Download The Supernormal Growth Example

The Supernormal Growth Example
Assuming the same grow pattern for dividends:
D0 = $2.00.
0 rs = 13%
g = 30%
1
2
g = 30%
2.600
2.301
2.647
3.045
46.114
54.107 = P̂0
3
g = 30%
3.380
4
g = 6%
4.394
4.658
4.658
= $66.54
P̂3 =
0.13 − 0.06
21
The Supernormal Growth Example
•
Dividend yield (first year)
= $2.60/$54.11 = 4.81%
•
Capital gains yield (first year)
= 13.00% – 4.81% = 8.19%
•
During nonconstant growth, dividend yield
and capital gains yield are not constant, and
capital gains yield ≠ g.
•
After t = 3, the stock has constant growth
and dividend yield = 7%, while capital gains
yield = 6%.
22
Nonconstant-Growth Stock Valuation
Example: g = 0% for 3 years before long-run
growth at the rate of 6%?
0 r = 13%
s
g = 0%
D0 = $2.00.
1.77
1
2
g = 0%
2.00
3
g = 0%
2.00
4
g = 6%
2.00
2.12
1.57
1.39
20.99
25.72 = P̂0
2.12
P̂3 =
= $30.29
0.13 − 0.06
23
Nonconstant-Growth Stock Valuation
Example continued,
•
Dividend yield (first year)
= $2.00/$25.72 = 7.78%
•
Capital gains yield (first year)
= 13.00% – 7.78% = 5.22%
•
After t = 3, the stock has constant growth
and dividend yield = 7%, while capital gains
yield = 6%.
24
Stock Paying Decreasing Dividends
•
If the stock was expected to decreasing stream of
dividends, say, with g = -6%, would anyone buy the
stock, and what is its value?
•
Yes. Even though the dividends are declining, the
stock is still producing cash flows and therefore has
positive value.
Pˆ0 =
D0 (1 + g)
D1
=
rs − g
rs − g
$2.00 × (0.94)
$1.88
=
=
= $9.89
0.13 − (−0.06)
0.19
25
Stock Paying Decreasing Dividends
The example continued:
•
Capital gains yield
= g = -6.00%
•
Dividend yield
= 13.00% – (-6.00%) = 19.00%
•
Since the stock is experiencing constant
growth, dividend yield and capital gains
yield are constant. Dividend yield is
sufficiently large (19%) to offset negative
capital gains.
26
About the Discounted Dividend Model
This model is more conceptual than practical
The formula gives the fundamental reason why
shares of stock have value
It may not be very practical for actual stock valuation
It is wrong to think that a firm can boost its
stock price by changing its dividend policy, as
seen below
27
Illustration of Irrelevance of
Dividend Policy
A no-growth firm pays out all its earnings
$100 every year. rS=10%.
100 100 100
Total Stock value = 1 + 2 + 3 + L = $1, 000
1.1 1.1 1.1
Alternatively, the firm retains its first year’s
earning and invest in a normal return project
(project that yields 10%).
Dividends: D1=0, D2=110, D3=110, D4=110, …
110 110 110
Total Stock value = 2 + 3 + 4 + L = $1, 000
1.1 1.1 1.1
28
Implications for Stock Valuation
You may see why actual dividend payout does
not matter through the relation between
dividend and future growth.
If more cash will be paid out as dividend, less will be
invested in business, and lower will be the future
grow g; and vice versa.
Applying the Discounted Dividend Model, you may
get the same stock price
What determines the stock value is not the
dividend actually paid, but the firm’s dividendpaying ability.
29
Corporate Valuation Model
A firm is able to pay dividend because it has
free cash flows, cash not needed for operation
and can be paid to finance providers
This second method to stock valuation is based
on Free Cash Flow (FCF). The value of the firm
equals the PV of future FCF.
FCF for a given year is:
Depr. and 

 Capital

FCF = EBIT(1 − T) +
− 
+ ∆ NWC

amortization 

expenditures

30
Corporate Valuation Model
•
FCF is what is available to pay back all who
provide financing to the firm.
•
The PV of its future FCF is the total market
value (MV) of the firm.
FCF3
FCF1
FCF2
Total Firm Value =
+
+
+ ......
2
3
(1 + R ) (1 + R )
(1 + R )
where the discount rate R is the rate of return required
by an average investor of the firm, as explained next.
32
Technical Issues Regarding the
Corporate Valuation Model
•
If the firm has more than equity shares in its
capital structure, the discount rate used in PV
calculation is the average of the rates of return
required by different groups of investors.
•
This rate is called the Weighted Average Cost of
Capital (WACC), which will be studied in detail
later.
•
The weight for one kind of capital in WACC is
the value of this kind of capital as a percentage
of the total capital.
Continued
Continued
33
Technical Issues Regarding the
Corporate Valuation Model
•
Similar to discounted dividend model, we may
simplify by assuming that at some point FCF
will grow at a constant rate thereafter.
•
Horizon value (HVN) represents value of firm
at the point when growth becomes constant.
•
This method is better for being more practical
• No need for assumptions about the firm’s dividend
policy
• The input for FCF comes from comprehensive
forecast of future accounting performance.
35
Use the Corporate Valuation Model to
Find the Firm’s Intrinsic Value
Given: Long-Run gFCF = 6% and WACC = 10%
0
r = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
3
10
20
4
g = 6%
21.20
21.20
530 =
= HV3
0.10 − 0.06
Continued
Continued
36