Name: ___________________________________
NetID: _______________________
Prof. Q. Ma, HADM 2222 Fall 2009
1/3
HADM 2222 Fall 2009, Prof. Q. Ma
Homework assignment
#3
[Due 10 a.m. Wednesday, October 7, 2009, Statler 435 drop box]
1.
Spears, Inc., has an odd dividend policy. The company has just paid a dividend of $7.00 per share and
has announced that it will increase the dividend by $4.00 per share for each of the next four years, and
then never pay another dividend. If you require an 11 percent return on the company’s stock, how much
will you pay for a share today?
Solution:
The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the
stock is the PV of these dividends using the required return. The price of the stock is:
P
0
= $11 / 1.11 + $15 /
1.11
2
+ $19 / 1.11
3
+ $23 / 1.11
4
= $51.13
2.
North Side Corporation is expected to pay the following dividends over the next four years: $8.00, $7.00,
$5.00, and $2.00. Afterward, the company pledges to maintain a constant 5 percent growth rate in
dividends forever. If the required return on the stock is 11 percent, what is the current share price?
Solution:
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth
rate, and then find the PV of the future stock price, plus the PV of all dividends during the supernormal
growth period. The stock begins constant growth in Year 4, so we can find the price of the stock in Year 4, at
the beginning of the constant dividend growth, as:
P
4
= D
4
(1 +
g
) / (
R
–
g
) = $2.00(1.05) / (.11 – .05) = $35.00
The price of the stock today is the PV of the first four dividends, plus the PV of the Year 3 stock price. So,
the price of the stock today will be:
P
0
= $8.00 / 1.11 + $7.00 / 1.11
2
+ $5.00 / 1.11
3
+ $2.00 / 1.11
4
+ $35.00 / 1.11
4
= $40.92
3.
Rizzi Co. is growing quickly. Dividends are expected to grow at a 25 percent rate for the next three years,
with the growth rate falling off to a constant 7 percent thereafter. If the required return is 13 percent and