividend in year 6 which grows at a constant rate of 3
D6=D5×(1 + g)
Step 3: Find the present value of all future dividends using the formula for
the present value of a growing perpetuity:
P V =D1
(1 + r)1+D2
(1 + r)2+... +D5
(1 + r)5+D6
(1 + r)6
where: - P V = Present value - r= Required rate of return
Given r= 10% = 0.10, compute the present value.
Step 4: Calculate the stock price by subtracting the present value of all
future dividends from the present value of a growing perpetuity:
Stock P rice =P V −D6
r−g
Compute the stock price.
Question 20
Question
A company is expected to pay a dividend of 3.00persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in year 2.
Dividend in year 2 = Dividend in year 1 ×(1 + growth rate)
13
Dividend in year 2 = $3.00 ×(1 + 0.05)
Dividend in year 2 = $3.00 ×1.05 = $3.15
Step 2: Calculate the dividend discount model value of the stock.
P0=D1
r−g
where: P0= price of the stock today D1= dividend in year 1 r= required rate
of return g= growth rate
Substitute the given values:
P0=$3.00
0.10 −0.05
P0=$3.00
0.05
P0= $60.00
Therefore, the current value of the stock is
$
60.00.
Question 21
Question
A company is expected to pay a dividend of 5persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividend one year from now. The dividend one year from
now (D1) can be calculated using the formula:
D1=D0×(1 + growth rate)
where - D0= dividend this year = 5 −Growthrate = 8
Therefore,
D1= 5 ×(1 + 0.08) = 5 ×1.08 = 5.40
Step 2: Calculate the current price of the stock using the constant growth
dividend valuation model formula. The price of the stock (P0) can be calculated
using the formula:
P0=D1
r−g
where - D1= dividend one year from now = 5.40−r= requiredrateof return =
12−g= growthrate = 8
Therefore,
P0=5.40
0.12 −0.08 =5.40
0.04 = 135
Hence, the current value of the stock is 135pershare.
14
Question 22
Question
A company’s stock is expected to pay a dividend of 3.50 next year and dividends
are expected to grow at a rate of 5% per year indefinitely. If the required rate
of return is 10%, what is the current value of the stock?
Solution
Step 1: Calculate the expected dividend for the second year. Given that divi-
dends are expected to grow at a rate of 5% per year, the expected dividend for
the second year can be calculated as follows:
Expected Dividend for Year 2 = Expected Dividend for Year 1×(1+Growth Rate)
Expected Dividend for Year 2 = 3.50 ×(1 + 0.05) = 3.50 ×1.05 = 3.675
Step 2: Determine the dividend discount model. The stock price can be
calculated using the dividend discount model, which is represented as:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 3: Calculate the current value of the stock. Substitute the given values
into the formula:
Stock Price = 3.50
0.10 −0.05 =3.50
0.05 = 70
Therefore, the current value of the stock is 70.
Question 23
Question
A company’s stock is currently priced at $100 per share. The company is ex-
pected to pay a dividend of $5 per share next year. If dividends are expected
to grow at a rate of 8
Solution
Let’s denote the required rate of return by r, the dividend next year by D1,
and the dividend growth rate by g. We can use the Dividend Discount Model
(DDM) to find the required rate of return:
P0=D1
r−g
15
Step 1: Find D1Given that the company is expected to pay a dividend of
$5 per share next year, D1= $5.
Step 2: Plug in the given values into the DDM formula We can plug
in the given values into the DDM formula:
100 = 5
r−0.08
Step 3: Solve for rSolving for r:
100 = 5
r−0.08
100r−8=5
100r= 13
r=13
100 = 0.13 = 13%
So, the stock’s required rate of return is 13
Question 24
Question
A company’s stock is currently trading at $50 per share. The company is ex-
pected to pay a dividend of $2 per share next year, with dividends expected to
grow at a rate of 5% per year indefinitely. If the required rate of return is 10%,
what is the intrinsic value of the stock?
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Expected Dividend for Next Year = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the expected dividend for the following year.
Expected Dividend in 2 Years = $2.10 ×(1 + 0.05) = $2.205
Step 3: Calculate the dividend yield, which is the expected dividend divided
by the current stock price.
Dividend Yield = $2.205
$50 = 0.0441
Step 4: Calculate the capital gains yield, which is the growth rate of divi-
dends.
Capital Gains Yield = 0.05 = 0.05
16
Step 5: Determine the total rate of return on the stock.
Total Rate of Return = Dividend Yield+Capital Gains Yield = 0.0441+0.05 = 0.0941
Step 6: Use the Gordon Growth Model to calculate the intrinsic value of the
stock.
V0=D1
r−g
V0=$2.10
0.10 −0.05
V0=$2.10
0.05
V0= $42
Therefore, the intrinsic value of the stock is $42.
Question 25
Question
A company’s dividends are expected to grow at a rate of 6
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = Previous dividend ×(1 + Growth rate)
Next dividend = $2.50 ×(1 + 0.06)
Next dividend = $2.50 ×1.06
Next dividend = $2.65
Step 2: Calculate the price of the stock using the dividend discount model.
Price = Next dividend
Required rate of return - Growth rate
Price = $2.65
0.10 −0.06
Price = $2.65
0.04
Price = $66.25
Therefore, the current price of the stock is
$
66.25.
17
Question 26
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowindef initelyataconstantrateof4
Solution
Step 1: Calculate the dividend in the following year using the growth rate:
Let D0be the dividend this year, D1be the dividend next year, and gbe the
growth rate. From the information provided, we have: D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.04) D1= 3.50 ×1.04 D1= 3.64
Step 2: Calculate the price of the stock using the Gordon Growth Model
formula: The Gordon Growth Model is given by: P0=D1
r−gwhere P0is the
current price of the stock, D1is the dividend next year, ris the required rate of
return, and gis the growth rate. Substitute the known values into the formula:
P0=3.64
0.10−0.04 P0=3.64
0.06 P0= 60.67
Therefore, the current price of the stock is 60.67pershare.
Question 27
Question
A company’s stock is expected to pay dividends of 2,2.50, and 3forthenextthreeyears.Af terthat, thedividendsareexpectedtogrowataconstantrateof 6
Solution
Step 1: Calculate the present value of the dividends for the first three years.
Given:
D1=
$
2
D2=
$
2.50
D3=
$
3
r= 10%
The present value of the first three dividends is calculated as follows:
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
P V =2
1.101+2.50
1.102+3
1.103
P V =2
1.10 +2.50
1.21 +3
1.331
P V ≈$5.37
18
Step 2: Calculate the present value of all future dividends. To find the value
of all future dividends after 3 years, we can use the Gordon Growth Model
formula:
P V =D3×(1 + g)
r−g
Where:
D3= 3
g= 6% = 0.06
r= 10% = 0.10
Substitute these values into the formula:
P V =3×(1 + 0.06)
0.10 −0.06
P V =3×1.06
0.04
P V =3.18
0.04
P V = $79.50
Step 3: Calculate the current value of the stock. The current value of the
stock is the sum of the present value of the first three dividends and the present
value of all future dividends:
Stock Value = $5.37 + $79.50
Stock Value = $84.87
Question 28
Question
You are considering investing in a company which is expected to pay an annual
dividend of 3.50pershareindefinitely.Iftherequiredrateof returnis10
Solution
Step 1: Calculate the price of the stock using the Gordon Growth Model. The
formula for the Gordon Growth Model is:
P=D
r−g
where: - P= Price of the stock - D= Annual dividend per share - r= Required
rate of return - g= Growth rate of dividends
19
Step 2: Substitute the given values into the formula:
P=3.50
0.10 −0
P=3.50
0.10
P= 35
Step 3: Therefore, the current value of the stock is 35pershare.
Question 29
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay an annual dividend of $5 per share indefinitely. If the required
rate of return for this stock is 10%, what is the estimated value of the stock
using the Gordon Growth Model?
Solution
Step 1: Calculate the growth rate using the dividend and required rate of return.
Dividend Growth Rate = Dividend per Share
Current Price per Share
Step 2: Plug in the values into the Gordon Growth Model formula.
P0=D0·(1 + g)
r−g
where: - P0= Estimated value of the stock - D0= Dividend per share - g=
Growth rate - r= Required rate of return
Step 3: Substitute the given values into the formula.
P0=$5 ·(1 + g)
0.10 −g
Step 4: Substitute the growth rate calculated in Step 1 into the formula
from Step 3.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate
Step 5: Solve for the estimated value of the stock P0by substituting the
given values.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate =?
20
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the constant growth
dividend valuation model to determine the current value of the stock.
Step 1: The dividend growth rate (g) is given as 5
Step 2: The constant growth dividend valuation model is given by:
P0=D1
r−g
Where: - P0= current value of the stock - D1= expected dividend per share
next year - r= required rate of return - g= dividend growth rate
Given D0= 3, g= 5%, r = 10%, Calculate D1:
D1=D0×(1 + g)=3×(1 + 0.05) = 3.15
Substitute the values into the formula:
P0=3.15
0.10 −0.05 =3.15
0.05 = 63
Therefore, the current value of the stock is 63pershare.
Question 3
Question
A company’s stock is expected to pay a dividend of 20persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the second year. Given that the dividends
are expected to grow at a rate of 5
D2=D1×(1 + g) = $20 ×(1 + 0.05) = $21
Step 2: Calculate the price of the stock using the Gordon Growth Model.
The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= Price of the stock today D1= Dividend expected next year r=
Required rate of return g= Growth rate of dividends
Substitute the known values into the equation:
P0=$20
0.10 −0.05 =$20
0.05 = $400
Therefore, the current price of the stock is
$
400 per share.
2
Question 4
Question
A company’s stock pays an annual dividend of 3.50.Iftherequiredrateof returnf orthisstockis10
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to find the current price of the stock.
Step 1:
The dividend growth rate (g) is given as 4
Step 2:
The Gordon Growth Model formula is:
P0=D0×(1 + g)
r−g
where: - P0= current price of the stock - D0= most recent dividend payment
= 3.50 −r= required rate of return = 10- g= dividend growth rate = 4
Plugging in the values, we get:
P0=3.50 ×(1 + 0.04)
0.10 −0.04
P0=3.50 ×1.04
0.06
P0=3.64
0.06
P0= 60.67
Therefore, the current price of the stock is 60.67.
Question 5
Question
A company is expected to pay an annual dividend of 4pershareindef initely.If therequiredrateofreturnis10
Solution
Step 1: Calculate the value of the stock using the dividend discount model
formula:
Stock Value = Dividend per share
Required rate of return
Step 2: Substitute the given values into the formula:
Stock Value = $4
0.10 = $40
Step 3: Therefore, the value of the stock is
$
40 per share.
3
Question 6
Question
A company’s stock currently has a dividend yield of 3
Solution
Step 1: Let’s denote the current stock price as P0, the dividend yield as D0=
0.03P0, the growth rate of dividends as g= 0.05, and the required rate of return
as r= 0.10.
Step 2: According to the dividend discount model, the stock price can be
calculated using the formula:
P0=D1
r−g
where D1is the dividend expected in the next year.
Step 3: We know that the dividend in the next year (D1) can be calculated
as:
D1=D0×(1 + g)
D1= 0.03P0×(1 + 0.05)
D1= 0.03P0×1.05
D1= 0.0315P0
Step 4: Now substitute D1= 0.0315P0,r= 0.10, and g= 0.05 into the
stock price formula from Step 2:
P0=0.0315P0
0.10 −0.05
Step 5: Simplify the equation:
P0=0.0315P0
0.05
P0= 0.63P0
Step 6: Divide both sides by P0to solve for P0:
1=0.63
P0=1
0.63
P0≈1.5873
Step 7: Therefore, the current stock price is approximately 1.5873.
4
Question 7
Question
A company pays an annual dividend of 5pershare, whichisexpectedtogrowataconstantrateof4
Solution
Step 1: Calculate the dividend growth rate. Given that the dividend is expected
to grow at a constant rate of 4
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model is given by:
P=D0×(1 + g)
R−g
where: P= Stock price D0= Dividend per share today = 5g= Dividend growth
rate = 0.04 R= Required rate of return = 8
Step 3: Substitute the given values into the formula.
P=5×(1 + 0.04)
0.08 −0.04
Step 4: Simplify the expression.
P=5×1.04
0.04
P=5.2
0.04
P= 130
Therefore, the stock price is 130pershare.
Question 8
Question
You are considering investing in a company that is expected to pay a dividend
of 5persharenextyear.T hedividendsareexpectedtogrowataconstantrateof 8
Solution
Step 1: Calculate the dividend in year 2. The dividend in year 2 can be calcu-
lated using the formula for dividend growth:
D2=D1×(1 + g)
5
where D1is the dividend in year 1, gis the growth rate, and D2is the dividend
in year 2. Plugging in the values, we get:
D2= 5 ×(1 + 0.08) = 5.4
Step 2: Calculate the dividend yield. The dividend yield can be calculated
using the formula:
Dividend yield =D2
R
where D2is the dividend in year 2 and Ris the required rate of return. Plugging
in the values, we get:
Dividend yield =5.4
0.12 = 45
Step 3: Calculate the stock price. The current value of the stock can be
calculated using the formula for a perpetuity:
P0=D1
R−g
where P0is the current value of the stock, D1is the dividend in year 1, Ris
the required rate of return, and gis the growth rate. Plugging in the values, we
get:
P0=5
0.12 −0.08 =5
0.04 = 125
Therefore, the current value of the stock is 125pershare.
Question 9
Question
A company is expected to pay an annual dividend of 3.00pershareindef initely.If therequiredrateofreturnis8%, whatisthevalueof thestock?
Solution
Step 1: Calculate the value of the stock using the Gordon Growth Model for-
mula:
P=D
r−g
where: P= Price of the stock D= Dividend per share r= Required rate of
return g= Growth rate of dividends
Step 2: Given data: D= $3.00 per share r= 8% = 0.08
Step 3: To calculate the growth rate (g), we can use the formula for the
Dividend Payout Ratio:
Dividend Payout Ratio = D
E
6
where: E= Earnings per share
Step 4: Since the dividend is paid out in full, the Dividend Payout Ratio is
equal to 1, and we can rearrange the formula to solve for E:
E=D
Dividend Payout Ratio =D
Step 5: The Gordon Growth Model formula can be rearranged to solve for
g:
g=r−D
P
Step 6: Substitute the known values into the formula:
g= 0.08 −3.00
P
Step 7: Since this is an indefinitely growing dividend, the growth rate g
should be less than the required rate of return r, so we can rewrite the formula
as:
0.08 >0.08 −3.00
P
Step 8: Solve for P:
0>−3.00
P
0>−3.00
This is true for all positive values of P, so the value of the stock is infinite
according to the Gordon Growth Model.
Question 10
Question
Company XYZ is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the expected dividend for the second year. Step 2: Use the
formula for the present value of a growing perpetuity to find the current stock
price.
Step 1: The dividend for the second year (D2) can be calculated using the
formula for a growing dividend:
D2=D1×(1 + g)
where D1= $5.00 (dividend for the first year), g= 8% = 0.08 (growth rate).
Substitute the given values:
D2= $5.00 ×(1 + 0.08) = $5.00 ×1.08 = $5.40
7
Therefore, the dividend for the second year is
$
5.40 per share.
Step 2: The present value of a growing perpetuity formula is given by:
P V =D
r−g
where D= $5.40 (dividend for the second year), r= 12% = 0.12 (required rate
of return), g= 8% = 0.08 (growth rate).
Substitute the values into the formula:
P V =$5.40
0.12 −0.08 =$5.40
0.04 = $135
Therefore, the current value of Company XYZ’s stock is
$
135 per share.
Question 11
Question
A company’s stock currently pays a dividend of 2.50pershare.Dividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the dividend growth rate. The dividend growth rate is given
as 5
Step 2: Calculate the dividend next year, D1.
D1=D0×(1 + growth rate) = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 3: Calculate the required rate of return, r. The required rate of return,
r, is given as 10
Step 4: Use the Gordon Growth Model formula to calculate the current value
of the stock, P0. The Gordon Growth Model formula is:
P0=D1
r−growth rate
Substitute the values into the formula:
P0=2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is 52.50pershare.
Question 12
Question
A company is expected to pay an annual dividend of 5pershareindef initely.If therequiredrateofreturnis10
8
Solution
Step 1: Calculate the stock price using the dividend discount model formula:
Stock Price = Dividend
Required Rate of Return
Step 2: Substitute the given values into the formula:
Stock Price = 5
0.10
Step 3: Perform the calculation:
Stock Price = $50
Step 4: Therefore, the value of the stock is
$
50 per share.
Question 13
Question
A company is expected to pay an annual dividend of 3.50pershareindef initely.If therequiredrateofreturnis8%, whatisthecurrentvalueof thestock?
Solution
Step 1: Calculate the present value of the perpetual annual dividend using the
Gordon Growth Model formula:
Present Value of Stock = Dividend
Required Rate of Return −Growth Rate
Step 2: Substitute the given values into the formula:
Present Value of Stock = 3.50
0.08 −0=3.50
0.08 = 43.75
Step 3: The current value of the stock is
$
43.75 per share.
Question 14
Question
A company’s stock is currently trading at $100 per share. The company is
expected to pay a dividend of $2 per share this year, and dividends are expected
to grow at a rate of 5% annually. If the required rate of return for this stock is
8%, what is the stock’s expected price in 5 years?
9
Solution
Step 1: Calculate the dividend in 5 years. Given that the dividend is expected
to grow at a rate of 5% annually, the dividend in 5 years will be:
D= $2 ×(1 + 0.05)5= $2 ×1.2763 = $2.5526.
Step 2: Calculate the expected price of the stock in 5 years using the Gordon
Growth Model. The Gordon Growth Model formula is:
P=D
r−g,
where: - Pis the expected price of the stock, - Dis the dividend in 5 years
(
$
2.5526), - ris the required rate of return (8- gis the growth rate of dividends
(5
Substitute the values into the formula:
P=$2.5526
0.08 −0.05 =$2.5526
0.03 = $85.087.
Therefore, the stock’s expected price in 5 years is $85.087.
Question 15
Question
A company’s stock is currently trading at $100 per share. It is expected to pay
a dividend of $5.00 per share at the end of the year. The expected growth rate
of the company’s dividends is 8% per year forever. If the required rate of return
is 12%, what is the value of the stock?
Solution
Step 1: Calculate the dividend expected at the end of the year using the growth
rate.
Dividend at the end of the year = Current dividend ×(1 + Growth rate)
= $5.00 ×(1 + 0.08)
= $5.40
Step 2: Use the Gordon Growth Model to find the value of the stock. The
Gordon Growth Model is given by:
Stock Value = Dividend at the end of the year
Required rate of return −Growth rate
10
Plugging in the values:
Stock Value = $5.40
0.12 −0.08
=$5.40
0.04
= $135.00
Therefore, the value of the stock is $135.00.
Question 16
Question
A company’s stock is expected to pay a dividend of $5 next year. The dividends
are expected to grow indefinitely at a constant rate of 4
Solution
Step 1: Calculate the dividend in the following year using the growth rate. Step
2: Calculate the price of the stock using the formula for the present value of a
perpetuity.
Step 1: The dividend expected to be paid next year is D1= $5. The growth
rate is 4
D2=D1×(1 + growth rate) = $5 ×(1 + 0.04) = $5.20
Step 2: To find the current value of the stock (P0), we can use the formula
for the present value of a perpetuity:
P0=D1
r−g
where: D1= expected dividend next year =
$
5, r= required rate of return =
10g= growth rate = 4
Plugging in the values, we get:
P0=5
0.10 −0.04 =5
0.06 = $83.33
Therefore, the current value of the stock is
$
83.33.
Question 17
Question
Company XYZ is expected to pay an annual dividend of 4.50pershareindef initely.If therequiredrateofreturnis10
11
Solution
Step 1: Calculate the stock price using the Gordon Growth Model formula:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 2: Since the company is expected to pay an annual dividend of 4.50pershareindefinitely, thegrowthratecanbeassumedtobezero(dividendsarenotexpectedtogrow).Stock Price =
4.50
0.10−0
Stock Price = 4.50
0.10
Step 3: Calculate the stock price:
Stock Price = 45
Therefore, the stock price of Company XYZ is 45pershare.
Question 18
Question
A company’s stock currently pays an annual dividend of 5pershare.Iftherequiredrateof returnforthisstockis10
Solution
Step 1: Calculate the dividend growth rate using the formula g=D1
D0−1, where
D1 is the next year’s dividend and D0 is the current dividend.
g=5(1 + 0.04)
5−1
= 0.04
Step 2: Calculate the dividend expected one year from now using the formula
D1 = D0(1 + g).
D1 = 5(1 + 0.04) = 5.2
Step 3: Calculate the stock price using the Gordon Growth Model formula
P0 = D1
r−g, where ris the required rate of return.
P0 = 5.2
0.10 −0.04
=5.2
0.06
= 86.67
Therefore, the current stock price is 86.67pershare.
12
Question 19
Question
A company is expected to pay a dividend of 5.00persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividends for the next 5 years using the dividend growth
rate formula:
Dn=D0×(1 + g)n
where: - Dn= Dividend in year n-D0= Dividend in the first year - g=
Growth rate - n= Number of years
Given D0= 5.00, g= 8% = 0.08, and n= 1,2,3,4,5, we can calculate: -
D1= 5.00 ×(1 + 0.08)1-D2= 5.00 ×(1 + 0.08)2-D3= 5.00 ×(1 + 0.08)3-
D4= 5.00 ×(1 + 0.08)4-D5= 5.00 ×(1 + 0.08)5
Step 2: Calculate the dividend in year 6 which grows at a constant rate of 3
D6=D5×(1 + g)
Step 3: Find the present value of all future dividends using the formula for
the present value of a growing perpetuity:
P V =D1
(1 + r)1+D2
(1 + r)2+... +D5
(1 + r)5+D6
(1 + r)6
where: - P V = Present value - r= Required rate of return
Given r= 10% = 0.10, compute the present value.
Step 4: Calculate the stock price by subtracting the present value of all
future dividends from the present value of a growing perpetuity:
Stock P rice =P V −D6
r−g
Compute the stock price.
Question 20
Question
A company is expected to pay a dividend of 3.00persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in year 2.
Dividend in year 2 = Dividend in year 1 ×(1 + growth rate)
13
Dividend in year 2 = $3.00 ×(1 + 0.05)
Dividend in year 2 = $3.00 ×1.05 = $3.15
Step 2: Calculate the dividend discount model value of the stock.
P0=D1
r−g
where: P0= price of the stock today D1= dividend in year 1 r= required rate
of return g= growth rate
Substitute the given values:
P0=$3.00
0.10 −0.05
P0=$3.00
0.05
P0= $60.00
Therefore, the current value of the stock is
$
60.00.
Question 21
Question
A company is expected to pay a dividend of 5persharenextyear.Dividendsareexpectedtogrowatarateof 8
Solution
Step 1: Calculate the dividend one year from now. The dividend one year from
now (D1) can be calculated using the formula:
D1=D0×(1 + growth rate)
where - D0= dividend this year = 5 −Growthrate = 8
Therefore,
D1= 5 ×(1 + 0.08) = 5 ×1.08 = 5.40
Step 2: Calculate the current price of the stock using the constant growth
dividend valuation model formula. The price of the stock (P0) can be calculated
using the formula:
P0=D1
r−g
where - D1= dividend one year from now = 5.40−r= requiredrateof return =
12−g= growthrate = 8
Therefore,
P0=5.40
0.12 −0.08 =5.40
0.04 = 135
Hence, the current value of the stock is 135pershare.
14
Question 22
Question
A company’s stock is expected to pay a dividend of 3.50 next year and dividends
are expected to grow at a rate of 5% per year indefinitely. If the required rate
of return is 10%, what is the current value of the stock?
Solution
Step 1: Calculate the expected dividend for the second year. Given that divi-
dends are expected to grow at a rate of 5% per year, the expected dividend for
the second year can be calculated as follows:
Expected Dividend for Year 2 = Expected Dividend for Year 1×(1+Growth Rate)
Expected Dividend for Year 2 = 3.50 ×(1 + 0.05) = 3.50 ×1.05 = 3.675
Step 2: Determine the dividend discount model. The stock price can be
calculated using the dividend discount model, which is represented as:
Stock Price = Dividend
Required Rate of Return −Growth Rate
Step 3: Calculate the current value of the stock. Substitute the given values
into the formula:
Stock Price = 3.50
0.10 −0.05 =3.50
0.05 = 70
Therefore, the current value of the stock is 70.
Question 23
Question
A company’s stock is currently priced at $100 per share. The company is ex-
pected to pay a dividend of $5 per share next year. If dividends are expected
to grow at a rate of 8
Solution
Let’s denote the required rate of return by r, the dividend next year by D1,
and the dividend growth rate by g. We can use the Dividend Discount Model
(DDM) to find the required rate of return:
P0=D1
r−g
15
Step 1: Find D1Given that the company is expected to pay a dividend of
$5 per share next year, D1= $5.
Step 2: Plug in the given values into the DDM formula We can plug
in the given values into the DDM formula:
100 = 5
r−0.08
Step 3: Solve for rSolving for r:
100 = 5
r−0.08
100r−8=5
100r= 13
r=13
100 = 0.13 = 13%
So, the stock’s required rate of return is 13
Question 24
Question
A company’s stock is currently trading at $50 per share. The company is ex-
pected to pay a dividend of $2 per share next year, with dividends expected to
grow at a rate of 5% per year indefinitely. If the required rate of return is 10%,
what is the intrinsic value of the stock?
Solution
Step 1: Calculate the expected dividend for next year using the growth rate.
Expected Dividend for Next Year = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the expected dividend for the following year.
Expected Dividend in 2 Years = $2.10 ×(1 + 0.05) = $2.205
Step 3: Calculate the dividend yield, which is the expected dividend divided
by the current stock price.
Dividend Yield = $2.205
$50 = 0.0441
Step 4: Calculate the capital gains yield, which is the growth rate of divi-
dends.
Capital Gains Yield = 0.05 = 0.05
16
Step 5: Determine the total rate of return on the stock.
Total Rate of Return = Dividend Yield+Capital Gains Yield = 0.0441+0.05 = 0.0941
Step 6: Use the Gordon Growth Model to calculate the intrinsic value of the
stock.
V0=D1
r−g
V0=$2.10
0.10 −0.05
V0=$2.10
0.05
V0= $42
Therefore, the intrinsic value of the stock is $42.
Question 25
Question
A company’s dividends are expected to grow at a rate of 6
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = Previous dividend ×(1 + Growth rate)
Next dividend = $2.50 ×(1 + 0.06)
Next dividend = $2.50 ×1.06
Next dividend = $2.65
Step 2: Calculate the price of the stock using the dividend discount model.
Price = Next dividend
Required rate of return - Growth rate
Price = $2.65
0.10 −0.06
Price = $2.65
0.04
Price = $66.25
Therefore, the current price of the stock is
$
66.25.
17
Question 26
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowindef initelyataconstantrateof4
Solution
Step 1: Calculate the dividend in the following year using the growth rate:
Let D0be the dividend this year, D1be the dividend next year, and gbe the
growth rate. From the information provided, we have: D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.04) D1= 3.50 ×1.04 D1= 3.64
Step 2: Calculate the price of the stock using the Gordon Growth Model
formula: The Gordon Growth Model is given by: P0=D1
r−gwhere P0is the
current price of the stock, D1is the dividend next year, ris the required rate of
return, and gis the growth rate. Substitute the known values into the formula:
P0=3.64
0.10−0.04 P0=3.64
0.06 P0= 60.67
Therefore, the current price of the stock is 60.67pershare.
Question 27
Question
A company’s stock is expected to pay dividends of 2,2.50, and 3forthenextthreeyears.Af terthat, thedividendsareexpectedtogrowataconstantrateof 6
Solution
Step 1: Calculate the present value of the dividends for the first three years.
Given:
D1=
$
2
D2=
$
2.50
D3=
$
3
r= 10%
The present value of the first three dividends is calculated as follows:
P V =D1
(1 + r)1+D2
(1 + r)2+D3
(1 + r)3
P V =2
1.101+2.50
1.102+3
1.103
P V =2
1.10 +2.50
1.21 +3
1.331
P V ≈$5.37
18
Step 2: Calculate the present value of all future dividends. To find the value
of all future dividends after 3 years, we can use the Gordon Growth Model
formula:
P V =D3×(1 + g)
r−g
Where:
D3= 3
g= 6% = 0.06
r= 10% = 0.10
Substitute these values into the formula:
P V =3×(1 + 0.06)
0.10 −0.06
P V =3×1.06
0.04
P V =3.18
0.04
P V = $79.50
Step 3: Calculate the current value of the stock. The current value of the
stock is the sum of the present value of the first three dividends and the present
value of all future dividends:
Stock Value = $5.37 + $79.50
Stock Value = $84.87
Question 28
Question
You are considering investing in a company which is expected to pay an annual
dividend of 3.50pershareindefinitely.Iftherequiredrateof returnis10
Solution
Step 1: Calculate the price of the stock using the Gordon Growth Model. The
formula for the Gordon Growth Model is:
P=D
r−g
where: - P= Price of the stock - D= Annual dividend per share - r= Required
rate of return - g= Growth rate of dividends
19
Step 2: Substitute the given values into the formula:
P=3.50
0.10 −0
P=3.50
0.10
P= 35
Step 3: Therefore, the current value of the stock is 35pershare.
Question 29
Question
A company’s stock is currently trading at $120 per share. The company is
expected to pay an annual dividend of $5 per share indefinitely. If the required
rate of return for this stock is 10%, what is the estimated value of the stock
using the Gordon Growth Model?
Solution
Step 1: Calculate the growth rate using the dividend and required rate of return.
Dividend Growth Rate = Dividend per Share
Current Price per Share
Step 2: Plug in the values into the Gordon Growth Model formula.
P0=D0·(1 + g)
r−g
where: - P0= Estimated value of the stock - D0= Dividend per share - g=
Growth rate - r= Required rate of return
Step 3: Substitute the given values into the formula.
P0=$5 ·(1 + g)
0.10 −g
Step 4: Substitute the growth rate calculated in Step 1 into the formula
from Step 3.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate
Step 5: Solve for the estimated value of the stock P0by substituting the
given values.
P0=5·(1 + Dividend Growth Rate)
0.10 −Dividend Growth Rate =?
20
Question 30
Question
You are analyzing a company’s stock for potential investment. The company is
expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the expected dividend for the second year. The expected div-
idend for the second year (D2) can be calculated using the formula for dividend
growth:
D2=D1×(1 + growth rate)
D2= 3.50 ×(1 + 0.05) = 3.50 ×1.05 = 3.675
Step 2: Calculate the expected dividend yield in the first year. The dividend
yield in the first year can be calculated using the formula:
Dividend Yield = DividendYear 1
Price of StockYear 0
Given that the dividend in the first year is 3.50andtherequiredrateof returnis103.50 =
3.50
Price of StockYear 0
Price of StockYear 0 =3.50
0.10 = 35
Step 3: Calculate the fair value of the stock using the dividend discount
model. The fair value of the stock can be calculated using the formula:
Fair Value = Dividend in Year 1
Rate of Return - Growth Rate
Substitute the values we have calculated:
Fair Value = 3.675
0.10 −0.05 =3.675
0.05 = 73.50
Therefore, the fair value of the stock is 73.50pershare.
21
