The DDM
and Common Stock Valuation
• Some quick examples, courtesy of Harcourt
– The Effect of Evolving Growth Rates
– Valuation via Operating Cash Flow
Assume beta = 1.2, kRF = 7%, and kM =
12%. What is the required rate of return
on the firm’s stock?
Use the SML to calculate ks:
ks= kRF + (kM – kRF)bFirm
= 7% + (12% – 7%) (1.2)
= 13%.
D0 was $2.00 and g is a constant 6%.
Find the expected dividends for the next
3 years, and their PVs. ks = 13%.
0
g = 6%
1
D0 = 2.00 2.12
13%
1.8761
1.7599
1.6509
2
2.247
3
2.382
What’s the stock’s market value?
D0 = 2.00, ks = 13%, g = 6%.
Constant growth model:
D1
$2.12
P0 =
=
ks – g
0.13 – 0.06
=
$2.12
0.07
= $30.29.
What is the stock’s market value one
^
year from now, P1?
• D1 will have been paid, so expected
dividends are D2, D3, D4 and so on. Thus,
D2
$2.247
P1 =
=
ks – g
0.13 – 0.06
Could also
find P1 as follows:
= $32.10.
^
^
^ = P (1.06) = $32.10.
P
1
0
Find the expected dividend yield, capital
gains yield, and total return during the
first year.
D1
$2.12
Dividend yld =
=
= 7.0%.
P0
$30.29
^
P1 – P0 $32.10 – $30.29
Cap gains yld =
=
$30.29
P0
= 6.0%.
Total return = 7.0% + 6.0% = 13.0%.
Rearrange model to rate of return form:
D
D
1
1
$
$
=
=
+ g.
P0
to k s
ks - g
P0
^
Then, ks = $2.12/$30.29 + 0.06
= 0.07 + 0.06 = 13%.
^
What would P0 be if g = 0?
The dividend stream would be a
perpetuity.
0
13%
1
2
3
...
2.00
2.00
2.00
PMT
$2.00
P0 =
=
= $15.38.
k
0.13
^
If we have supernormal growth of 30% for
3 years, then a long-run constant
^
g = 6%, what is P0? k is still 13%.
• Can no longer use constant growth model.
• However, growth becomes constant after 3
years.
Nonconstant growth followed by constant
growth:
0 k = 13% 1
s
g = 30%
D0 = 2.00
2
g = 30%
2.600
3
g = 30%
3.380
4
...
g = 6%
4.394
4.658
2.301
2.647
3.045
P$ 3 =
46.116
54.109
^
= P0
4.658
.
= $66.54
0 .13 - 0.06
What is the expected dividend yield and
capital gains yield at t = 0?
At t = 4?
$2.60
Div. yield0 =
= 4.81%.
$54.11
Cap. gain0 = 13.00% – 4.81% = 8.19%.
• During nonconstant growth, D/P and capital
gains yield are not constant, and capital
gains yield is less than g.
• After t = 3, g = constant = 6% = capital
gains yield; k = 13%; so D/P = 13% – 6% =
7%.
Suppose g = 0 for t = 1 to 3, and then g is
^
a constant 6%. What is P0?
0
ks=13%
g = 0%
2.00
1.77
1.57
1.39
20.99
25.72
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
...
2.12
2.12
$ =
= 30.29.
P
3
0.07
What is D/P and capital gains yield at
t = 0 and at t = 3?
t = 0:
D1 $2.00
=
= 7.78%.
P0 $25.72
CGY = 13% – 7.78% = 5.22%.
t = 3: Now have constant growth
with g = capital gains yield = 6% and
D/P = 7%.
If g = -6%, would anyone buy the stock?
If so, at what price?
Firm still has earnings and still pays
dividends, so P0 > 0:
(
+ g)
D
1
D
0
1
$0 =
=
P
ks - g
ks - g
$2.00(0.94)
$1.88
=
=
= $9.89.
0.13 – (-0.06)
0.19
What is the annual D/P and capital gains
yield?
Capital gains yield = g = -6.0%,
Dividend yield= 13.0% – (-6.0%) = 19%.
D/P and cap. gains yield are constant,
with high dividend yield (19%) offsetting
negative capital gains yield.
Free Cash Flow Method
• The free cash flow method suggests that the
value of the entire firm equals the present
value of the firm’s free cash flows
(calculated on an after-tax basis).
• Recall that the free cash flow in any given
year can be calculated as:
NOPAT – Net capital investment.
Using the Free Cash Flow Method
• Once the value of the firm is estimated, an
estimate of the stock price can be found as
follows:
– MV of common stock (market capitalization) =
MV of firm – MV of debt and preferred stock.
^
–P
= MV of common stock/# of shares.
Issues Regarding the Free Cash Flow
Method
• Free cash flow method is often preferred to
the dividend growth model--particularly for
the large number of companies that don’t
pay a dividend, or for whom it is hard to
forecast dividends.
(More...)
FCF Method Issues Continued
• Similar to the dividend growth model, the
free cash flow method generally assumes
that at some point in time, the growth rate in
free cash flow will become constant.
• Terminal value represents the value of the
firm at the point in which growth becomes
constant.
FCF estimates for the next 3 years are
-$5, $10, and $20 million, after which
the FCF is expected to grow at 6%. The
overall firm cost of capital is 10%.
0
k = 10%
1
2
3
4
g = 6%
-5
-4.545
8.264
15.026
398.197
416.942
10
20
...
21.20
21.20
530 =
= *TV3
0.04
*TV3 represents the terminal value of
the firm, at t = 3.
If the firm has $40 million in debt and
has 10 million shares of stock, what is
the price per share?
Value of equity = Total value – Value of debt
= $416.94 – $40
= $376.94 million.
Price per share = Value of equity/# of shares
= $376.94/10
= $37.69.