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Solution Key to Problem Set 3
ECN 134
Finance Economics
Prof. Farshid Mojaver
Stock Valuation 1
1.
We need to find the required return of the stock. Using the constant growth model, we
can solve the equation for k. Doing so, we find:
k
= (D
1
/ P
0
) +
g
= ($3.10 / $48.00) + .05 = 11.46%
2.
Using the constant growth model, we find the price of the stock today is:
P
0
= D
1
/ (k
–
g
) = $3.60 / (.13 – .045) = $42.35
3.
We know the stock has a required return of 12 percent, and the dividend and capital
gains yield are equal, so:
Dividend yield = 1/2(.12) = .06 = Capital gains yield
Now we know both the dividend yield and capital gains yield. The dividend is simply the
stock price times the dividend yield, so:
D
1
= .06($70) = $4.20
This is the dividend next year. The question asks for the dividend this year. Using the
relationship between the dividend this year and the dividend next year:
D
1
= D
0
(1 +
g
)
We can solve for the dividend that was just paid:
$4.20 = D0 (1 + .06)
D
0
= $4.20 / 1.06 = $3.96
4.
The price of any financial instrument is the PV of the future cash flows. The future
dividends of this stock are an annuity for eight years, so the price of the stock is the PVA,
which will be:
P
0
= $12.00(PV
10%,8
) = $64.02
5.
i)
Suppose we were in year three, then use the perpetuity formula:
8/0.16=50. This is the value of the stream in year three.
ii)
Then the same stream must be additionally discounted by 1/(1+r) in year two (discount
one):
50/(1+0.16) = 43.1
Similarly, the stream must be worth
50/(1+0.16)
2
= 37.16 in year one, and
50/(1+0.16)
3
= 32.04 in year zero.
In year four, the exdividend price will be 50 again.
6.
i)
The dividends grow by 14% for the next 20 years, and then by 6% every year after
that, forever:
In 1996 the dividend was $100. Note: We do not count this in our PV calculations, we
only use this as a reference point from which we make our calculations.
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View Full DocumentDividend in 1 year:
100*(1.14) = 114.0
Dividend in 2 years:
100*(1.14)
2
= 129.96
Dividend in 10 years: 100*(1.14)
10
= 370.72
Dividend in
20
year: 100*(1.14)
20
= 1374.3
Dividend in
21
year: 100*(1.14)
20
(1.06)
1
= 1456.8
Note: These are the actual dividends paid in the corresponding years, not their PV.
ii)
Use growing annuity formula:
+
+


=
T
r
g
g
r
C
Annuity
Growing
PV
1
1
1
1
)
(
Note: This give us the PV of the growing annuity the year before the payments start. In
this case, the dividends start in year 1, so the formula will give us the value in year 0,
which is what we want.
02
.
2421
237
.
21
114
12
.
0
1
14
.
0
1
1
14
.
0
12
.
0
114
1
1
1
20
=
×
=
+
+


=
+
+


T
r
g
g
r
C
iii)
Use the growing perpetuity formula:
g
r
C
Annuity
Growing
PV

=
)
(
Note: The formula gives the PV for the period before the first payment of the growing
perpetuity. In our problem, the growing perpetuity starts in year 21, so the formula will
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 Summer '08
 MOJAVER
 Economics

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