126
Business Finance
Lecture 24
Review of the Previous Lecture
•
Some Special Cases in Stock Valuation
–
Zero growth Stocks
–
Constant Growth Stocks
–
NonConstant Growth Stocks
Topics under Discussion
•
Nonconstant Growth Stocks (cont.)
•
Components of Required Return
•
Common Stock Features
•
Preferred Stock Features
NonConstant Growth Stocks
•
CR Inc.: A Case of Supernormal Growth
–
The company has been growing at a phenomenal rate of 30% per year. You expect that this
growth rate to last for 3 more years and the rate will then drop to 10% per year.
•
Total dividends just paid were $5 million, and required return is 20%
•
If the growth rate then remains at 10% indefinitely, what is the total value of the stock?
•
It is unlikely that a 30% supernormal growth rate can be sustained for any extended length of
time.
•
To value the equity in this company, we first need to calculate the total dividend over the
supernormal growth period:
Year
Total Dividend (in millions)
1
$5.00 x 1.3 = $ 6.500
2
$6.50 x 1.3 =
8.450
3
$8.45 x 1.3 =
10.985
•
The price at time 3 can be calculated as:
P
3
= D
3
x (1 + g)
/(R  g)
where g is the longrun growth rate. So we have:
P
3
= $10.985x1.10/(0.20 – 0.10) = $120.835
NonConstant Growth Stocks
•
To determine the value today, we need the present value of this amount plus the present value
of the total dividends:
P
0
=
D
1
D
2
D
3
_
P
3
_
(1 + R)
1
(1 + R)
2
(1 + R)
3
(1 + R)
3
$6.50
8.45
10.985
120.835_
1.10
1
1.10
2
1.10
3
1.10
3
= $5.42 + 5.87 + 6.36 + 69.93 = $87.58 (mill.)
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•
The per share value will be
$87.58 / 20 = $4.38 per share
Components of Required Return
•
Let’s examine the implications of the dividend growth model for the required return of
Discount rate R.
•
We calculated
P0 as
P
0
= D
1
/ (R  g)
•
Rearranging it to solve for R, we get
R – g = D
1
/P
0
R = D
1
/P
0
+ g
•
This tells us that the total return, R, has two components
–
D
1
/P
0
is called the
Dividend Yield
. Because this is calculated as the expected cash
dividend by the current price, it is conceptually similar to the current yield on a bond
–
Growth rate, g, is also the rate at which the stock price grows. So it can be interpreted as
capital gains yield
•
Suppose a stock is selling for $20 per share. The next dividend is $1 per share and it is
expected to grow by 10% more or less indefinitely. What return does this stock offer you if
this is correct?
•
The dividend growth model calculates the total return as
R = D
1
/P
0
+ g
= $1/20 + 10% = 5% + 10% = 15%
•
We can verify this answer by calculating the price in one year, P1, using 15% as the required
return.
•
Based on the dividend growth model, the price is:
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 Spring '11
 NA
 Dividend, dividend growth model, nonconstant growth stocks

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