這是用戶在 2025-2-5 7:56 為 https://app.immersivetranslate.com/pdf-pro/887fde44-c6e8-4aac-b9d8-69e1437730da 保存的雙語快照頁面,由 沉浸式翻譯 提供雙語支持。了解如何保存?

Stock Valuation  股票估值

MGMT 408: Foundations of Finance Tyler Muir
MGMT 408: 財務基礎 Tyler Muir

UCLA  加州大學洛杉磯分校

Fundamentals of Stock Valuation
股票估值的基本原理

Stock valuation  股票估值
What determines the value of a stock?
是什麼決定了股票的價值?

supply / demand  供應/需求
cash flow  現金流量
dividends  股息
brand value  品牌價值
P/E  市盈率
interest rates Fed  利率 美聯儲
Net income earnings projections
淨收入盈利預測

Learning Objectives for Stock Valuation
股票估值的學習目標

Goal:  目標:

How to value stocks.
如何評估股票價值。
  • The dividend discount model
    股利貼現模型
  • A general framework for thinking about the value of stock
    思考股票價值的一般架構
  • Investment and Growth  投資與成長
  • Multistage growth model  多階段成長模型
  • Price/Earnings ratio and growth prospects
    市盈率與成長前景
  • Optimal growth path  最佳成長路徑
■ Valuation using comparable firms analysis
使用可比公司分析進行估值

Example: One-year holding period valuation
範例:一年持有期估值

  • You plan to buy a stock in 3 M and hold it for one year.
    您計劃在 3 M 購買一隻股票並持有一年。
  • At the end of the year, you expect the stock price for 3 M will be $ 86 $ 86 $86\$ 86 per share.
    年底時,您預計 3 M 的股票價格為每股 $ 86 $ 86 $86\$ 86
  • This stock will also pay a dividend of $ 1.92 $ 1.92 $1.92\$ 1.92 per share at the end of the year.
    這隻股票也會在年底支付每股 $ 1.92 $ 1.92 $1.92\$ 1.92 的股利。
  • Investments with equivalent risks have an expected return of r E = 12 % r E = 12 % r_(E)=12%r_{E}=12 \%
    具有同等風險的投資,其預期報酬率為 r E = 12 % r E = 12 % r_(E)=12%r_{E}=12 \%
  • What are you willing to pay for the stock today?
    您今天願意為這隻股票付多少錢?

    0
    P 0 P 0 P_(0)P_{0}

Solutifn   解決方案

Today’s Price = P 0 = Div 1 + P 1 1 + r E = 1.92 + 86.00 1.12 = 78.50 = P 0 = Div 1 + P 1 1 + r E = 1.92 + 86.00 1.12 = 78.50 =P_(0)=(Div_(1)+P_(1))/(1+r_(E))=(1.92+86.00)/(1.12)=78.50=P_{0}=\frac{\operatorname{Div}_{1}+P_{1}}{1+r_{E}}=\frac{1.92+86.00}{1.12}=78.50  今日價格 = P 0 = Div 1 + P 1 1 + r E = 1.92 + 86.00 1.12 = 78.50 = P 0 = Div 1 + P 1 1 + r E = 1.92 + 86.00 1.12 = 78.50 =P_(0)=(Div_(1)+P_(1))/(1+r_(E))=(1.92+86.00)/(1.12)=78.50=P_{0}=\frac{\operatorname{Div}_{1}+P_{1}}{1+r_{E}}=\frac{1.92+86.00}{1.12}=78.50
Dividend Yield = Div 1 P 0 = 1.92 78.50 = 2.45 % =  Div  1 P 0 = 1.92 78.50 = 2.45 % =(" Div "_(1))/(P_(0))=(1.92)/(78.50)=2.45%=\frac{\text { Div }_{1}}{P_{0}}=\frac{1.92}{78.50}=2.45 \%
股利收益率 = Div 1 P 0 = 1.92 78.50 = 2.45 % =  Div  1 P 0 = 1.92 78.50 = 2.45 % =(" Div "_(1))/(P_(0))=(1.92)/(78.50)=2.45%=\frac{\text { Div }_{1}}{P_{0}}=\frac{1.92}{78.50}=2.45 \%

Capital Gain Rate = P 1 P 0 P 0 = 86.00 78.50 78.50 = 9.55 % = P 1 P 0 P 0 = 86.00 78.50 78.50 = 9.55 % =(P_(1)-P_(0))/(P_(0))=(86.00-78.50)/(78.50)=9.55%=\frac{P_{1}-P_{0}}{P_{0}}=\frac{86.00-78.50}{78.50}=9.55 \%
資本收益率 = P 1 P 0 P 0 = 86.00 78.50 78.50 = 9.55 % = P 1 P 0 P 0 = 86.00 78.50 78.50 = 9.55 % =(P_(1)-P_(0))/(P_(0))=(86.00-78.50)/(78.50)=9.55%=\frac{P_{1}-P_{0}}{P_{0}}=\frac{86.00-78.50}{78.50}=9.55 \%

One-year Valuation Formula
一年估值公式

Today’s price is the present value of the expected dividend and the expected price at the end of the year:
今天的價格是預期股息與年底預期價格的現值:
P 0 = Div 1 + P 1 1 + r E P 0 = Div 1 + P 1 1 + r E P_(0)=(Div_(1)+P_(1))/(1+r_(E))P_{0}=\frac{\operatorname{Div}_{1}+P_{1}}{1+r_{E}}
Can rearrange to get
可以重新排列得到
r E = Div 1 P 0 Dividend Yield + P 1 P 0 P 0 Capital Gain Rate r E =  Div  1 P 0 Dividend Yield  + P 1 P 0 P 0 Capital Gain Rate  r_(E)=ubrace((" Div "_(1))/(P_(0))ubrace)_("Dividend Yield ")+ubrace((P_(1)-P_(0))/(P_(0))ubrace)_("Capital Gain Rate ")r_{E}=\underbrace{\frac{\text { Div }_{1}}{P_{0}}}_{\text {Dividend Yield }}+\underbrace{\frac{P_{1}-P_{0}}{P_{0}}}_{\text {Capital Gain Rate }}

The Dividend Discount Model
股利折扣模式

The general dividend discount model
一般股利貼現模型
P 0 = P 1 + D 1 1 + r , : P 1 := P 2 + D 2 1 + r P 0 = D 1 1 + r + D 2 ( 1 + r ) 2 + P 2 ( appens i + 1 P 0 = D 1 ( 1 + r ) + D 2 ( 1 + r ) 2 + D 3 ( 1 + r ) 3 + . P 0 = P 1 + D 1 1 + r , : P 1 := P 2 + D 2 1 + r P 0 = D 1 1 + r + D 2 ( 1 + r ) 2 + P 2 (  appens  i + 1 P 0 = D 1 ( 1 + r ) + D 2 ( 1 + r ) 2 + D 3 ( 1 + r ) 3 + . {:[P_(0)=(P_(1)+D_(1))/(1+r)",":P_(1):=(P_(2)+D_(2))/(1+r)],[P_(0)=(D_(1))/(1+r)+(D_(2))/((1+r)^(2))+(P_(2))/((" appens "i+1)],[P_(0)=(D_(1))/((1+r))+(D_(2))/((1+r)^(2))+(D_(3))/((1+r)^(3))+dots.]:}\begin{aligned} & P_{0}=\frac{P_{1}+D_{1}}{1+r},: P_{1}:=\frac{P_{2}+D_{2}}{1+r} \\ & P_{0}=\frac{D_{1}}{1+r}+\frac{D_{2}}{(1+r)^{2}}+\frac{P_{2}}{(\text { appens } i+1} \\ & P_{0}=\frac{D_{1}}{(1+r)}+\frac{D_{2}}{(1+r)^{2}}+\frac{D_{3}}{(1+r)^{3}}+\ldots . \end{aligned}

The general dividend discount model
一般股利貼現模型

The formula for the price of a stock in its most general form
最一般形式的股票價格公式
P 0 = t = 1 Div t ( 1 + r E ) t P 0 = t = 1 Div t 1 + r E t P_(0)=sum_(t=1)^(oo)(Div_(t))/((1+r_(E))^(t))P_{0}=\sum_{t=1}^{\infty} \frac{\operatorname{Div}_{t}}{\left(1+r_{E}\right)^{t}}
The real world  真實世界
Is this model useful?
這個模型有用嗎?

Kinda?  有點?
Cash flow projection  現金流量預測
(Dividend forccasts)
Example: Constant dividend growth Perpetuity!
範例:恆定股利成長 永續性!
  • AT&T plans to pay $ 1.44 $ 1.44 $1.44\$ 1.44 per share in dividends in the coming year.
    AT&T 計劃在來年每股派發 $ 1.44 $ 1.44 $1.44\$ 1.44 股利。
  • Dividends are expected to grow by 4 % 4 % 4%4 \% per
    股利預期每股成長 4 % 4 % 4%4 \%
  • Divednds are expected to grow by 4 % 4 % 4%4 \% per
    Divednds 預計會以每秒 4 % 4 % 4%4 \% 的速度成長。

    year in the future.
    年的未來。
  • The expected return of AT&T stock is 8 % 8 % 8%8 \%.
    AT&T 股票的預期回報率為 8 % 8 % 8%8 \%
  • What is the value of AT&T’s stock?
    AT&T 股票的價值是多少?
  • Can you use this example to come up with a useful version of the dividend discount model?
    您可以利用這個範例提出股利折現模型的有用版本嗎?

Solution  解決方案

  • We have Div 1 = 1.44 , r E = 8 % Div 1 = 1.44 , r E = 8 % Div_(1)=1.44,r_(E)=8%\operatorname{Div}_{1}=1.44, r_{E}=8 \%, and g = 4 % g = 4 % g=4%g=4 \%.
    我們有 Div 1 = 1.44 , r E = 8 % Div 1 = 1.44 , r E = 8 % Div_(1)=1.44,r_(E)=8%\operatorname{Div}_{1}=1.44, r_{E}=8 \% ,和 g = 4 % g = 4 % g=4%g=4 \%
  • Recognize the stock is a growing perpetuity
    認識到股票是永續成長的
  • Using the value of a growing perpetuity, we have
    使用永續成長的價值,我們有
P 0 = Div 1 r E g = 1.44 0.08 0.04 = 36.00 . P 0 = Div 1 r E g = 1.44 0.08 0.04 = 36.00 . P_(0)=(Div_(1))/(r_(E)-g)=(1.44)/(0.08-0.04)=36.00.P_{0}=\frac{\operatorname{Div}_{1}}{r_{E}-g}=\frac{1.44}{0.08-0.04}=36.00 .

R $ 1 $ 1 $1\$ 1.

Invest back into busi Ace.
投資回 Ace.

Investment and growth  投資與成長

Growth in earnings  收益成長
What drives earnings and dividend growth?
是什麼驅使獲利與股利成長?

Investment!  投資!

Modeling growth  模擬成長

How can we use the tools that we have developed so far to assess the impact of investment and growth on value?
我們如何運用目前已開發的工具來評估投資與成長對價值的影響?


Earnings, investment, and dividends
收益、投資與股利

Let’s use some notation  讓我們使用一些符號
Div t = Div t = Div_(t)=\operatorname{Div}_{t}= Dividends per share at the end of year t ; t ; t;t ;
Div t = Div t = Div_(t)=\operatorname{Div}_{t}= 年底每股股利 t ; t ; t;t ;

EPS t = EPS t = EPS_(t)=\mathrm{EPS}_{t}= Earnings (CF from operations) per share at the end of year t t tt; Inv t = Inv t = Inv_(t)=\operatorname{Inv}_{t}= New investment per share at the end of year t t tt.
EPS t = EPS t = EPS_(t)=\mathrm{EPS}_{t}= 年末每股盈餘(營運所得 CF) t t tt ; Inv t = Inv t = Inv_(t)=\operatorname{Inv}_{t}= 年末每股新增投資 t t tt .
Earnings are either paid out as dividends or invested, so
賺來的錢會以股利的方式派發或投資,因此
EPS t = Div t + In v t EPS t = Div t + In v t EPS_(t)=Div_(t)+Inv_(t)\mathrm{EPS}_{t}=\operatorname{Div}_{t}+\operatorname{In} v_{t}
Or, equivalently  或者,等同於
Div t = EPS t ln t Div t = EPS t ln t Div_(t)=EPS_(t)-ln_(t)\operatorname{Div}_{t}=\mathrm{EPS}_{t}-\ln _{t}

Stock prices and earnings
股票價格和收益

We can apply the dividend discount model to get
我們可以運用股利貼現模型得到
P 0 = t = 1 EPS t Inv t ( 1 + r E ) t P 0 = t = 1 EPS t Inv t 1 + r E t P_(0)=sum_(t=1)^(oo)(EPS_(t)-Inv)/(t)_((1+r_(E))^(t))P_{0}=\sum_{t=1}^{\infty} \frac{\mathrm{EPS}_{t}-\operatorname{Inv}}{t}{ }_{\left(1+r_{E}\right)^{t}}
Investing for growth  為成長而投資
Growth in earnings comes from new investment
盈利增長來自新投資
ngs comes trom new investment this Earn next year - Earn this EPS t + 1 EPS t = lnv t × Return on New Investment r ROI  ngs comes trom new investment this   Earn next year - Earn this  EPS t + 1 EPS t = lnv t ×  Return on New Investment  r ROI  {:[" ngs comes trom new investment this "],[" Earn next year - Earn this "],[EPS_(t+1)-EPS_(t)=lnv_(t)xxubrace(" Return on New Investment "ubrace)_(r_("ROI "))]:}\begin{aligned} & \text { ngs comes trom new investment this } \\ & \text { Earn next year - Earn this } \\ & \mathrm{EPS}_{t+1}-\mathrm{EPS}_{t}=\operatorname{lnv}_{t} \times \underbrace{\text { Return on New Investment }}_{r_{\text {ROI }}} \end{aligned}
Investment comes out of earnings
投資來自收益
So the earnings growth rate is
因此盈利成長率為
(g) Earnings Growth Rate = Change in Earnings Earnings = b × r ROI E P S + + 1 E P S + E P S +  (g) Earnings Growth Rate  =  Change in Earnings   Earnings  = b × r ROI  E P S + + 1 E P S + E P S + {:[" (g) Earnings Growth Rate "=(" Change in Earnings ")/(" Earnings ")=b xxr_("ROI ")],[(EPS_(++1)-EPS_(+))/(EPS_(+))]:}\begin{aligned} & \text { (g) Earnings Growth Rate }=\frac{\text { Change in Earnings }}{\text { Earnings }}=b \times r_{\text {ROI }} \\ & \frac{E P S_{++1}-E P S_{+}}{E P S_{+}} \end{aligned}
The return on new investment and (un)profitable growth
新投資的回報與 (非) 盈利性成長
What rule should we apply if we want to create the most value for the firm?
如果我們想為公司創造最大價值,應該運用什麼規則?
The return on new investment and (un)profitable growth
新投資的回報與 (非) 盈利性成長
What rule should we apply if we want to create the most value for the firm?
如果我們想為公司創造最大價值,應該運用什麼規則?

THE NPV RULE  淨現值規則
The return on new investment and (un)profitable growth
新投資的回報與 (非) 盈利性成長
What rule should we apply if we want to create the most value for the firm?
如果我們想為公司創造最大價值,應該運用什麼規則?

THE NPV RULE  淨現值規則

How does it apply in this setting?
在此環境中如何應用?
NPV of New Investment = Inv t × r ROI r E Inv t = lnv t ( r ROI r E r E )  NPV of New Investment  = Inv t × r ROI r E Inv t = lnv t r ROI r E r E " NPV of New Investment "=(Inv_(t)xxr_(ROI))/(r_(E))-Inv_(t)=lnv_(t)((r_(ROI)-r_(E))/(r_(E)))\text { NPV of New Investment }=\frac{\operatorname{Inv}_{t} \times r_{\mathrm{ROI}}}{r_{E}}-\operatorname{Inv}_{t}=\operatorname{lnv}_{t}\left(\frac{r_{\mathrm{ROI}}-r_{E}}{r_{E}}\right)
Assuming that investment leads to a permanent increase in earnings.
假設投資會導致收益永久增加。
The return on new investment and (un)profitable growth
新投資的回報與 (非) 盈利性成長
What rule should we apply if we want to create the most value for the firm?
如果我們想為公司創造最大價值,應該運用什麼規則?

THE NPV RULE  淨現值規則

How does it apply in this setting?
在此環境中如何應用?
NPV of New Investment = Inv t × r ROI r E lnv t = lnv t ( r ROI r E r E )  NPV of New Investment  = Inv t × r ROI r E lnv t = lnv t r ROI r E r E " NPV of New Investment "=(Inv_(t)xxr_(ROI))/(r_(E))-lnv_(t)=lnv_(t)((r_(ROI)-r_(E))/(r_(E)))\text { NPV of New Investment }=\frac{\operatorname{Inv}_{t} \times r_{\mathrm{ROI}}}{r_{E}}-\operatorname{lnv}_{t}=\operatorname{lnv}_{t}\left(\frac{r_{\mathrm{ROI}}-r_{E}}{r_{E}}\right)
Assuming that investment leads to a permanent increase in earnings.
假設投資會導致收益永久增加。

When should firms choose to invest in generating new earning, i.e., set b > 0 b > 0 b > 0b>0 ?
公司應該何時選擇投資於產生新的賺錢機會,也就是設定 b > 0 b > 0 b > 0b>0 ?
N P V > 0 if ROI>r (IRR rale) N P V > 0  if ROI>r   (IRR rale)  {:[NPV > 0quad" if ROI>r "],[" (IRR rale) "]:}\begin{gathered} N P V>0 \quad \text { if ROI>r } \\ \text { (IRR rale) } \end{gathered}
Pay out all g = 0 g = 0 ∼g=0\sim g=0 qquad\qquad
支付所有 g = 0 g = 0 ∼g=0\sim g=0 qquad\qquad

Example: Cutung Dividends for Profitable Growth
範例:減少股利以獲取利潤成長
  • Crane Sporting Goods (Ticker: CSG) expects to have earnings per share of $ 6 $ 6 $6\$ 6 in the coming year.
    Crane Sporting Goods (Ticker: CSG) 預計來年每股盈餘為 $ 6 $ 6 $6\$ 6
  • Rather than reinvest these earnings and grow, CSG plans to pay out all of its earnings as a dividend.
    CSG 並未將這些盈利進行再投資和增長,而是計劃將其盈利全部作為股息派發。
  • With these expectations and no growth, CSG’s current share price is $ 60 $ 60 $60\$ 60.
    在這些預期和沒有增長的情況下,CSG 目前的股價是 $ 60 $ 60 $60\$ 60
  • Now suppose that CSG could cut its dividend payout rate to 75 % 75 % 75%75 \% for the foreseeable future and use the retained earnings to open new stores.
    現在假設南玻可以在可預見的未來將股利支付率降低到 75 % 75 % 75%75 \% ,並將留存收益用於開設新店。
  • The return on CSG’s investment in these stores is expected to be 12 % 12 % 12%12 \%. ROL
    預計 CSG 在這些店鋪的投資回報為 12 % 12 % 12%12 \% 。ROL
■ Assuming CSG’s expected return on equity is unchanged, what effect would this new policy have on CSG’s stock price?
假設 CSG 的預期股本報酬率維持不變,這項新政策對 CSG 的股票價格有何影響?
  • Hint: the above assumptions imply CSG’s expected return on equity is 10 % 10 % 10%10 \%.
    提示:上述假設意味著南玻的預期股本回報率為 10 % 10 % 10%10 \%
D 1 →→ 1 g p 1 + e D 1 →→ 1 g p 1 + e (D_(1)rarr rarr)/(1-g rarrp_(1)+e)\frac{D_{1} \rightarrow \rightarrow}{1-g \rightarrow p_{1}+e}
Disount E ^("E "){ }^{\text {E }} inte  卸載 E ^("E "){ }^{\text {E }} inte

Your Answers  您的答案

P = D 1 r g Example Solution How to estimate Cran's's equity cost of capital. = 6 10 % = 60 P = D 1 r g  Example Solution   How to estimate Cran's's equity cost of capital.  = 6 10 % = 60 P=(D_(1))/(r-g)quad{:[" Example Solution "],[" How to estimate Cran's's equity cost of capital. "]:}quad=(6)/(10%)=60P=\frac{D_{1}}{r-g} \quad \begin{aligned} & \text { Example Solution } \\ & \text { How to estimate Cran's's equity cost of capital. } \end{aligned} \quad=\frac{6}{10 \%}=60