Solution Key to Problem Set 4
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.
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 Spring '10
 FARSHIDMOJAVER
 Time Value Of Money, Perpetuity, Dividend yield, share price

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