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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  ^("E "){ }^{\text {E }} inte  卸載 E 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
■ No growth implies g = 0 g = 0 g=0g=0, so
沒有成長意味著 g = 0 g = 0 g=0g=0 ，所以
r E = Div 1 P 0 + g = 6 60 + 0 = 10 % r E = Div 1 P 0 + g = 6 60 + 0 = 10 % r_(E)=(Div_(1))/(P_(0))+g=(6)/(60)+0=10%r_{E}=\frac{\operatorname{Div}_{1}}{P_{0}}+g=\frac{6}{60}+0=10 \%
Second, we consider the effect of the new policy.
其次，我們考慮新政策的效果。
  • Div 1 ′ = 75 % × 6 = 4.50 Div 1 ′ = 75 % × 6 = 4.50 Div_(1)^(')=75%xx6=4.50\operatorname{Div}_{1}^{\prime}=75 \% \times 6=4.50. ( 1 − 0.75 ) = 0.25 ( 1 − 0.75 ) = 0.25 (1-0.75)=0.25(1-0.75)=0.25
  • Crane will reinvest b ′ = 25 % b ′ = 25 % b^(')=25%b^{\prime}=25 \% of its earnings
    Crane 將收益的 b ′ = 25 % b ′ = 25 % b^(')=25%b^{\prime}=25 \% 再投資
■ New investments are expected to generate a return of r ROI = 12 % r ROI  = 12 % r_("ROI ")=12%r_{\text {ROI }}=12 \%,
新投資預期會產生 r ROI = 12 % r ROI  = 12 % r_("ROI ")=12%r_{\text {ROI }}=12 \% 的回報、
  • Growth rate of earnings and dividends will be g ′ = 12 % × 25 % = 3 % g ′ = 12 % × 25 % = 3 % g^(')=12%xx25%=3%g^{\prime}=12 \% \times 25 \%=3 \%.
    收益與股利的成長率將是 g ′ = 12 % × 25 % = 3 % g ′ = 12 % × 25 % = 3 % g^(')=12%xx25%=3%g^{\prime}=12 \% \times 25 \%=3 \% 。
  • Assuming r E r E r_(E)r_{E} does not change, we can use the constant growth formula again:
    假設 r E r E r_(E)r_{E} 不變，我們可以再次使用恆定成長公式：
P 0 = Div 1 ′ r E − g ′ = 4.50 0.10 − 0.03 = 64.29 > 60.00 P 0 = Div 1 ′ r E − g ′ = 4.50 0.10 − 0.03 = 64.29 > 60.00 P_(0)=(Div_(1)^('))/(r_(E)-g^('))=(4.50)/(0.10-0.03)=64.29 > 60.00P_{0}=\frac{\mathrm{Div}_{1}^{\prime}}{r_{E}-g^{\prime}}=\frac{4.50}{0.10-0.03}=64.29>60.00

Stock prices and earnings
股票價格和收益

The dividend discount model dealt with the effect of dividends on value, but an often used measure of a stock’s value is the price-earnings ( P / E P / E P//EP / E ) ratio.
股利折現模型處理的是股利對價值的影響，但常用來衡量股票價值的方法是市盈率 ( P / E P / E P//EP / E )。
Amazon: P 0 EPS 1 = 51.07 Ratheon: P 0 EPS 1 = 14.78  Amazon:  P 0 EPS 1 = 51.07  Ratheon:  P 0 EPS 1 = 14.78 {:[" Amazon: "(P_(0))/(EPS_(1))=51.07],[" Ratheon: "(P_(0))/(EPS_(1))=14.78]:}\begin{aligned} & \text { Amazon: } \frac{P_{0}}{\mathrm{EPS}_{1}}=51.07 \\ & \text { Ratheon: } \frac{P_{0}}{\mathrm{EPS}_{1}}=14.78 \end{aligned}
Why is there such a big difference?
為什麼會有這麼大的差異？
P / E P / E P//EP / E ratios and growth
P / E P / E P//EP / E 比率與成長
What is the P / E P / E P//EP / E ratio for Crane’s before it starts investing? What about after?
Crane's 開始投資之前的 P / E P / E P//EP / E 比率是多少？之後呢？
Before: : 60 6 = 10 , After: 64 6 > 10  Before:  : 60 6 = 10 , After:  64 6 > 10 " Before: ":(60)/(6)=10", After: "(64)/(6) > 10\text { Before: }: \frac{60}{6}=10 \text {, After: } \frac{64}{6}>10
How valuable are Crane’s growth opportunities?
Crane 的成長機會有多大價值？
P 0 ( w / Growth ) = P 0 ( w / o Growth ) + P V ( Growth Opportunities ) = EPS 1 r E ⏟ + P V ( Growth Opportunities ) P 0 ( w /  Growth  ) = P 0 ( w /  o Growth  ) + P V (  Growth Opportunities  ) = EPS 1 r E ⏟ + P V (  Growth Opportunities  ) {:[P_(0)(w//" Growth ")=P_(0)(w//" o Growth ")+PV(" Growth Opportunities ")],[=ubrace((EPS_(1))/(r_(E))ubrace)+PV(" Growth Opportunities ")]:}\begin{aligned} P_{0}(\mathrm{w} / \text { Growth }) & =P_{0}(\mathrm{w} / \text { o Growth })+P V(\text { Growth Opportunities }) \\ & =\underbrace{\frac{\mathrm{EPS}_{1}}{r_{E}}}+P V(\text { Growth Opportunities }) \end{aligned}
What does the P / E P / E P//EP / E ratio represent how that we have ncluded investment?
P / E P / E P//EP / E 比率代表什麼？
60 + 4.29 60 + 4.29 60+4.2960+4.29
High ROI for a while ROI “Growth phase” ROI ↓↓↓ ↓↓↓ darr darr darr\downarrow \downarrow \downarrow
一時的高 ROI ROI「成長階段」 ROI ↓↓↓ ↓↓↓ darr darr darr\downarrow \downarrow \downarrow

Example: Modeling Growth in Stages
範例：分階段建立成長模型

  • New Venture, Inc. (NVI) expects to generate total earnings of $ 50 $ 50 $50\$ 50 million in year 1.
    New Venture, Inc. (NVI) 預計第一年的總收益為 $ 50 $ 50 $50\$ 50 百萬元。
  • Without further investment, NVI will continue to generate $ 50 $ 50 $50\$ 50 million per year.
    如果沒有進一步的投資，NVI 將繼續每年產生 $ 50 $ 50 $50\$ 50 百萬。
  • As a young firm, NVI has very valuable investment opportunities that yield r ROI = 50 % r ROI  = 50 % r_("ROI ")=50%r_{\text {ROI }}=50 \%.
    作為一家年輕的公司，NVI 擁有非常寶貴的投資機會，能產生 r ROI = 50 % r ROI  = 50 % r_("ROI ")=50%r_{\text {ROI }}=50 \% 。
  • Specifically, NVI can invest up to an additional $ 600 $ 600 $600\$ 600 million at this return on investment.
    具體而言，NVI 最多可按此投資報酬率額外投資 $ 600 $ 600 $600\$ 600 百萬美元。
  • Any further investment yields only a return on investment of 7 % 7 % 7%7 \%.
    任何進一步的投資都只能獲得 7 % 7 % 7%7 \% 的投資回報。

Modeling Growth in Stages Continued
分階段建立成長模型 續

  • Like most young and entrepreneurial firms, NVI plans to plow back all of its earnings until total additional investment reaches $ 600 $ 600 $600\$ 600 million, and to pay out all earnings as dividends after that.
    就像大多數年輕的創業公司一樣，NVI 計畫在額外投資總額達到 $ 600 $ 600 $600\$ 600 百萬之前，將所有收益回饋給公司，之後所有收益將以股利形式發放。
  • If the required rate of return (same as expected return on equity) fo NVI is 8 % 8 % 8%8 \%, what is the value of NVI ?
    如果 NVI 的規定回報率（與預期股權回報率相同）為 8 % 8 % 8%8 \% ，NVI 的值是多少？
  • What is the P/E ratio for NVI
    NVI 的市盈率是多少？
  • Note that the above quantities are not on a per-share basis. Let us define the following notation for this problem:
    請注意，上述數量並非以每股為單位。讓我們為這個問題定義以下符號：
Firm Value = V 0 = P 0 × # Shares Outstanding Total Earnings at t = E t = EPS t × # Shares Outstanding Total Dividends at t = D t = Div t × # Shares Outstanding  Firm Value  = V 0 = P 0 × #  Shares Outstanding   Total Earnings at  t = E t = EPS t × #  Shares Outstanding   Total Dividends at  t = D t = Div t × #  Shares Outstanding  {:[" Firm Value "=V_(0)=P_(0)xx#" Shares Outstanding "],[" Total Earnings at "t=E_(t)=EPS_(t)xx#" Shares Outstanding "],[" Total Dividends at "t=D_(t)=Div_(t)xx#" Shares Outstanding "]:}\begin{aligned} \text { Firm Value } & =V_{0}=P_{0} \times \# \text { Shares Outstanding } \\ \text { Total Earnings at } t & =E_{t}=\operatorname{EPS}_{t} \times \# \text { Shares Outstanding } \\ \text { Total Dividends at } t & =D_{t}=\operatorname{Div}_{t} \times \# \text { Shares Outstanding } \end{aligned}
New Venture Inc Answers
New Venture Inc 答案

Example Solution  解決方案範例

First determine the growth path
首先確定成長路徑

Example Solution cont.  範例解決方案續

First dividend of Div 5 = 59 5 = 59 _(5)=59_{5}=59 paid at EOY 5. After that dividends are constant at Div = 350 = 350 =350=350 for all time. Dividend discount model
在 EOY 5 派發第一次股息 Div 5 = 59 5 = 59 _(5)=59_{5}=59 。之後，股利一直維持在 Div = 350 = 350 =350=350 。股利折現模型
V 0 = 59 ( 1.08 ) 5 + 1 ( 1.08 ) 5 350 0.08 = 3018 V 0 = 59 ( 1.08 ) 5 + 1 ( 1.08 ) 5 350 0.08 = 3018 V_(0)=(59)/((1.08)^(5))+(1)/((1.08)^(5))(350)/(0.08)=3018V_{0}=\frac{59}{(1.08)^{5}}+\frac{1}{(1.08)^{5}} \frac{350}{0.08}=3018
The P / E P / E P//EP / E ratio is given by
P / E P / E P//EP / E 比率由以下公式得出
P / E = 3018 50 = 60 P / E = 3018 50 = 60 P//E=(3018)/(50)=60P / E=\frac{3018}{50}=60

Next time  下一次

Valuation Based on Comparable Firms
根據可比公司進行估值

Stock multiples  股票倍數

P / E P / E P//E\mathrm{P} / \mathrm{E} ratio just one popular multiple, but there are many others. E.g.:
P / E P / E P//E\mathrm{P} / \mathrm{E} 比率只是一種流行的倍數，但還有許多其他的倍數。例如：
  • Ratio of equity value to net income
    權益價值與淨收入的比率
  • Ratio of equity value to total investment
    權益價值與投資總額的比率
Note: Equity value is sometime also called Market Capitalization (Market Cap for short)
註：股權價值有時也稱為市值 (Market Capitalization，簡稱 Market Cap)。
Market Cap = = == Price per share × # × # xx#\times \# Shares outstanding
市值 = = == 每股價格 × # × # xx#\times \# 已發行股份

Comparables valuation  可比估值

The method:  方法：
1 Find a set of firms that are roughly similar, i.e., comparable, to the firm you wish to value. Called comps.
1 尋找一組與您希望估值的公司大致類似（即可比較）的公司。稱為 Comps。
2 Choose a ratio, e.g., P / E P / E P//E\mathrm{P} / \mathrm{E}
2 選擇一個比率，例如 P / E P / E P//E\mathrm{P} / \mathrm{E}
3 Take the average of that ratio for your set of comparable firms.
3 取一系列可比公司的平均比率。
4 Multiple the average ratio by the corresponding number, e.g., EPS, of the firm you wish to value.
4 將平均比率乘以您希望估值的公司的對應數字，例如 EPS。

Example: Valuing Fiat-Chrysler
範例：評估 Fiat-Chrysler

Let’s say Ford and GM are comps for Fiat-Chrysler.
比方說，Ford 和 GM 是 Fiat-Chrysler 的比較對象。
Ford: P 0 EPS 1 = 8.45 GM : P 0 EPS 1 = 7.19  Ford:  P 0 EPS 1 = 8.45 GM : P 0 EPS 1 = 7.19 {:[" Ford: "(P_(0))/(EPS_(1))=8.45],[GM:(P_(0))/(EPS_(1))=7.19]:}\begin{aligned} & \text { Ford: } \frac{P_{0}}{\mathrm{EPS}_{1}}=8.45 \\ & \mathrm{GM}: \frac{P_{0}}{\mathrm{EPS}_{1}}=7.19 \end{aligned}
Projected EPS 1 EPS 1 EPS_(1)\mathrm{EPS}_{1} for Fiat-Chrysler is 1.44, what is the value of their stock according to the comparables approach?
Fiat-Chrysler 的預測 EPS 1 EPS 1 EPS_(1)\mathrm{EPS}_{1} 為 1.44，根據可比方法，其股票價值為何？

Example Solution  解決方案範例

First find the average P / E P / E P//EP / E ratio
首先找出平均 P / E P / E P//EP / E 比率
1 2 ( 8.45 + 7.19 ) = 7.82 1 2 ( 8.45 + 7.19 ) = 7.82 (1)/(2)(8.45+7.19)=7.82\frac{1}{2}(8.45+7.19)=7.82
Then multiply that by the EPS for Fiat-Chrysler
然後再乘以 Fiat-Chrysler 的 EPS
P 0 = 7.82 × 1.44 = $ 11.26 P 0 = 7.82 × 1.44 = $ 11.26 P_(0)=7.82 xx1.44=$11.26P_{0}=7.82 \times 1.44=\$ 11.26
Note the actual price is $ 16.20 $ 16.20 $16.20\$ 16.20, what explains the difference?
請注意實際價格是 $ 16.20 $ 16.20 $16.20\$ 16.20 ，差異的原因為何？

Concept Check  概念檢查

Concept Check  概念檢查

Where does equity value come from?
股權價值從何而來？

Future dividends  未來股利

The Dividend Discount Model
股利折扣模式
  • One year holding period valuation
    一年持有期估值
  • Constant dividend growth
    股利持續成長
  • Interpretation of the P / E P / E P//E\mathrm{P} / \mathrm{E} ratio
    P / E P / E P//E\mathrm{P} / \mathrm{E} 比率的詮釋
  • Multi-stage growth model
    多階段成長模型
Valuation using comparable firms and valuation ratios
使用可比公司和估值比率進行估值