BUSI 683 - MONEY AND CAPITAL
MARKETS - Stock Valuation
Question Bank - Set 4
Liberty University
Question 1
Question
You are analyzing the stock of a company that is expected to pay a dividend of
3.00persharenextyear.T hedividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the dividend in the future at t= 1.
Dividend at t= 1 = $3.00 ×(1 + 5%) = $3.15
Step 2: Use the Gordon Growth Model to calculate the current value of the
stock.
P0=D1
r−g
where: - P0is the current price of the stock, - D1is the dividend at t= 1, - r
is the required rate of return, and - gis the growth rate of the dividends.
Substitute the given values:
P0=$3.15
0.10 −0.05
P0=$3.15
0.05
P0= $63.00
The current value of the stock is
$
63.00.
Question 2
Question
An investor is considering purchasing stock in a company that is expected to pay
a dividend of 3.00nextyear.T heinvestor′srequiredrateof returnis10%, andthestockisexpectedtogrowataconstantrateof 5%peryear.If thecurrentstockpriceis60.00,
should the investor purchase the stock?
Solution
Step 1: Calculate the expected dividend for the next year using the constant
growth rate formula:
D1 = D0×(1 + g)
where: - D1 is the dividend for the next year, - D0 is the current dividend, and
-gis the growth rate.
Substitute the given values:
D1=3.00 ×(1 + 0.05) = 3.00 ×1.05 = 3.15
Step 2: Calculate the expected price of the stock in one year using the
constant growth model:
P1 = D1
r−g
where: - P1 is the price of the stock in one year, - ris the required rate of
return, and - gis the growth rate.
Substitute the given values:
P1 = 3.15
0.10 −0.05 =3.15
0.05 = 63.00
Step 3: Determine whether the investor should purchase the stock by com-
paring the expected price in one year to the current price. If the expected price
is higher, then the stock is undervalued and the investor should purchase the
stock.
Since the expected price in one year is 63.00, whichishigherthanthecurrentpriceof60.00,
the investor should purchase the stock.
Question 3
Question
A company’s stock is expected to pay dividends in perpetuity. The next dividend
payment will be
$
5 per share and dividends are expected to grow at a rate of 3
2
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current price of the stock.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
where: - g= growth rate of dividends - D0= latest dividend payment - D1=
next dividend payment
Substitute the given values:
g=5×1.03
5−1
g= 0.03
So, g= 3%.
Step 2: The current price (P0) of the stock can be calculated using the
Gordon Growth Model formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= next dividend payment - r=
required rate of return - g= growth rate of dividends
Substitute the given values:
P0=5×1.03
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the current price of the stock is
$
103.
Question 4
Question
A company pays an annual dividend of 5pershare.Iftherequiredrateof returnis12
3
Solution
Step 1: Calculate the dividend growth rate using the formula: g=D1−D0
D0.
g=D1−D0
D0
=5×(1 + 0.05) −5
5
=5.25 −5
5
=0.25
5
= 0.05
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model formula is: P0=D1
r−g. Given that D1=5×(1 + 0.05) =
5.25, r= 0.12, and g= 0.05.
P0=5.25
0.12 −0.05
=5.25
0.07
= 75
Therefore, the current stock price is 75pershare.
Question 5
Question
A company is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in the following year. Since dividends are ex-
pected to grow at a rate of 5
D1=D0×(1 + g) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Use the dividend discount model to calculate the value of the stock
today. The value of a stock today using the dividend discount model is given
by:
P0=D1
r−g
where: - P0= value of the stock today - D1= dividend in the following year -
r= required rate of return - g= growth rate of dividends
4
Step 3: Substitute the values into the formula and calculate.
P0=$3.675
0.08 −0.05 =$3.675
0.03 = $122.50
Therefore, the value of the stock today is
$
122.50.
Question 6
Question
A company is expected to pay a dividend of 2.50pershareattheendoftheyear.Dividendsareexpectedtogrowatarateof5
Solution
Step 1: Calculate the dividend one year from now.
Dividend next year = Dividend this year ×(1 + Growth rate)
Dividend next year = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 2: Calculate the dividend discount model value of the stock.
Stock value = Dividend next year
Required return −Growth rate
Stock value = 2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is $52.50pershare.
Question 7
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 6
Solution
Step 1: Calculate the dividend growth rate.
Dividend Growth Rate (g) = 6% = 0.06
5
Step 2: Use the dividend discount model (DDM) formula to calculate the
price of the stock.
Price of Stock = Dividend Next Year
Required Rate of Return −Dividend Growth Rate
=3.50
0.10 −0.06
=3.50
0.04
= $87.50
Therefore, the price of Company XYZ’s stock today is
$
87.50.
Question 8
Question
A company’s stock is expected to pay a dividend of
$
2 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Let’s denote the current value of the stock as P0. We can use the Gordon
Growth Model to calculate the current stock price:
P0=D1
r−g
where: D1= $2 (next year’s dividend), r= 0.10 (required rate of return), and
g= 0.05 (dividend growth rate).
Step 1: Calculate the current value of the stock using the Gordon Growth
Model.
P0=2
0.10 −0.05
=2
0.05
= $40
Therefore, the current value of the stock is
$
40.
Question 9
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. If the dividend is expected
to grow at a constant rate of 8% indefinitely, what is the expected rate of return
on this stock?
6
Solution
Step 1: Calculate the dividend in the next year using the growth rate formula.
Dividend in one year = $2 ×(1 + 0.08) = $2.16
Step 2: Use the dividend discount model to calculate the expected rate of
return.
Expected Rate of Return = Dividend in one year
Current Price + Growth Rate
Expected Rate of Return = $2.16
$50 + 0.08
Expected Rate of Return = 0.0432 + 0.08
Expected Rate of Return = 0.1232
Step 3: Convert the expected rate of return to a percentage.
Expected Rate of Return = 0.1232 ×100% = 12.32%
Therefore, the expected rate of return on this stock is 12.32%.
Question 10
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
It is expected to grow its dividends at a constant rate of 6
Solution
Step 1: Calculate the dividend in the future year 1. The dividend in the next
year (D1) can be calculated using the formula: D1 = D0×(1 + g) where: -
D0 is the dividend this year (
$
2.50) - gis the growth rate (6Therefore, D1 =
$2.50 ×(1 + 0.06) = $2.50 ×1.06 = $2.65
Step 2: Calculate the price of the stock. The price of the stock can be
determined using the dividend discount model: P0 = D1
r−gwhere: - D1 is the
dividend in the next year (
$
2.65) - ris the required rate of return (10- gis the
growth rate (6Plugging in the values, P0 = $2.65
0.10−0.06 =$2.65
0.04 = $66.25
Therefore, the current value of the stock is
$
66.25.
Question 11
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. Dividends are expected to
grow at a constant rate of 5% per year indefinitely. If the required rate of return
is 10%, what is the intrinsic value of the stock?
7
Solution
Step 1: Calculate the expected dividend in the future The dividend next year is
given as D1= $2 Since the dividends are expected to grow at a constant rate,
the dividend in the second year (D2) can be calculated using the formula for
growth:
D2=D1×(1 + g)
where gis the growth rate. In this case, g= 5% = 0.05. So, D2= $2 ×(1 +
0.05) = $2.10
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model The intrinsic value of the stock can be calculated using the Gordon
Growth Model:
P0=D1
r−g
where: P0= Intrinsic value of the stock D1= Dividend next year r= Required
rate of return g= Growth rate
Plugging in the values, we get:
P0=$2.10
0.10 −0.05 =$2.10
0.05 = $42
Therefore, the intrinsic value of the stock is $42 per share.
Question 12
Question
A company’s stock is expected to pay a dividend of
$
2 per share 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 in year 2 using the growth rate. Step
2: Calculate the present value of the dividends in year 1 and 2. Step 3: Use the
formula for the present value of a growing perpetuity to find the present value
of all future dividends. Step 4: Add the present value of future dividends to
find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated as follows:
D2=D1×(1 + g) = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the present value of the dividends in year 1 and year 2:
P V (D1) = D1
1 + r=$2
1+0.10 = $1.82
8
P V (D2) = D2
(1 + r)2=$2.10
(1 + 0.10)2= $1.72
Step 3: Use the formula for the present value of a growing perpetuity:
P V =D1
r−g
Substitute the values to find the present value of all future dividends:
P V =$2
0.10 −0.05 = $40
Step 4: Add the present value of future dividends to find the current value
of the stock:
Current Value = P V (D1) + P V (D2) + P V = $1.82 + $1.72 + $40 = $43.54
Therefore, the current value of the stock is
$
43.54.
Question 13
Question
A company has a constant growth rate of dividends at 5
Solution
Step 1: Calculate the dividend growth rate. The formula for dividend growth
rate is given by:
Dividend Growth Rate = Dividend per Share at Time t−Dividend per Share at Time t−1
Dividend per Share at Time t−1
Given that the most recent dividend paid was
$
2.50, we find:
Dividend Growth Rate = 2.50 −2.50
2.50 = 0
Step 2: Calculate the dividend at time t+ 1. The formula for calculating
the dividend at time t+ 1 is:
Dividend at Time t+ 1 = Dividend at Time t×(1 + Dividend Growth Rate)
Substitute the values:
Dividend at Time t+ 1 = 2.50 ×(1 + 0.05) = 2.625
Step 3: Calculate the stock price using the dividend discount model. The
dividend discount model is given by:
P0=D1
r−g
9
Where: P0= Current stock price D1= Dividend at time t+ 1 =
$
2.625 r
= Required return on the stock = 12g= Dividend Growth Rate = 5
Substitute the values:
P0=2.625
0.12 −0.05 =2.625
0.07 ≈$37.50
Therefore, the current stock price using the dividend discount model is ap-
proximately
$
37.50.
Question 14
Question
A company’s stock currently pays a dividend of 3pershareandisexpectedtogrowatarateof5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Calculate the present value of the dividends. Step 3: Calculate the stock’s
present value by adding the present value of dividends.
Step 1: The expected dividend next year can be calculated using the growth
rate:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.05) = 3 ×1.05 = 3.15
Step 2: The present value of dividends can be calculated using the formula
for the present value of a growing perpetuity:
P V =D1
r−g
where: - D1= 3.15 (next year’s dividend), - r= 0.10 (required rate of return),
-g= 0.05 (growth rate).
P V =3.15
0.10 −0.05 =3.15
0.05 = 63
Step 3: The current value of the stock is the present value of dividends:
Stock Value = P V = 63
Therefore, the current value of the stock is 63pershare.
Question 15
Question
A company’s stock is currently trading at 75 per share. The company is expected
to pay an annual dividend of 3 per share forever. If the required rate of return
is 8
10
Solution
Step 1: Calculate the growth rate using the dividend growth model formula.
Given: Current stock price (P) = 75Dividendpershare(D) =3 Required rate
of return (r) = 8
The dividend growth model formula is:
D=D0×(1 + g)
r−g
Substitute the given values into the formula:
3 = 3×(1 + g)
0.08 −g
Simplify the equation:
3 = 3+3g
0.08 −g
3(0.08 −g) = 3 + 3g
0.24 −3g= 3 + 3g
0.24 −3=6g
−2.76 = 6g
g=−0.46
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model.
The Gordon Growth Model formula is:
P=D
r−g
Substitute the values of D, r, and g into the formula:
P=3
0.08 −(−0.46)
P=3
0.54
P=
5.56
Therefore, the intrinsic value of the stock is 56pershare.
11
Question 16
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 8
Solution
Step 1: Calculate the dividend next year using the formula for dividend growth:
Dividend next year = Dividend this year ×(1 + growth rate)
Dividend next year = $2.50 ×(1 + 0.08) = $2.50 ×1.08 = $2.70
Step 2: Calculate the price of the stock using the dividend discount model:
P0=D1
r−g
where: - P0= current price of the stock - D1= dividend next year - r= required
rate of return - g= growth rate
Substitute the values into the formula:
P0=$2.70
0.12 −0.08
P0=$2.70
0.04
P0= $67.50
Therefore, the current price of the stock is
$
67.50.
Question 17
Question
A company’s stock is expected to pay dividends of
$
2,
$
2.20,
$
2.42, and
$
2.66
over the next four years. If the required rate of return is 8%, what is the current
value of the stock?
Solution
Step 1: Calculate the present value of each dividend. Step 2: Add up the present
values of all dividends to find the current value of the stock.
Step 1: The present value (PV) of a dividend can be calculated using the
formula:
P V =D
(1 + r)n
12
where: - Dis the dividend amount, - ris the required rate of return, and - nis
the time period.
Given that r= 0.08,
P V1=2
(1+0.08)1=2
1.08 ≈1.85
P V2=2.20
(1+0.08)2=2.20
1.1664 ≈1.89
P V3=2.42
(1+0.08)3=2.42
1.2597 ≈1.92
P V4=2.66
(1+0.08)4=2.66
1.3605 ≈1.95
Step 2: The current value of the stock is the sum of the present values of
all dividends:
Stock Value = P V1+P V2+P V3+P V4
Stock Value = 1.85 + 1.89 + 1.92 + 1.95 = 7.61
Therefore, the current value of the stock is approximately
$
7.61.
Question 18
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 7
Solution
Step 1: Calculate the expected dividend next year using the dividend growth
rate. Step 2: Calculate the price of the stock using the dividend discount model.
Step 1: The expected dividend next year can be calculated as follows:
D1 = D0×(1 + g)
where: D1 = Expected dividend next year, D0 = Dividend this year, g=
Growth rate of dividends.
Given that D0 =
$
3.50, and g= 7% = 0.07, we have:
D1=3.50 ×(1 + 0.07) = 3.50 ×1.07 = $3.745
Step 2: The price of the stock using the dividend discount model is calculated
as:
P=D1
r−g
where: P= Price of the stock, D1 = Expected dividend next year, r= Required
rate of return, g= Growth rate of dividends.
Substitute D1 =
$
3.745, r= 10% = 0.10, and g=7%=0.07 into the
formula:
P=3.745
0.10 −0.07 =3.745
0.03 = $124.83
Therefore, the current value of the stock is
$
124.83.
13
Question 19
Question
A company’s stock is expected to pay a dividend of 3.00persharenextyearanddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the following year using the growth rate.
Dividend for next year = $3.00 ×(1 + 0.05) = $3.15
Step 2: Calculate the dividend yield, which is the dividend for next year
divided by the required rate of return.
Dividend yield = $3.15
0.10 = $31.50
Step 3: Calculate the growth rate minus the required rate of return.
0.05 −0.10 = −0.05
Step 4: Use the dividend yield and the growth rate minus the required rate
of return to calculate the stock price.
Stock P rice =Dividend yield
Growth rate −Required rate of return
Stock P rice =$31.50
−0.05 =−$630.00
Step 5: Interpretation The negative value for the stock price indicates that
there may have been an error in the calculations. The reason for this discrepancy
may be due to the assumption of perpetual growth at a constant rate, which
may not hold in reality.
Question 20
Question
A company pays an annual dividend of 3.50pershareandisexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current stock price.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
14
where: D1= expected dividend next year = 3.50 ×(1 + 5%) = 3.675D0=
current dividend = 3.50
Therefore,
g=3.675
3.50 −1=0.05 = 5%
Step 2: The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= current stock price r= required rate of return = 10g= dividend
growth rate = 5
Plugging in the values, we get:
P0=3.675
0.10 −0.05 =3.675
0.05 = 73.50
Therefore, the current stock price is $73.50.
Question 21
Question
A company’s stock currently pays a dividend of $4 per share. The dividend
is 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 current value of the stock?
Solution
Step 1: Calculate the growth rate gusing the formula:
g=Dividend Growth Rate
Required Rate of Return
g=0.05
0.10 = 0.5 = 5%
Step 2: Use the Gordon Growth Model to calculate the stock value:
Stock Value = Dividend
Required Rate of Return - Growth Rate
Stock Value = $4
0.10 −0.05
Stock Value = $4
0.05 = $80
Therefore, the current value of the stock is $80 per share.
15
Question 22
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Use the dividend discount model to find the current stock price.
Step 1: Let D0be the current dividend per share, and gbe the growth rate
of dividends. The expected dividend next year, D1, can be calculated using the
formula:
D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.05)
D1= 3.50 ×1.05
D1= 3.675
Step 2: The dividend discount model formula for the stock price, P0, is given
by:
P0=D1
r−g
where ris the required rate of return. Substitute the values into the formula:
P0=3.675
0.12 −0.05
P0=3.675
0.07
P0≈52.50
Therefore, the current stock price is approximately 52.50pershare.
Question 23
Question
A company’s stock currently has a dividend yield of 4
16
Solution
Step 1: The dividend yield can be used to find the dividend per share. The
dividend yield is calculated as the dividend per share divided by the stock price:
Dividend Yield = Dividend per share
Stock Price
Given that the dividend yield is 4
Dividend per share = Dividend Yield ×Stock Price = 0.04 ×120 = $4.80
Step 2: The company’s cost of equity can be calculated using the dividend
growth model:
r=D1
P0
+g
where: - ris the cost of equity, - D1is the next year’s dividend ($4.80 ×1.06 =
$5.088), - P0is the current stock price ($120), and - gis the growth rate of
dividends (6
Substitute the values into the formula:
r=5.088
120 + 0.06 = 0.0424 + 0.06 = 0.1024
Therefore, the company’s cost of equity is 10.24
Question 24
Question
A company is expected to pay a dividend of 2.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = $2.50 ×(1 + 0.05) = $2.625
Step 2: Use the dividend discount model to calculate the current value of
the stock.
V=D
r−g
where: V= current value of the stock, D= next dividend, r= required rate of
return, and g= growth rate of dividends.
Step 3: Substitute the values into the formula and calculate.
V=2.625
0.10 −0.05
V=2.625
0.05
V= 52.50
Therefore, the current value of the stock is
$
52.50.
17
Question 25
Question
A company pays a constant annual dividend of $4 per share. If the required
rate of return is 10%, what is the value of the stock?
Solution
Let’s denote the constant annual dividend by Dand the required rate of return
by r. The formula for valuing a stock using the constant growth dividend model
is given by:
P0=D
r−g
Where: - P0is the price of the stock today, - Dis the constant annual dividend,
and - gis the growth rate of the dividend.
In this case, the growth rate of the dividend is the same as the required rate
of return, (r=g), because the dividend is assumed to grow at a constant rate.
Step 1: Calculate the value of the stock using the formula.
P0=D
r−g
=4
0.10 −0.10
=4
0(Division by zero is undefined)
Since the denominator evaluates to zero, this is an example where the con-
stant growth dividend model is not applicable. In cases where the required rate
of return is equal to the growth rate of the dividend, different valuation meth-
ods need to be used, such as the two-stage dividend discount model or other
industry-specific models.
Question 26
Question
A company’s stock is currently trading at 58.50pershare.T hecompanyisexpectedtopayanannualdividendof 2.00
per share indefinitely. If the required rate of return on the stock is 8%, what is
the stock’s intrinsic value?
18
Solution
Step 1: Calculate the annual dividend growth rate using the dividend discount
model formula:
Dividend Growth Rate = Dividend per Share Next Year −Dividend per Share This Year
Dividend per Share This Year
Dividend Growth Rate = $2.00 −$2.00
$2.00 = 0%
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model formula:
Intrinsic Value = Dividend per Share Next Year
Required Rate of Return −Dividend Growth Rate
Intrinsic Value = $2.00
0.08 −0= $25.00
Therefore, the intrinsic value of the stock is
$
25.00 per share.
Question 27
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend one year from now. Given that the dividend next
year is 3.50pershareandthegrowthrateis5D1=D0×(1+g)=3.50×(1+0.05) =
3.675
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model. The intrinsic value of a stock can be calculated using the dividend
discount model formula:
V0=D1
r−g
where D1is the dividend one year from now, ris the required rate of return,
and gis the growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
V0=3.675
0.10 −0.05 =3.675
0.05 = 73.5
Therefore, the intrinsic value of the stock today is 73.50pershare.
19
Question 28
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Step 1: Calculate the current dividend per share using the dividend growth rate
formula.
Current Dividend Per Share = Dividend Next Year
Required Rate of Return −Growth Rate
Current Dividend Per Share = $2.50
0.10 −0.05 = $50
Step 2: Calculate the price of the stock using the dividend discount model.
Price of Stock = Dividend Next Year
Required Rate of Return −Growth Rate
Price of Stock = $2.50
0.10 −0.05 = $50
The current value of the stock is
$
50 per share.
Question 29
Question
A company’s stock is expected to pay a dividend of $2 per share next year.
Dividends are expected to grow at a constant rate of 4% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Let’s denote the current value of the stock as P, the next year dividend as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the next year dividend D1using the formula D1=D0×
(1 + g), where D0is the current dividend.
D1= $2 ×(1 + 0.04) = $2.08
Step 2: Calculate the required rate of return ras a decimal.
r= 10% = 0.10
20
Step 3: Calculate the growth rate gas a decimal.
g= 4% = 0.04
Step 4: Use the Gordon Growth Model formula to find the current value of
the stock:
P=D1
r−g
Step 5: Substitute the values of D1,r, and ginto the formula:
P=$2.08
0.10 −0.04 = $34.67
Step 6: Therefore, the current value of the stock is $34.67.
Question 30
Question
A company’s stock currently pays an annual dividend of 2pershare.T hedividendsareexpectedtogrowatarateof 5
Solution
Let’s denote: - Das the current dividend per share (
$
2), - gas the growth rate
of dividends (5- ras the required rate of return (10
The formula for the price of a stock using the Dividend Discount Model
(DDM) is:
P0=D0×(1 + g)
r−g
Step 1: Substitute the given values into the DDM formula:
P0=2×(1 + 0.05)
0.10 −0.05
Step 2: Simplify the expression:
P0=2×1.05
0.05 =2.1
0.05 = 42
Step 3: Therefore, the current value of the stock is
$
42.
21
Question 2
Question
An investor is considering purchasing stock in a company that is expected to pay
a dividend of 3.00nextyear.T heinvestor′srequiredrateof returnis10%, andthestockisexpectedtogrowataconstantrateof 5%peryear.If thecurrentstockpriceis60.00,
should the investor purchase the stock?
Solution
Step 1: Calculate the expected dividend for the next year using the constant
growth rate formula:
D1 = D0×(1 + g)
where: - D1 is the dividend for the next year, - D0 is the current dividend, and
-gis the growth rate.
Substitute the given values:
D1=3.00 ×(1 + 0.05) = 3.00 ×1.05 = 3.15
Step 2: Calculate the expected price of the stock in one year using the
constant growth model:
P1 = D1
r−g
where: - P1 is the price of the stock in one year, - ris the required rate of
return, and - gis the growth rate.
Substitute the given values:
P1 = 3.15
0.10 −0.05 =3.15
0.05 = 63.00
Step 3: Determine whether the investor should purchase the stock by com-
paring the expected price in one year to the current price. If the expected price
is higher, then the stock is undervalued and the investor should purchase the
stock.
Since the expected price in one year is 63.00, whichishigherthanthecurrentpriceof60.00,
the investor should purchase the stock.
Question 3
Question
A company’s stock is expected to pay dividends in perpetuity. The next dividend
payment will be
$
5 per share and dividends are expected to grow at a rate of 3
2
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current price of the stock.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
where: - g= growth rate of dividends - D0= latest dividend payment - D1=
next dividend payment
Substitute the given values:
g=5×1.03
5−1
g= 0.03
So, g= 3%.
Step 2: The current price (P0) of the stock can be calculated using the
Gordon Growth Model formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= next dividend payment - r=
required rate of return - g= growth rate of dividends
Substitute the given values:
P0=5×1.03
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the current price of the stock is
$
103.
Question 4
Question
A company pays an annual dividend of 5pershare.Iftherequiredrateof returnis12
3
Solution
Step 1: Calculate the dividend growth rate using the formula: g=D1−D0
D0.
g=D1−D0
D0
=5×(1 + 0.05) −5
5
=5.25 −5
5
=0.25
5
= 0.05
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model formula is: P0=D1
r−g. Given that D1=5×(1 + 0.05) =
5.25, r= 0.12, and g= 0.05.
P0=5.25
0.12 −0.05
=5.25
0.07
= 75
Therefore, the current stock price is 75pershare.
Question 5
Question
A company is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in the following year. Since dividends are ex-
pected to grow at a rate of 5
D1=D0×(1 + g) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Use the dividend discount model to calculate the value of the stock
today. The value of a stock today using the dividend discount model is given
by:
P0=D1
r−g
where: - P0= value of the stock today - D1= dividend in the following year -
r= required rate of return - g= growth rate of dividends
4
Step 3: Substitute the values into the formula and calculate.
P0=$3.675
0.08 −0.05 =$3.675
0.03 = $122.50
Therefore, the value of the stock today is
$
122.50.
Question 6
Question
A company is expected to pay a dividend of 2.50pershareattheendof theyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend one year from now.
Dividend next year = Dividend this year ×(1 + Growth rate)
Dividend next year = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 2: Calculate the dividend discount model value of the stock.
Stock value = Dividend next year
Required return −Growth rate
Stock value = 2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is $52.50pershare.
Question 7
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 6
Solution
Step 1: Calculate the dividend growth rate.
Dividend Growth Rate (g) = 6% = 0.06
5
Step 2: Use the dividend discount model (DDM) formula to calculate the
price of the stock.
Price of Stock = Dividend Next Year
Required Rate of Return −Dividend Growth Rate
=3.50
0.10 −0.06
=3.50
0.04
= $87.50
Therefore, the price of Company XYZ’s stock today is
$
87.50.
Question 8
Question
A company’s stock is expected to pay a dividend of
$
2 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Let’s denote the current value of the stock as P0. We can use the Gordon
Growth Model to calculate the current stock price:
P0=D1
r−g
where: D1= $2 (next year’s dividend), r= 0.10 (required rate of return), and
g= 0.05 (dividend growth rate).
Step 1: Calculate the current value of the stock using the Gordon Growth
Model.
P0=2
0.10 −0.05
=2
0.05
= $40
Therefore, the current value of the stock is
$
40.
Question 9
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. If the dividend is expected
to grow at a constant rate of 8% indefinitely, what is the expected rate of return
on this stock?
6
Solution
Step 1: Calculate the dividend in the next year using the growth rate formula.
Dividend in one year = $2 ×(1 + 0.08) = $2.16
Step 2: Use the dividend discount model to calculate the expected rate of
return.
Expected Rate of Return = Dividend in one year
Current Price + Growth Rate
Expected Rate of Return = $2.16
$50 + 0.08
Expected Rate of Return = 0.0432 + 0.08
Expected Rate of Return = 0.1232
Step 3: Convert the expected rate of return to a percentage.
Expected Rate of Return = 0.1232 ×100% = 12.32%
Therefore, the expected rate of return on this stock is 12.32%.
Question 10
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
It is expected to grow its dividends at a constant rate of 6
Solution
Step 1: Calculate the dividend in the future year 1. The dividend in the next
year (D1) can be calculated using the formula: D1 = D0×(1 + g) where: -
D0 is the dividend this year (
$
2.50) - gis the growth rate (6Therefore, D1 =
$2.50 ×(1 + 0.06) = $2.50 ×1.06 = $2.65
Step 2: Calculate the price of the stock. The price of the stock can be
determined using the dividend discount model: P0 = D1
r−gwhere: - D1 is the
dividend in the next year (
$
2.65) - ris the required rate of return (10- gis the
growth rate (6Plugging in the values, P0 = $2.65
0.10−0.06 =$2.65
0.04 = $66.25
Therefore, the current value of the stock is
$
66.25.
Question 11
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. Dividends are expected to
grow at a constant rate of 5% per year indefinitely. If the required rate of return
is 10%, what is the intrinsic value of the stock?
7
Solution
Step 1: Calculate the expected dividend in the future The dividend next year is
given as D1= $2 Since the dividends are expected to grow at a constant rate,
the dividend in the second year (D2) can be calculated using the formula for
growth:
D2=D1×(1 + g)
where gis the growth rate. In this case, g= 5% = 0.05. So, D2= $2 ×(1 +
0.05) = $2.10
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model The intrinsic value of the stock can be calculated using the Gordon
Growth Model:
P0=D1
r−g
where: P0= Intrinsic value of the stock D1= Dividend next year r= Required
rate of return g= Growth rate
Plugging in the values, we get:
P0=$2.10
0.10 −0.05 =$2.10
0.05 = $42
Therefore, the intrinsic value of the stock is $42 per share.
Question 12
Question
A company’s stock is expected to pay a dividend of
$
2 per share 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 in year 2 using the growth rate. Step
2: Calculate the present value of the dividends in year 1 and 2. Step 3: Use the
formula for the present value of a growing perpetuity to find the present value
of all future dividends. Step 4: Add the present value of future dividends to
find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated as follows:
D2=D1×(1 + g) = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the present value of the dividends in year 1 and year 2:
P V (D1) = D1
1 + r=$2
1+0.10 = $1.82
8
P V (D2) = D2
(1 + r)2=$2.10
(1 + 0.10)2= $1.72
Step 3: Use the formula for the present value of a growing perpetuity:
P V =D1
r−g
Substitute the values to find the present value of all future dividends:
P V =$2
0.10 −0.05 = $40
Step 4: Add the present value of future dividends to find the current value
of the stock:
Current Value = P V (D1) + P V (D2) + P V = $1.82 + $1.72 + $40 = $43.54
Therefore, the current value of the stock is
$
43.54.
Question 13
Question
A company has a constant growth rate of dividends at 5
Solution
Step 1: Calculate the dividend growth rate. The formula for dividend growth
rate is given by:
Dividend Growth Rate = Dividend per Share at Time t−Dividend per Share at Time t−1
Dividend per Share at Time t−1
Given that the most recent dividend paid was
$
2.50, we find:
Dividend Growth Rate = 2.50 −2.50
2.50 = 0
Step 2: Calculate the dividend at time t+ 1. The formula for calculating
the dividend at time t+ 1 is:
Dividend at Time t+ 1 = Dividend at Time t×(1 + Dividend Growth Rate)
Substitute the values:
Dividend at Time t+ 1 = 2.50 ×(1 + 0.05) = 2.625
Step 3: Calculate the stock price using the dividend discount model. The
dividend discount model is given by:
P0=D1
r−g
9
Where: P0= Current stock price D1= Dividend at time t+ 1 =
$
2.625 r
= Required return on the stock = 12g= Dividend Growth Rate = 5
Substitute the values:
P0=2.625
0.12 −0.05 =2.625
0.07 ≈$37.50
Therefore, the current stock price using the dividend discount model is ap-
proximately
$
37.50.
Question 14
Question
A company’s stock currently pays a dividend of 3pershareandisexpectedtogrowatarateof5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Calculate the present value of the dividends. Step 3: Calculate the stock’s
present value by adding the present value of dividends.
Step 1: The expected dividend next year can be calculated using the growth
rate:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.05) = 3 ×1.05 = 3.15
Step 2: The present value of dividends can be calculated using the formula
for the present value of a growing perpetuity:
P V =D1
r−g
where: - D1= 3.15 (next year’s dividend), - r= 0.10 (required rate of return),
-g= 0.05 (growth rate).
P V =3.15
0.10 −0.05 =3.15
0.05 = 63
Step 3: The current value of the stock is the present value of dividends:
Stock Value = P V = 63
Therefore, the current value of the stock is 63pershare.
Question 15
Question
A company’s stock is currently trading at 75 per share. The company is expected
to pay an annual dividend of 3 per share forever. If the required rate of return
is 8
10
Solution
Step 1: Calculate the growth rate using the dividend growth model formula.
Given: Current stock price (P) = 75Dividendpershare(D) =3 Required rate
of return (r) = 8
The dividend growth model formula is:
D=D0×(1 + g)
r−g
Substitute the given values into the formula:
3 = 3×(1 + g)
0.08 −g
Simplify the equation:
3 = 3+3g
0.08 −g
3(0.08 −g) = 3 + 3g
0.24 −3g= 3 + 3g
0.24 −3=6g
−2.76 = 6g
g=−0.46
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model.
The Gordon Growth Model formula is:
P=D
r−g
Substitute the values of D, r, and g into the formula:
P=3
0.08 −(−0.46)
P=3
0.54
P=
5.56
Therefore, the intrinsic value of the stock is 56pershare.
11
Question 16
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 8
Solution
Step 1: Calculate the dividend next year using the formula for dividend growth:
Dividend next year = Dividend this year ×(1 + growth rate)
Dividend next year = $2.50 ×(1 + 0.08) = $2.50 ×1.08 = $2.70
Step 2: Calculate the price of the stock using the dividend discount model:
P0=D1
r−g
where: - P0= current price of the stock - D1= dividend next year - r= required
rate of return - g= growth rate
Substitute the values into the formula:
P0=$2.70
0.12 −0.08
P0=$2.70
0.04
P0= $67.50
Therefore, the current price of the stock is
$
67.50.
Question 17
Question
A company’s stock is expected to pay dividends of
$
2,
$
2.20,
$
2.42, and
$
2.66
over the next four years. If the required rate of return is 8%, what is the current
value of the stock?
Solution
Step 1: Calculate the present value of each dividend. Step 2: Add up the present
values of all dividends to find the current value of the stock.
Step 1: The present value (PV) of a dividend can be calculated using the
formula:
P V =D
(1 + r)n
12
where: - Dis the dividend amount, - ris the required rate of return, and - nis
the time period.
Given that r= 0.08,
P V1=2
(1+0.08)1=2
1.08 ≈1.85
P V2=2.20
(1+0.08)2=2.20
1.1664 ≈1.89
P V3=2.42
(1+0.08)3=2.42
1.2597 ≈1.92
P V4=2.66
(1+0.08)4=2.66
1.3605 ≈1.95
Step 2: The current value of the stock is the sum of the present values of
all dividends:
Stock Value = P V1+P V2+P V3+P V4
Stock Value = 1.85 + 1.89 + 1.92 + 1.95 = 7.61
Therefore, the current value of the stock is approximately
$
7.61.
Question 18
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 7
Solution
Step 1: Calculate the expected dividend next year using the dividend growth
rate. Step 2: Calculate the price of the stock using the dividend discount model.
Step 1: The expected dividend next year can be calculated as follows:
D1 = D0×(1 + g)
where: D1 = Expected dividend next year, D0 = Dividend this year, g=
Growth rate of dividends.
Given that D0 =
$
3.50, and g= 7% = 0.07, we have:
D1=3.50 ×(1 + 0.07) = 3.50 ×1.07 = $3.745
Step 2: The price of the stock using the dividend discount model is calculated
as:
P=D1
r−g
where: P= Price of the stock, D1 = Expected dividend next year, r= Required
rate of return, g= Growth rate of dividends.
Substitute D1 =
$
3.745, r= 10% = 0.10, and g=7%=0.07 into the
formula:
P=3.745
0.10 −0.07 =3.745
0.03 = $124.83
Therefore, the current value of the stock is
$
124.83.
13
Question 19
Question
A company’s stock is expected to pay a dividend of 3.00persharenextyearanddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the following year using the growth rate.
Dividend for next year = $3.00 ×(1 + 0.05) = $3.15
Step 2: Calculate the dividend yield, which is the dividend for next year
divided by the required rate of return.
Dividend yield = $3.15
0.10 = $31.50
Step 3: Calculate the growth rate minus the required rate of return.
0.05 −0.10 = −0.05
Step 4: Use the dividend yield and the growth rate minus the required rate
of return to calculate the stock price.
Stock P rice =Dividend yield
Growth rate −Required rate of return
Stock P rice =$31.50
−0.05 =−$630.00
Step 5: Interpretation The negative value for the stock price indicates that
there may have been an error in the calculations. The reason for this discrepancy
may be due to the assumption of perpetual growth at a constant rate, which
may not hold in reality.
Question 20
Question
A company pays an annual dividend of 3.50pershareandisexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current stock price.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
14
where: D1= expected dividend next year = 3.50 ×(1 + 5%) = 3.675D0=
current dividend = 3.50
Therefore,
g=3.675
3.50 −1=0.05 = 5%
Step 2: The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= current stock price r= required rate of return = 10g= dividend
growth rate = 5
Plugging in the values, we get:
P0=3.675
0.10 −0.05 =3.675
0.05 = 73.50
Therefore, the current stock price is $73.50.
Question 21
Question
A company’s stock currently pays a dividend of $4 per share. The dividend
is 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 current value of the stock?
Solution
Step 1: Calculate the growth rate gusing the formula:
g=Dividend Growth Rate
Required Rate of Return
g=0.05
0.10 = 0.5 = 5%
Step 2: Use the Gordon Growth Model to calculate the stock value:
Stock Value = Dividend
Required Rate of Return - Growth Rate
Stock Value = $4
0.10 −0.05
Stock Value = $4
0.05 = $80
Therefore, the current value of the stock is $80 per share.
15
Question 22
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Use the dividend discount model to find the current stock price.
Step 1: Let D0be the current dividend per share, and gbe the growth rate
of dividends. The expected dividend next year, D1, can be calculated using the
formula:
D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.05)
D1= 3.50 ×1.05
D1= 3.675
Step 2: The dividend discount model formula for the stock price, P0, is given
by:
P0=D1
r−g
where ris the required rate of return. Substitute the values into the formula:
P0=3.675
0.12 −0.05
P0=3.675
0.07
P0≈52.50
Therefore, the current stock price is approximately 52.50pershare.
Question 23
Question
A company’s stock currently has a dividend yield of 4
16
Solution
Step 1: The dividend yield can be used to find the dividend per share. The
dividend yield is calculated as the dividend per share divided by the stock price:
Dividend Yield = Dividend per share
Stock Price
Given that the dividend yield is 4
Dividend per share = Dividend Yield ×Stock Price = 0.04 ×120 = $4.80
Step 2: The company’s cost of equity can be calculated using the dividend
growth model:
r=D1
P0
+g
where: - ris the cost of equity, - D1is the next year’s dividend ($4.80 ×1.06 =
$5.088), - P0is the current stock price ($120), and - gis the growth rate of
dividends (6
Substitute the values into the formula:
r=5.088
120 + 0.06 = 0.0424 + 0.06 = 0.1024
Therefore, the company’s cost of equity is 10.24
Question 24
Question
A company is expected to pay a dividend of 2.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = $2.50 ×(1 + 0.05) = $2.625
Step 2: Use the dividend discount model to calculate the current value of
the stock.
V=D
r−g
where: V= current value of the stock, D= next dividend, r= required rate of
return, and g= growth rate of dividends.
Step 3: Substitute the values into the formula and calculate.
V=2.625
0.10 −0.05
V=2.625
0.05
V= 52.50
Therefore, the current value of the stock is
$
52.50.
17
Question 25
Question
A company pays a constant annual dividend of $4 per share. If the required
rate of return is 10%, what is the value of the stock?
Solution
Let’s denote the constant annual dividend by Dand the required rate of return
by r. The formula for valuing a stock using the constant growth dividend model
is given by:
P0=D
r−g
Where: - P0is the price of the stock today, - Dis the constant annual dividend,
and - gis the growth rate of the dividend.
In this case, the growth rate of the dividend is the same as the required rate
of return, (r=g), because the dividend is assumed to grow at a constant rate.
Step 1: Calculate the value of the stock using the formula.
P0=D
r−g
=4
0.10 −0.10
=4
0(Division by zero is undefined)
Since the denominator evaluates to zero, this is an example where the con-
stant growth dividend model is not applicable. In cases where the required rate
of return is equal to the growth rate of the dividend, different valuation meth-
ods need to be used, such as the two-stage dividend discount model or other
industry-specific models.
Question 26
Question
A company’s stock is currently trading at 58.50pershare.T hecompanyisexpectedtopayanannualdividendof 2.00
per share indefinitely. If the required rate of return on the stock is 8%, what is
the stock’s intrinsic value?
18
Solution
Step 1: Calculate the annual dividend growth rate using the dividend discount
model formula:
Dividend Growth Rate = Dividend per Share Next Year −Dividend per Share This Year
Dividend per Share This Year
Dividend Growth Rate = $2.00 −$2.00
$2.00 = 0%
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model formula:
Intrinsic Value = Dividend per Share Next Year
Required Rate of Return −Dividend Growth Rate
Intrinsic Value = $2.00
0.08 −0= $25.00
Therefore, the intrinsic value of the stock is
$
25.00 per share.
Question 27
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend one year from now. Given that the dividend next
year is 3.50pershareandthegrowthrateis5D1=D0×(1+g)=3.50×(1+0.05) =
3.675
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model. The intrinsic value of a stock can be calculated using the dividend
discount model formula:
V0=D1
r−g
where D1is the dividend one year from now, ris the required rate of return,
and gis the growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
V0=3.675
0.10 −0.05 =3.675
0.05 = 73.5
Therefore, the intrinsic value of the stock today is 73.50pershare.
19
Question 28
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Step 1: Calculate the current dividend per share using the dividend growth rate
formula.
Current Dividend Per Share = Dividend Next Year
Required Rate of Return −Growth Rate
Current Dividend Per Share = $2.50
0.10 −0.05 = $50
Step 2: Calculate the price of the stock using the dividend discount model.
Price of Stock = Dividend Next Year
Required Rate of Return −Growth Rate
Price of Stock = $2.50
0.10 −0.05 = $50
The current value of the stock is
$
50 per share.
Question 29
Question
A company’s stock is expected to pay a dividend of $2 per share next year.
Dividends are expected to grow at a constant rate of 4% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Let’s denote the current value of the stock as P, the next year dividend as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the next year dividend D1using the formula D1=D0×
(1 + g), where D0is the current dividend.
D1= $2 ×(1 + 0.04) = $2.08
Step 2: Calculate the required rate of return ras a decimal.
r= 10% = 0.10
20
Step 3: Calculate the growth rate gas a decimal.
g= 4% = 0.04
Step 4: Use the Gordon Growth Model formula to find the current value of
the stock:
P=D1
r−g
Step 5: Substitute the values of D1,r, and ginto the formula:
P=$2.08
0.10 −0.04 = $34.67
Step 6: Therefore, the current value of the stock is $34.67.
Question 30
Question
A company’s stock currently pays an annual dividend of 2pershare.T hedividendsareexpectedtogrowatarateof 5
Solution
Let’s denote: - Das the current dividend per share (
$
2), - gas the growth rate
of dividends (5- ras the required rate of return (10
The formula for the price of a stock using the Dividend Discount Model
(DDM) is:
P0=D0×(1 + g)
r−g
Step 1: Substitute the given values into the DDM formula:
P0=2×(1 + 0.05)
0.10 −0.05
Step 2: Simplify the expression:
P0=2×1.05
0.05 =2.1
0.05 = 42
Step 3: Therefore, the current value of the stock is
$
42.
21
Question 2
Question
An investor is considering purchasing stock in a company that is expected to pay
a dividend of 3.00nextyear.T heinvestor′srequiredrateof returnis10%, andthestockisexpectedtogrowataconstantrateof 5%peryear.If thecurrentstockpriceis60.00,
should the investor purchase the stock?
Solution
Step 1: Calculate the expected dividend for the next year using the constant
growth rate formula:
D1 = D0×(1 + g)
where: - D1 is the dividend for the next year, - D0 is the current dividend, and
-gis the growth rate.
Substitute the given values:
D1=3.00 ×(1 + 0.05) = 3.00 ×1.05 = 3.15
Step 2: Calculate the expected price of the stock in one year using the
constant growth model:
P1 = D1
r−g
where: - P1 is the price of the stock in one year, - ris the required rate of
return, and - gis the growth rate.
Substitute the given values:
P1 = 3.15
0.10 −0.05 =3.15
0.05 = 63.00
Step 3: Determine whether the investor should purchase the stock by com-
paring the expected price in one year to the current price. If the expected price
is higher, then the stock is undervalued and the investor should purchase the
stock.
Since the expected price in one year is 63.00, whichishigherthanthecurrentpriceof60.00,
the investor should purchase the stock.
Question 3
Question
A company’s stock is expected to pay dividends in perpetuity. The next dividend
payment will be
$
5 per share and dividends are expected to grow at a rate of 3
2
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current price of the stock.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
where: - g= growth rate of dividends - D0= latest dividend payment - D1=
next dividend payment
Substitute the given values:
g=5×1.03
5−1
g= 0.03
So, g= 3%.
Step 2: The current price (P0) of the stock can be calculated using the
Gordon Growth Model formula:
P0=D1
r−g
where: - P0= current price of the stock - D1= next dividend payment - r=
required rate of return - g= growth rate of dividends
Substitute the given values:
P0=5×1.03
0.08 −0.03
P0=5.15
0.05
P0= 103
Therefore, the current price of the stock is
$
103.
Question 4
Question
A company pays an annual dividend of 5pershare.Iftherequiredrateof returnis12
3
Solution
Step 1: Calculate the dividend growth rate using the formula: g=D1−D0
D0.
g=D1−D0
D0
=5×(1 + 0.05) −5
5
=5.25 −5
5
=0.25
5
= 0.05
Step 2: Use the Gordon Growth Model to calculate the stock price. The
Gordon Growth Model formula is: P0=D1
r−g. Given that D1=5×(1 + 0.05) =
5.25, r= 0.12, and g= 0.05.
P0=5.25
0.12 −0.05
=5.25
0.07
= 75
Therefore, the current stock price is 75pershare.
Question 5
Question
A company is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend in the following year. Since dividends are ex-
pected to grow at a rate of 5
D1=D0×(1 + g) = $3.50 ×(1 + 0.05) = $3.675
Step 2: Use the dividend discount model to calculate the value of the stock
today. The value of a stock today using the dividend discount model is given
by:
P0=D1
r−g
where: - P0= value of the stock today - D1= dividend in the following year -
r= required rate of return - g= growth rate of dividends
4
Step 3: Substitute the values into the formula and calculate.
P0=$3.675
0.08 −0.05 =$3.675
0.03 = $122.50
Therefore, the value of the stock today is
$
122.50.
Question 6
Question
A company is expected to pay a dividend of 2.50pershareattheendof theyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend one year from now.
Dividend next year = Dividend this year ×(1 + Growth rate)
Dividend next year = 2.50 ×(1 + 0.05) = 2.50 ×1.05 = 2.625
Step 2: Calculate the dividend discount model value of the stock.
Stock value = Dividend next year
Required return −Growth rate
Stock value = 2.625
0.10 −0.05 =2.625
0.05 = 52.50
Therefore, the current value of the stock is $52.50pershare.
Question 7
Question
Company XYZ is expected to pay a dividend of 3.50persharenextyear.Dividendsareexpectedtogrowatarateof 6
Solution
Step 1: Calculate the dividend growth rate.
Dividend Growth Rate (g) = 6% = 0.06
5
Step 2: Use the dividend discount model (DDM) formula to calculate the
price of the stock.
Price of Stock = Dividend Next Year
Required Rate of Return −Dividend Growth Rate
=3.50
0.10 −0.06
=3.50
0.04
= $87.50
Therefore, the price of Company XYZ’s stock today is
$
87.50.
Question 8
Question
A company’s stock is expected to pay a dividend of
$
2 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Let’s denote the current value of the stock as P0. We can use the Gordon
Growth Model to calculate the current stock price:
P0=D1
r−g
where: D1= $2 (next year’s dividend), r= 0.10 (required rate of return), and
g= 0.05 (dividend growth rate).
Step 1: Calculate the current value of the stock using the Gordon Growth
Model.
P0=2
0.10 −0.05
=2
0.05
= $40
Therefore, the current value of the stock is
$
40.
Question 9
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. If the dividend is expected
to grow at a constant rate of 8% indefinitely, what is the expected rate of return
on this stock?
6
Solution
Step 1: Calculate the dividend in the next year using the growth rate formula.
Dividend in one year = $2 ×(1 + 0.08) = $2.16
Step 2: Use the dividend discount model to calculate the expected rate of
return.
Expected Rate of Return = Dividend in one year
Current Price + Growth Rate
Expected Rate of Return = $2.16
$50 + 0.08
Expected Rate of Return = 0.0432 + 0.08
Expected Rate of Return = 0.1232
Step 3: Convert the expected rate of return to a percentage.
Expected Rate of Return = 0.1232 ×100% = 12.32%
Therefore, the expected rate of return on this stock is 12.32%.
Question 10
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
It is expected to grow its dividends at a constant rate of 6
Solution
Step 1: Calculate the dividend in the future year 1. The dividend in the next
year (D1) can be calculated using the formula: D1 = D0×(1 + g) where: -
D0 is the dividend this year (
$
2.50) - gis the growth rate (6Therefore, D1 =
$2.50 ×(1 + 0.06) = $2.50 ×1.06 = $2.65
Step 2: Calculate the price of the stock. The price of the stock can be
determined using the dividend discount model: P0 = D1
r−gwhere: - D1 is the
dividend in the next year (
$
2.65) - ris the required rate of return (10- gis the
growth rate (6Plugging in the values, P0 = $2.65
0.10−0.06 =$2.65
0.04 = $66.25
Therefore, the current value of the stock is
$
66.25.
Question 11
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. Dividends are expected to
grow at a constant rate of 5% per year indefinitely. If the required rate of return
is 10%, what is the intrinsic value of the stock?
7
Solution
Step 1: Calculate the expected dividend in the future The dividend next year is
given as D1= $2 Since the dividends are expected to grow at a constant rate,
the dividend in the second year (D2) can be calculated using the formula for
growth:
D2=D1×(1 + g)
where gis the growth rate. In this case, g= 5% = 0.05. So, D2= $2 ×(1 +
0.05) = $2.10
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model The intrinsic value of the stock can be calculated using the Gordon
Growth Model:
P0=D1
r−g
where: P0= Intrinsic value of the stock D1= Dividend next year r= Required
rate of return g= Growth rate
Plugging in the values, we get:
P0=$2.10
0.10 −0.05 =$2.10
0.05 = $42
Therefore, the intrinsic value of the stock is $42 per share.
Question 12
Question
A company’s stock is expected to pay a dividend of
$
2 per share 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 in year 2 using the growth rate. Step
2: Calculate the present value of the dividends in year 1 and 2. Step 3: Use the
formula for the present value of a growing perpetuity to find the present value
of all future dividends. Step 4: Add the present value of future dividends to
find the current value of the stock.
Step 1: The expected dividend in year 2 can be calculated as follows:
D2=D1×(1 + g) = $2 ×(1 + 0.05) = $2.10
Step 2: Calculate the present value of the dividends in year 1 and year 2:
P V (D1) = D1
1 + r=$2
1+0.10 = $1.82
8
P V (D2) = D2
(1 + r)2=$2.10
(1 + 0.10)2= $1.72
Step 3: Use the formula for the present value of a growing perpetuity:
P V =D1
r−g
Substitute the values to find the present value of all future dividends:
P V =$2
0.10 −0.05 = $40
Step 4: Add the present value of future dividends to find the current value
of the stock:
Current Value = P V (D1) + P V (D2) + P V = $1.82 + $1.72 + $40 = $43.54
Therefore, the current value of the stock is
$
43.54.
Question 13
Question
A company has a constant growth rate of dividends at 5
Solution
Step 1: Calculate the dividend growth rate. The formula for dividend growth
rate is given by:
Dividend Growth Rate = Dividend per Share at Time t−Dividend per Share at Time t−1
Dividend per Share at Time t−1
Given that the most recent dividend paid was
$
2.50, we find:
Dividend Growth Rate = 2.50 −2.50
2.50 = 0
Step 2: Calculate the dividend at time t+ 1. The formula for calculating
the dividend at time t+ 1 is:
Dividend at Time t+ 1 = Dividend at Time t×(1 + Dividend Growth Rate)
Substitute the values:
Dividend at Time t+ 1 = 2.50 ×(1 + 0.05) = 2.625
Step 3: Calculate the stock price using the dividend discount model. The
dividend discount model is given by:
P0=D1
r−g
9
Where: P0= Current stock price D1= Dividend at time t+ 1 =
$
2.625 r
= Required return on the stock = 12g= Dividend Growth Rate = 5
Substitute the values:
P0=2.625
0.12 −0.05 =2.625
0.07 ≈$37.50
Therefore, the current stock price using the dividend discount model is ap-
proximately
$
37.50.
Question 14
Question
A company’s stock currently pays a dividend of 3pershareandisexpectedtogrowatarateof5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Calculate the present value of the dividends. Step 3: Calculate the stock’s
present value by adding the present value of dividends.
Step 1: The expected dividend next year can be calculated using the growth
rate:
D1=D0×(1 + g)
D1= 3 ×(1 + 0.05) = 3 ×1.05 = 3.15
Step 2: The present value of dividends can be calculated using the formula
for the present value of a growing perpetuity:
P V =D1
r−g
where: - D1= 3.15 (next year’s dividend), - r= 0.10 (required rate of return),
-g= 0.05 (growth rate).
P V =3.15
0.10 −0.05 =3.15
0.05 = 63
Step 3: The current value of the stock is the present value of dividends:
Stock Value = P V = 63
Therefore, the current value of the stock is 63pershare.
Question 15
Question
A company’s stock is currently trading at 75 per share. The company is expected
to pay an annual dividend of 3 per share forever. If the required rate of return
is 8
10
Solution
Step 1: Calculate the growth rate using the dividend growth model formula.
Given: Current stock price (P) = 75Dividendpershare(D) =3 Required rate
of return (r) = 8
The dividend growth model formula is:
D=D0×(1 + g)
r−g
Substitute the given values into the formula:
3 = 3×(1 + g)
0.08 −g
Simplify the equation:
3 = 3+3g
0.08 −g
3(0.08 −g) = 3 + 3g
0.24 −3g= 3 + 3g
0.24 −3=6g
−2.76 = 6g
g=−0.46
Step 2: Calculate the intrinsic value of the stock using the Gordon Growth
Model.
The Gordon Growth Model formula is:
P=D
r−g
Substitute the values of D, r, and g into the formula:
P=3
0.08 −(−0.46)
P=3
0.54
P=
5.56
Therefore, the intrinsic value of the stock is 56pershare.
11
Question 16
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 8
Solution
Step 1: Calculate the dividend next year using the formula for dividend growth:
Dividend next year = Dividend this year ×(1 + growth rate)
Dividend next year = $2.50 ×(1 + 0.08) = $2.50 ×1.08 = $2.70
Step 2: Calculate the price of the stock using the dividend discount model:
P0=D1
r−g
where: - P0= current price of the stock - D1= dividend next year - r= required
rate of return - g= growth rate
Substitute the values into the formula:
P0=$2.70
0.12 −0.08
P0=$2.70
0.04
P0= $67.50
Therefore, the current price of the stock is
$
67.50.
Question 17
Question
A company’s stock is expected to pay dividends of
$
2,
$
2.20,
$
2.42, and
$
2.66
over the next four years. If the required rate of return is 8%, what is the current
value of the stock?
Solution
Step 1: Calculate the present value of each dividend. Step 2: Add up the present
values of all dividends to find the current value of the stock.
Step 1: The present value (PV) of a dividend can be calculated using the
formula:
P V =D
(1 + r)n
12
where: - Dis the dividend amount, - ris the required rate of return, and - nis
the time period.
Given that r= 0.08,
P V1=2
(1+0.08)1=2
1.08 ≈1.85
P V2=2.20
(1+0.08)2=2.20
1.1664 ≈1.89
P V3=2.42
(1+0.08)3=2.42
1.2597 ≈1.92
P V4=2.66
(1+0.08)4=2.66
1.3605 ≈1.95
Step 2: The current value of the stock is the sum of the present values of
all dividends:
Stock Value = P V1+P V2+P V3+P V4
Stock Value = 1.85 + 1.89 + 1.92 + 1.95 = 7.61
Therefore, the current value of the stock is approximately
$
7.61.
Question 18
Question
A company is expected to pay a dividend of 3.50persharenextyear.T hedividendsareexpectedtogrowatarateof 7
Solution
Step 1: Calculate the expected dividend next year using the dividend growth
rate. Step 2: Calculate the price of the stock using the dividend discount model.
Step 1: The expected dividend next year can be calculated as follows:
D1 = D0×(1 + g)
where: D1 = Expected dividend next year, D0 = Dividend this year, g=
Growth rate of dividends.
Given that D0 =
$
3.50, and g= 7% = 0.07, we have:
D1=3.50 ×(1 + 0.07) = 3.50 ×1.07 = $3.745
Step 2: The price of the stock using the dividend discount model is calculated
as:
P=D1
r−g
where: P= Price of the stock, D1 = Expected dividend next year, r= Required
rate of return, g= Growth rate of dividends.
Substitute D1 =
$
3.745, r= 10% = 0.10, and g=7%=0.07 into the
formula:
P=3.745
0.10 −0.07 =3.745
0.03 = $124.83
Therefore, the current value of the stock is
$
124.83.
13
Question 19
Question
A company’s stock is expected to pay a dividend of 3.00persharenextyearanddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend for the following year using the growth rate.
Dividend for next year = $3.00 ×(1 + 0.05) = $3.15
Step 2: Calculate the dividend yield, which is the dividend for next year
divided by the required rate of return.
Dividend yield = $3.15
0.10 = $31.50
Step 3: Calculate the growth rate minus the required rate of return.
0.05 −0.10 = −0.05
Step 4: Use the dividend yield and the growth rate minus the required rate
of return to calculate the stock price.
Stock P rice =Dividend yield
Growth rate −Required rate of return
Stock P rice =$31.50
−0.05 =−$630.00
Step 5: Interpretation The negative value for the stock price indicates that
there may have been an error in the calculations. The reason for this discrepancy
may be due to the assumption of perpetual growth at a constant rate, which
may not hold in reality.
Question 20
Question
A company pays an annual dividend of 3.50pershareandisexpectedtogrowataconstantrateof5
Solution
Step 1: Calculate the dividend growth rate. Step 2: Use the Gordon Growth
Model to calculate the current stock price.
Step 1: The dividend growth rate can be calculated using the formula:
g=D1
D0
−1
14
where: D1= expected dividend next year = 3.50 ×(1 + 5%) = 3.675D0=
current dividend = 3.50
Therefore,
g=3.675
3.50 −1=0.05 = 5%
Step 2: The Gordon Growth Model is given by:
P0=D1
r−g
where: P0= current stock price r= required rate of return = 10g= dividend
growth rate = 5
Plugging in the values, we get:
P0=3.675
0.10 −0.05 =3.675
0.05 = 73.50
Therefore, the current stock price is $73.50.
Question 21
Question
A company’s stock currently pays a dividend of $4 per share. The dividend
is 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 current value of the stock?
Solution
Step 1: Calculate the growth rate gusing the formula:
g=Dividend Growth Rate
Required Rate of Return
g=0.05
0.10 = 0.5 = 5%
Step 2: Use the Gordon Growth Model to calculate the stock value:
Stock Value = Dividend
Required Rate of Return - Growth Rate
Stock Value = $4
0.10 −0.05
Stock Value = $4
0.05 = $80
Therefore, the current value of the stock is $80 per share.
15
Question 22
Question
A company’s stock currently pays an annual dividend of 3.50pershare.T hedividendsareexpectedtogrowataconstantrateof 5
Solution
Step 1: Calculate the expected dividend next year using the growth rate. Step
2: Use the dividend discount model to find the current stock price.
Step 1: Let D0be the current dividend per share, and gbe the growth rate
of dividends. The expected dividend next year, D1, can be calculated using the
formula:
D1=D0×(1 + g)
D1= 3.50 ×(1 + 0.05)
D1= 3.50 ×1.05
D1= 3.675
Step 2: The dividend discount model formula for the stock price, P0, is given
by:
P0=D1
r−g
where ris the required rate of return. Substitute the values into the formula:
P0=3.675
0.12 −0.05
P0=3.675
0.07
P0≈52.50
Therefore, the current stock price is approximately 52.50pershare.
Question 23
Question
A company’s stock currently has a dividend yield of 4
16
Solution
Step 1: The dividend yield can be used to find the dividend per share. The
dividend yield is calculated as the dividend per share divided by the stock price:
Dividend Yield = Dividend per share
Stock Price
Given that the dividend yield is 4
Dividend per share = Dividend Yield ×Stock Price = 0.04 ×120 = $4.80
Step 2: The company’s cost of equity can be calculated using the dividend
growth model:
r=D1
P0
+g
where: - ris the cost of equity, - D1is the next year’s dividend ($4.80 ×1.06 =
$5.088), - P0is the current stock price ($120), and - gis the growth rate of
dividends (6
Substitute the values into the formula:
r=5.088
120 + 0.06 = 0.0424 + 0.06 = 0.1024
Therefore, the company’s cost of equity is 10.24
Question 24
Question
A company is expected to pay a dividend of 2.50persharenextyear.Dividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the next dividend using the growth rate.
Next dividend = $2.50 ×(1 + 0.05) = $2.625
Step 2: Use the dividend discount model to calculate the current value of
the stock.
V=D
r−g
where: V= current value of the stock, D= next dividend, r= required rate of
return, and g= growth rate of dividends.
Step 3: Substitute the values into the formula and calculate.
V=2.625
0.10 −0.05
V=2.625
0.05
V= 52.50
Therefore, the current value of the stock is
$
52.50.
17
Question 25
Question
A company pays a constant annual dividend of $4 per share. If the required
rate of return is 10%, what is the value of the stock?
Solution
Let’s denote the constant annual dividend by Dand the required rate of return
by r. The formula for valuing a stock using the constant growth dividend model
is given by:
P0=D
r−g
Where: - P0is the price of the stock today, - Dis the constant annual dividend,
and - gis the growth rate of the dividend.
In this case, the growth rate of the dividend is the same as the required rate
of return, (r=g), because the dividend is assumed to grow at a constant rate.
Step 1: Calculate the value of the stock using the formula.
P0=D
r−g
=4
0.10 −0.10
=4
0(Division by zero is undefined)
Since the denominator evaluates to zero, this is an example where the con-
stant growth dividend model is not applicable. In cases where the required rate
of return is equal to the growth rate of the dividend, different valuation meth-
ods need to be used, such as the two-stage dividend discount model or other
industry-specific models.
Question 26
Question
A company’s stock is currently trading at 58.50pershare.T hecompanyisexpectedtopayanannualdividendof 2.00
per share indefinitely. If the required rate of return on the stock is 8%, what is
the stock’s intrinsic value?
18
Solution
Step 1: Calculate the annual dividend growth rate using the dividend discount
model formula:
Dividend Growth Rate = Dividend per Share Next Year −Dividend per Share This Year
Dividend per Share This Year
Dividend Growth Rate = $2.00 −$2.00
$2.00 = 0%
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model formula:
Intrinsic Value = Dividend per Share Next Year
Required Rate of Return −Dividend Growth Rate
Intrinsic Value = $2.00
0.08 −0= $25.00
Therefore, the intrinsic value of the stock is
$
25.00 per share.
Question 27
Question
A company’s stock is expected to pay a dividend of 3.50persharenextyear, anddividendsareexpectedtogrowatarateof 5
Solution
Step 1: Calculate the dividend one year from now. Given that the dividend next
year is 3.50pershareandthegrowthrateis5D1=D0×(1+g)=3.50×(1+0.05) =
3.675
Step 2: Calculate the intrinsic value of the stock using the dividend discount
model. The intrinsic value of a stock can be calculated using the dividend
discount model formula:
V0=D1
r−g
where D1is the dividend one year from now, ris the required rate of return,
and gis the growth rate of dividends.
Step 3: Substitute the values into the formula. Plugging in the values we
have:
V0=3.675
0.10 −0.05 =3.675
0.05 = 73.5
Therefore, the intrinsic value of the stock today is 73.50pershare.
19
Question 28
Question
A company’s stock is expected to pay a dividend of
$
2.50 per share next year.
Dividends are expected to grow at a rate of 5
Solution
Step 1: Calculate the current dividend per share using the dividend growth rate
formula.
Current Dividend Per Share = Dividend Next Year
Required Rate of Return −Growth Rate
Current Dividend Per Share = $2.50
0.10 −0.05 = $50
Step 2: Calculate the price of the stock using the dividend discount model.
Price of Stock = Dividend Next Year
Required Rate of Return −Growth Rate
Price of Stock = $2.50
0.10 −0.05 = $50
The current value of the stock is
$
50 per share.
Question 29
Question
A company’s stock is expected to pay a dividend of $2 per share next year.
Dividends are expected to grow at a constant rate of 4% per year indefinitely.
If the required rate of return on the stock is 10%, what is the current value of
the stock?
Solution
Let’s denote the current value of the stock as P, the next year dividend as D1,
the growth rate of dividends as g, and the required rate of return as r.
Step 1: Calculate the next year dividend D1using the formula D1=D0×
(1 + g), where D0is the current dividend.
D1= $2 ×(1 + 0.04) = $2.08
Step 2: Calculate the required rate of return ras a decimal.
r= 10% = 0.10
20
Step 3: Calculate the growth rate gas a decimal.
g= 4% = 0.04
Step 4: Use the Gordon Growth Model formula to find the current value of
the stock:
P=D1
r−g
Step 5: Substitute the values of D1,r, and ginto the formula:
P=$2.08
0.10 −0.04 = $34.67
Step 6: Therefore, the current value of the stock is $34.67.
Question 30
Question
A company’s stock currently pays an annual dividend of 2pershare.T hedividendsareexpectedtogrowatarateof 5
Solution
Let’s denote: - Das the current dividend per share (
$
2), - gas the growth rate
of dividends (5- ras the required rate of return (10
The formula for the price of a stock using the Dividend Discount Model
(DDM) is:
P0=D0×(1 + g)
r−g
Step 1: Substitute the given values into the DDM formula:
P0=2×(1 + 0.05)
0.10 −0.05
Step 2: Simplify the expression:
P0=2×1.05
0.05 =2.1
0.05 = 42
Step 3: Therefore, the current value of the stock is
$
42.
21
