Model(股利折现模型)

6-4 Simplifying the Dividend Discount Model(股利折現模型)
■ simplifying case 1: the dividend discount model with no growth
●
assumption: A company pays out all its earnings to its common shareholders. It does not raise any money either. [The company does not have good investment opportunities in the future.]
implication: Such a company could not grow because it could not reinvest.
Stockholders might enjoy a generous immediate dividend, but
they could forecast no increase in future dividends.
The company ’s stock would offer a perpetual stream of equal
cash payments, i.e., DIV 1 = DIV 2 = … = DIV t = …, where
DIV t denotes dividends per share(每股股利) at year t.
● today ’s price of the stock: r DIV r DIV r DIV r DIV P t 112110...)
1(...)1(1=+++++++= <= Please see valuing perpetuities in chapter 4.
●
Since the company pays out all its earnings as dividends, earnings and dividends are the same, i.e., EPS 1 = DIV 1, where EPS 1 is the next year ’s earnings per share(每股盈餘) of the stock.
=> the value of a no-growth stock: r EPS P 10=. ● estimating the expected rate of return: 0
1P EPS r = ■ simplifying case 2: the constant-growth dividend discount model
● assumption: Forecast dividends grow at a constant rate into the indefinite future.
=> future dividends: ,...,)1(),1(,213121g DIV DIV g DIV DIV DIV +=+=
...,)1(11-+=t t g DIV DIV
a note:
DIV t
DIV 0
t
● the value of a constant-growth stock: ...)
1(...)1()1(1332210+++++++++=t t r DIV r DIV r DIV r DIV P ...)
1()1(...)1()1()1()1(11
1321211++++++++++++=-t t r g DIV r g DIV r g DIV r DIV ...)
1()1(...)1()1()1()1(1)1()[11(13312211++++++++++++++=t t r g DIV r g DIV r g DIV r g DIV g ...])11(...11()11(11)[(1(321++++++++++++++=t r
g r g r g r g g DIV r g if g
r g g DIV <-++=)1)(1(1 r g if g r DIV <-=
1. ● Example 6-3: DIV 1 = $3.0, g = 8%, r = 12%
75$04.03$08.012.03$10==-=-=g r DIV P
● estimating the expected rate of return: g P DIV r g r DIV P +=⇒-=0
110= dividend yield (股利收益率) + growth rate Example above: r = 3/75 + 8% = 4% + 8% = 12%
a note: 下學期的內容有一個重點是討論r 如何決定。

When we use the rule r = DIV 1/ P 0 + g, we are not saying that the expected rate of return, r, is determined by the rule. It is determined by the rate of return offered by other equally risky stocks. However, we could try to estimate r by using the formula.
● practical use:
In some mature industries, growth is reasonable stable and constant-growth model is approximately(近似、接近的) valid(有效、妥當的).
Example: GDP growth
Taiwan (mature economy): 4%~5%
China (growing economy): past 15%, present 10%
■ Example 6-5 (changing growth rates)
Many companies grow at rapid rates for several years before finally settling down(安定、穩定) at moderate(穩健、溫和、適度的) growth rate.
United Bird ’s Seed ’s Stock:
Year 1 2 3 4 … EPS $2.45 $3.11 $3.78 5% growth thereafter DPS $1.00 $1.20 $1.44 5% growth thereafter r = 10%
notes: 1) The first 3-year expected dividends grow at 20%.
2) P 3 = PV(DIV 4, DIV 5, …, DIV t , …).
Estimation of stock price:
33332210)1()1()1(1r P r DIV r DIV r DIV P +++++++=
1) Dividends are expected to grow at a constant rate of g = 0.05 after Year 3. What is P 3?
DIV 4 = 1.05×DIV 3 = 1.05×$1.44 = $1.512 (∵ g = 0.05) 24.30$05
.010.0512.1$43=-=-=⇒g r DIV P 2) Estimate P 0. 33201
.124.30$1.144.1$1.120.1$1.100.1$+++=P = $25.70 6-5 Growth Stocks and Income Stocks
■ growth stocks:
Investors buy them in the expectation of capital gain . That is, they are interested in the future growth of earnings rather than in next year ’s dividends.
■ income stocks:
Investors buy them for the cash dividends .
■ some terminology(術語、專有名詞):
assumption: Assets are all equity financed. Therefore, assets equal equity.
1) earnings per share (EPS) = total earnings / total shares outstanding
2) payout rate (POR, 股利支付率) = DIV/EPS
3) plowback ratio (PBR, 再投資比率)
= retained earnings/total earnings
= (total earnings – total dividends)/total earnings
= 1 – POR
a note: total earnings = total dividends + retained earnings
4) return on equity (ROE, 股本報酬率)
= total earnings/total book value of equity(總和帳面股本值)
= EPS/BVPS
where BVPS denotes the book value of equity per share(每股帳面股本值).
a note: ROE and r
ROE is the rate of return on equity investment(帳面股本投資報酬率).
r is the required rate of return on equity(股本應有報酬率，既股票的市
場報酬率), i.e., the opportunity cost of equity capital (股本資本的機
會成本).
5) growth rate of assets, earnings, or dividends: g = ROE × PBR
notes: 1) If all of the earnings were plowed back into the firm, equity (or assets) will grow at the rate equal to ROE, i.e., g = ROE.
(股本或資產的報酬率既是成長率。

)
2) If a portion of earnings is not reinvested(i.e., is paid out as cash
dividends), equity will grow less than ROE, i.e., g = ROE ×PBR.
3) Since equity and assets grow by g, earnings and dividends grow by
g too.。