# 14 Stock-and-Their-Valuation ```Stock and their Valuation
Jimalaya Quizon- MBAN 1206
Stocks
Common Stocks
- represents ownership
-ownership implies control
-stockholders elect Directors
-Management's goal is to maximize stock price
Types of stock market transactions
• Initial public offering market (“going public”)
- type of public offering where shares of stock in a company are sold
to the general public, on a securities exchange
- are used by companies to raise expansion capital, monetize the
investments of early private investors, and become publicly traded
enterprises
Types of stock market transactions
• Secondary Market
-is a registered offering of a large block of a security that has been
previously issued to the public
-blocks being offered may have been held by large investors or
institutions, and proceeds of the sale go to those holders, not the issuing
company
-also sometimes called secondary distribution
Different Approaches for Valuing
Common Stocks
• Dividend growth model
• Corporate value model
• Using the multiples of comparable firms
Dividend growth model
• Value of a stock is the present value of the future
dividends expected to be generated by the stock.
D3
D1
D2
D∞
P0 =
+
+
+ ... +
1
2
3
∞
(1 + rs )
(1 + rs )
(1 + rs )
(1 + rs )
^
Constant growth stock
• A stock whose dividends are expected to grow forever
at a constant rate, g.
D1 = D0 (1+g)1
D2 = D0 (1+g)2
Dt = D0 (1+g)t
• If g is constant, the dividend growth formula converges
to: ^ D0 (1 + g) D1
P0 =
rs - g
=
rs - g
Future dividends and their present
values
\$
0.25
PVD
t
Dt
=
( 1 + r )t
P0 = ∑ PVD
0
t
Dt = D0 (1 + g )
t
Years (t)
What happens if g &gt; rs?
• If g &gt; rs, the constant growth formula leads to a negative
stock price, which does not make sense
• The constant growth model can only be used if:
• rs &gt; g
• g is expected to be constant forever
If rRF = 7%, rM = 12%, and b = 1.2, what is
the required rate of return on the firm’s
stock?
• Use the SML to calculate the required rate of return (rs):
rs = rRF + (rM – rRF)b
= 7% + (12% - 7%)1.2
= 13%
If D0 = \$2 and g is a constant 6%, find the
expected dividend stream for the next 3
years, and their PVs.
0
g = 6%
D0 = 2.00
1.8761
1.7599
1.6509
1
2
2.12
2.247
rs = 13%
3
2.382
What is the stock’s intrinsic value?
• Using the constant growth model:
ˆP = D1 = \$2.12
0
rs - g 0.13 - 0.06
\$2.12
=
0.07
= \$30.29
What is the expected market price of
the stock, one year from now?
• D1 will have been paid out already. So, P1 is the present value
(as of year 1) of D2, D3, D4, etc.
D2
\$2.247
P1 =
=
rs - g 0.13 - 0.06
^
= \$32.10
• Could also find expected P1 as:
^
P1 = P0 (1.06) = \$32.10
What are the expected dividend yield, capital gains
yield, and total return during the first year?
• Dividend yield
= D1 / P0 = \$2.12 / \$30.29 = 7.0%
• Capital gains yield
= (P1 – P0) / P0
= (\$32.10 - \$30.29) / \$30.29 = 6.0%
• Total return (rs)
= Dividend Yield + Capital Gains Yield
= 7.0% + 6.0% = 13.0%
What would the expected price today
be, if g = 0?
• The dividend stream would be a perpetuity.
0
1
rs = 13%
P0
3
...
2.00
^
2
PMT
=
r
2.00
\$2.00
=
0.13
2.00
= \$15.38
Supernormal growth:
What if g = 30% for 3 years before
achieving long-run growth of 6%?
• Can no longer use just the constant growth model to find
stock value
• However, the growth does become constant after 3 years
Valuing common stock with non
constant growth
0 rs = 13% 1
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 =
46.114
^
54.107 = P0
4.658
0.13 - 0.06
= \$66.54
Find expected dividend and capital
gains yields during the first and fourth
years.
• Dividend yield (first year)
= \$2.60 / \$54.11 = 4.81%
• Capital gains yield (first year)
= 13.00% - 4.81% = 8.19%
• During non constant 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%.
Non constant growth:
What if g = 0% for 3 years before long-run growth of
6%?
0 r = 13%
s
g = 0%
D0 = 2.00
1
2
3
g = 0%
g = 0%
2.00 2.00
2.00
4
g = 6%
...
2.12
1.77
1.57
1.39
20.99
^
25.72 = P0
P\$ 3 =
2.12
0.13 - 0.06
= \$30.29
Find expected dividend and capital
gains yields during the first and fourth
years.
• 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%.
If the stock was expected to have
negative growth (g = -6%), would
anyone buy the stock, and what is its
value?
• The firm still has earnings and pays dividends, even though
they may be declining, they still have value.
D1
D0 ( 1 + g )
P0 =
=
rs - g
rs - g
^
\$2.00 (0.94) \$1.88
=
=
= \$9.89
0.13 - (-0.06) 0.19
Find expected annual dividend and
capital gains yields.
• 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 a negative capital gains.
Corporate value model
• Also called the free cash flow method. Suggests the
value of the entire firm equals the present value of the
firm’s free cash flows.
• Remember, free cash flow is the firm’s after-tax
operating income less the net capital investment
• FCF = NOPAT – Net capital investment
Applying the corporate value model
• Find the market value (MV) of the firm, by finding the PV
of the firm’s future FCFs.
• Subtract MV of firm’s debt and preferred stock to get
MV of common stock.
• Divide MV of common stock by the number of shares
outstanding to get intrinsic stock price (value).
Issues regarding the corporate value
model
• Often preferred to the dividend growth model, especially
when considering number of firms that don’t pay
dividends or when dividends are hard to forecast.
• Similar to dividend growth model, assumes at some
point free cash flow will grow at a constant rate.
• Terminal value (TVN) represents value of firm at the
point that growth becomes constant.
Given the long-run gFCF = 6%, and WACC of
10%, use the corporate value model to find the
firm’s intrinsic value.
0 r = 10%
1
-5
-4.545
8.264
15.026
398.197
416.942
2
10
3
20
530 =
4
g = 6%
...
21.20
21.20
0.10 - 0.06
= TV3
If the firm has \$40 million in debt and
has 10 million shares of stock, what is
the firm’s intrinsic value per share?
• MV of equity
= MV of firm – MV of debt
= \$416.94 - \$40
= \$376.94 million
• Value per share
= MV of equity / # of shares
= \$376.94 / 10
= \$37.69
Firm multiples method
• Analysts often use the following multiples to value
stocks.
•P/ E
• P / CF
• P / Sales
• EXAMPLE: Based on comparable firms, estimate the
appropriate P/E. Multiply this by expected earnings to
back out an estimate of the stock price.
What is market equilibrium?
• In equilibrium, stock prices are stable and there is
no general tendency for people to buy versus to sell.
• In equilibrium, two conditions hold:
• The current market stock price equals its intrinsic
value (P0 = P0).
• Expected returns must equal required returns.
D1
rs =
+g
P0
^
=
^
rs = rRF + (rM − rRF )b
Market equilibrium
• Expected returns are determined by estimating
dividends and expected capital gains
• Required returns are determined by estimating risk and
applying the CAPM
How is market equilibrium
established?
• If price is below intrinsic value …
• The current price (P0) is “too low” and offers a
bargain.
• Buy orders will be greater than sell orders.
• P0 will be bid up until expected return equals required
return.
How are the equilibrium values
determined?
• Are the equilibrium intrinsic value and expected return
estimated by managers or are they determined by
something else?
Equilibrium levels are based on the market’s estimate of intrinsic value
and the market’s required rate of return, which are both dependent
upon the attitudes of the marginal investor.
Preferred stock
• Hybrid security
• Like bonds, preferred stockholders receive a fixed
dividend that must be paid before dividends are paid to
common stockholders
• However, companies can omit preferred dividend
payments without fear of pushing the firm into
bankruptcy
If preferred stock with an annual dividend
of \$5 sells for \$50, what is the preferred
stock’s expected return?
Vp = D / r p
\$50 = \$5 / rp
^r = \$5 / \$50
p
= 0.10 = 10%
Reference:
• https://www.slideshare.net/Zorro29/chapter-7-stocks-and-their-valuation
• https://www.studyblue.com/notes/note/n/chapter-9-stocks-their-valuation/deck/14523421
• https://www.investopedia.com/articles/fundamental-analysis/11/choosing-valuation-methods.asp
• https://www.karvyonline.com/knowledge-center/beginner/stock-valuation
• https://slideplayer.com/slide/5276307/
• https://www.dividendmonk.com/stock-valuation-methods/
• https://courses.lumenlearning.com/boundless-finance/chapter/the-security-markets/
• https://www.wiziq.com/tutorial/764785-Stocks-and-Their-Valuation
THANK YOU!
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