Transcript Document 7877515

Besley: Chapter 7
Assignment 5
Pg. 324 7-3; 7-4
Pg. 325 7-6
Pg. 327 7-11
Pg 324 7-3
Your broker offers to sell you some shares of
Wingler & Co. common stock that paid a dividend of
$2 yesterday. You expect the dividend to grow at
the rate of five percent per year for the next three
years, and if you buy the stock you plan to hold it
for three years and then sell it.

Find the expected dividend for each of the next
three years; that is, calculate D^1, D^2, and D^3.
Note that D0 = $2.

D1  $2(1.05)  $2.10

D 2  $2(1.05) 2  $2.21

D3  $2(1.05)3
 $2.32
Pg 324 7-3 continued

Given that the appropriate discount rate is 12
percent and that the first of these dividend
payments will occur one year from now, find
the present value of the dividend stream; that
is, calculate the PV of D^1, D^2, and D^3, and
then sum these PVs.
PV = $2.10(0.8929)+$2.21(0.7972)+$2.32(0.7118)
= $5.29
Pg 324 7-3 continued

You expect the price of the stock three years
from now to be $34.73; that is you expect P^3
to equal $34.73. Discount at a 12 percent
rate, what is the present value of this
expected future stock price? In other words,
calculate the PV of $34.73
PV of P^3 = $34.72(0.7118) = $24.72
Pg 324 7-3 continued

If you plan to buy the stock, hold it for three
years, and then sell it for $34.73, what is the
most you should pay for it?
P^0 = $24.72 + $5.29 = $30.01

Use Equation 7-6 to calculate the present
value of this stock. Assume that g = 5%, and
it is constant.

P0 
D 0(1  g )
ks  g


D1
ks  g

$2.10
 $30.00
0.12  0.05
Pg 324 7-3 continued

Is the value of this stock dependent upon how
long you plan to hold it? In other words, if
your planned holding period were two years or
five years rather than three years, would this
affect the value of the stock today, P^0?
The value of the stock is not dependent on the
holding period, but rather is dependent on the
cash flow stream.
Pg 324 7-4
You buy a share of Damanpour Corporation stock
for $21.40. You expect it to pay dividends of
$1.07, $1.1449, and $1.2250 in Years 1,2, and 3,
respectively, and you expect to sell it at a price of
$26.22 at the end of three years.
•
Calculate the growth rate in dividends.
g1 = (1.1449-1.07)/1.07
g2 = 1.2250/1.1449 – 1.0
= 7%
= 7%
Pg 324 7-4 continued

Calculate the expected dividend yield.
$1.07/$21.40 = 5%
•
Assuming that the calculated growth rate is
expected to continue, you can add the
dividend yield to the expected growth rate to
get the expected total rate of return. What is
this stock’s expected total rate of return?

ks 

D1
P0
g
 5%  7%  12%
Pg 325 7-6
Bayboro Sails is expected to pay
dividends of $2.50, $3.00, and $4.00
in the next three years-D^1, D^2, and
D^3, respectively. After three years,
the dividend is expected to grow at a
constant rate equal to four percent per
year indefinitely. Stockholders require
a return of 14% to invest in the
common stock of Bayboro Sails.
Pg 325 7-6 continue

Compute the present value of the dividends Bayboro is
expected to pay over the next three years.
PV = $2.50(0.8772) + $3.00(0.7695) + $4.00(0.6750)
= $7.20
•
For what price should investors expect to be able to sell
the common stock of Bayboro at the end of three
years? (Hint: The dividend will grow at a constant 4
percent in Year 4, Year 5, and every year thereafter, so
Equation 7-6 can be used to find P^3-the appropriate
dividend to use in the numerator is D^4.)

P3
$4(1  0.04)

 $4.16  $41.60
0.10
0.14  0.04
Pg 325 7-6 continue
•
Compute the value of Bayboro’s
common stock today, P^0.

P 0  PV of dividends + PV of price
= $7.20 + $41.60(0.6750)
= $35.28
Pg 327 7-11
Suppose Sartoris Chemical Company’s management
conducts a study and concludes that if Sartoris
expanded its consumer products division (which is
less risky that its primary business, industrial
chemicals), the firm’s beta would decline from 1.2
to 0.9. However, consumer products have a
somewhat lower profit margin, and this would cause
Sartoris’s constant growth rate in earnings and
dividends to fall from seven to five percent.
Pg 327 7-11 continued
•
Should management make the change? Assume the
following: km = 12%; krf = 9%’ D0 = $2.
ks OLD

P0 

D1
ks  g
=
=
=
P0OLD =
=
ks NEW = kRF + (ks-kRF)bs
kRF + (ks-kRF)bs
= 9%+(12%-9%)0.9
9%+(12%-9%)1.2
= 11.7%
12.6%
$2(1.07)/(.126-.07) P0NEW = $2(1.05)/(.117-.05)
= $31.34
$38.21
Since the New price is lower than the Old price, the
expansion into the less risky consumer products
market.
Pg 327 7-11 continued
•
Assume all the facts as given above expect the change
in the beta coefficient. How low would the beta have to
fall to cause the expansion to be a good one? (Hint:
Set P^0 under the new policy equal to P^0 under the old
one, and find the new beta that will produce this
equality.
POLD  $38.21 
$2(1.05)
ks  0.05
Solve for ks $2.10 = $38.21(ks)-1.9105
$4.0105 = $38.21(ks)
ks = 0.10496
Solve for bs 10.496% = 9% + 3%(bs)
1.496% = 3%(bs)
bs = 0.49865
 PNEW