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Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin
6
Common Stock Valuation
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Common Stock Valuation
Our goal in this chapter is to examine the methods commonly used by financial analysts to assess the economic value of common stocks.
These methods are grouped into two categories:
Dividend discount models
Price ratio models
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Security Analysis: Be Careful Out There
Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock.
The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell.
In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst (未必显现真实价格）.
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The Dividend Discount Model
The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The DDM equation is:
In the DDM equation:
V(0) = the present value of all future dividends
D(t) = the dividend to be paid t years from now
k = the appropriate risk-adjusted discount rate (市场预期收益）
D(1) is next year dividend.
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Example: The Dividend Discount Model
Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%.
In this case, what is the value of the stock today?
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The Dividend Discount Model:
the Constant Growth Rate Model
Assume that the dividends will grow at a constant growth rate g.
Then, the dividend next period (t + 1) is:
In this case, the DDM formula becomes:
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Example: The Constant Growth Rate Model
Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%.
What is the value of the stock, based on the constant growth rate model?
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The Dividend Discount Model:
the Constant Perpetual Growth Model.
Assuming that the dividends will grow forever at a constant growth rate g.
In this case, the DDM formula becomes:
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Example: Constant Perpetual Growth Model
Think about the electric utility industry.
In mid-2003, the dividend paid by the utility company, American Electric Power (AEP), was $.
Using D(0)=$, k = %, and g = %, calculate an estimated value for AEP.
Note: the actual mid-2003 stock price of AEP was $.
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The Dividend Discount Model:
Estimating the Growth Rate
The growth rate in dividends (g) can be estimated in a number of ways.
Using the company’s historical average growth rate.
Using an industry median or average growth rate.
Using the sustainable growth rate.
How could we get k? Yahoo, Finance
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The Historical Average Growth Rate
Suppose the Kiwi Company paid the following dividends:
1998: $ 2001: $
1999: $ 2002: $
2000: $ 2003: $
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.
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The Sustainable Growth Rate
Return on Equity (ROE) = Net Income / Equity
Payout Ratio (红利发放率) = Proportion of earnings paid out as dividends
Retention Ratio = Proportion of earnings retained for investment
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Example: Calculating and Using the
Sustainable Growth Rate
In 2003, AEP had an ROE of 10%, projected earnings per share of $, and a per-share dividend of $. What was AEP’s
Retention rate?
Sustainable growth rate?
Payout ratio = $ / $ = .636
So, retention ratio = 1 – .636 = .364 or %
Therefore, AEP’s sustainable growth rate = 10% .364 = %
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Example: Calculating and Using the
Sustainable Growth Rate, Cont.
What is the value of AEP stock, using the perpetual growth model, and a discount rate of %?
Recall the actual mid-2003 stock price of AEP was $.
It is important to note that dividend growth models do not capture severe uncertainty well.
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The Two-Stage Dividend Growth Model
You know the Value of T.
The two-stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years, and thereafter grow at a rate g2 < k during a perpetual second stage of growth.
The Two-Stage Dividend Growth Model formula is:
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Using the Two-Stage
Dividend Growth Model, I.
Although the formula looks complicated, think of it as two parts:
Part 1 is the present value of the first T dividends (it is the same formula we used for the constant growth model).
Part 2 is the present value of all subsequent dividends.
So, suppose has a current dividend of D(0) = $5, which is expected to “shrink” at the rate g1 = -10% for 5 years, but grow at the rate g2 = 4% forever.
With a discount rate of k = 10%, what is the present value of the stock?
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Using the Two-Stage
Dividend Growth Model, II.
The total value of $ is the sum of a $ present value of the first five dividends, plus a $ present value of all subsequent dividends.
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Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, I.
Value a Firm
Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year.
You believe that this rate will last for only three more years.
Then, you think the rate will drop to 10% per year.
Total dividends just paid were $5 Million.
The required rate of return is 20%.
What is the total value of Chain Reaction, Inc.?
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Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, II.
First, calculate the total dividends over the “supernormal” growth period:
Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as:
V(3) = [D(3) x (1 + g)] / (k – g)
V(3) = [$ x ] / ( – ) = $
Year
Total Dividend: (in $millions)
1
$ x = $
2
$ x = $
3
$ x = $
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Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth, III.
Therefore, to determine the present value of the firm today, we need the present value of $ and the present value of the dividends paid in the first 3 years:
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Discount Rates for
Dividend Discount Models
The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ).
We will discuss the CAPM in a later chapter.
However, we can estimate the discount rate for a stock using this formula(How to calculate the Value of k) :
Discount rate = time value of money + risk premium
= . T-bill rate + (stock beta x stock market risk premium)
T-bill rate:
return on 90-day . T-bills
Stock Beta:
risk relative to an average stock
Stock Market Risk Premium:
risk premium for an average stock
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Based on the CAPM, next five year k = %
If T-bill = 2%
k = 2% + ( %) = %
We should use % to forecast.
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Observations on Dividend
Discount Models, I.
Constant Perpetual Growth Model:
Simple to compute
Not usable for firms that do not pay dividends
Is sensitive to the choice of g and k
(容易受到 k和 g选择的影响）
k and g may be difficult to estimate（估计）accurately.
Constant perpetual growth is often an unrealistic（不切实际的）assumption.
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Observations on Dividend
Discount Models, II.
Two-Stage Dividend Growth Model:
More realistic in that it accounts for two stages of growth
Usable when g > k in the first stage
Not usable for firms that do not pay dividends
Is sensitive to the choice of g and k
k and g may be difficult to estimate accurately.
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Price Ratio Analysis, I.
(1) Price-earnings ratio (P/E ratio)
Current stock price divided by annual earnings per share (EPS)
Earnings yield
Inverse of the P/E ratio: earnings divided by price (E/P)
High-P/E stocks are often referred to as growth stocks, while low-P/E stocks are often referred to as value stocks.
Expected stock price = historical P/E ratio Current EPS （1+ projected EPS growth rate ）
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Price/Earnings Analysis, Intel Corp.
Expected stock price =
historical P/E ratio Current EPS （1+ projected EPS growth rate ）
Intel Corp (INTC) - Earnings (P/E) Analysis
Current EPS $
5-year average P/E ratio
EPS growth rate %
$ = ($ )
Early-2003 stock price = $
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Price Ratio Analysis, II.
(2) Price-cash flow ratio (P/CF ratio)
Current stock price divided by current cash flow per share (CFPS)
In this context, cash flow is usually taken to be net income plus depreciation（折旧）.
Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income.
Earnings and cash flow that are far from each other may be a signal of poor quality earnings.（信用卡消费）
Expected stock price = historical average P/CF ratio CFPS （1+ projected CFPS growth rate）
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Price/Cash Flow Analysis, Intel Corp.
Expected stock price =
historical P/CF ratio CFPS （1+ projected CFPS growth rate）
Intel Corp (INTC) - Cash Flow (P/CF) Analysis
Current CFPS $
5-year average P/CF ratio
CFPS growth rate %
$ = ($ )
Early-2003 stock price = $
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Price Ratio Analysis, III.
(3) Price-sales ratio (P/S ratio)
Current stock price divided by annual sales per share（SPS）
A high P/S ratio suggests high sales growth, while a low P/S ratio suggests sluggish sales growth.
Expected stock price =
historical Average P/S ratio SPS (1+ projected SPS growth rate)
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Price/Sales Analysis, Intel Corp.
Expected stock price =
historical Average P/S ratio SPS （1+ projected SPS growth rate）
Intel Corp (INTC) - Sales (P/S) Analysis
Current SPS $
5-year average P/S ratio
SPS growth rate %
$ = ($ )
Early-2003 stock price = $
(4) Price-book ratio (P/B ratio)
Market value of a company’s common stock divided by its book (accounting) value of equity
A ratio bigger than indicates that the firm is creating value for its stockholders.
book (accounting) value of equity: 股票账面价值又称股票净值或每股净资产，是每股股票所代表的实际资产的价值。每股账面价值是以公司净资产减去优先股账面价值后，除以发行在外的普通股票的股数求得的。
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An Analysis of the
McGraw-Hill Company
The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.
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The McGraw-Hill Company Analysis, I.
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The McGraw-Hill Company Analysis, II.
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The McGraw-Hill Company Analysis, III.
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The McGraw-Hill Company Analysis, IV.
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The McGraw-Hill Company Analysis, V.
Based on the CAPM, k = 1% + (.80 9%) = %
Retention ratio = 1 – $ = %
Sustainable g = .6625 26% = %
Because g > k, the constant growth rate model cannot be used. (We would get a value of -$ per share)
However, using a growth rate of % is not realistic.
Using the actual dividend growth rate of % (over the last 10 years), yields a stock price of $.
Recent price in Value Line: $
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The McGraw-Hill Company Analysis, VII.
Recent price in Value Line: $
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Useful Internet Sites
(the New York Society of Security Analysts)
(the American Association of Individual Investors)
(the Association for Investment Management and Research)
(the home of the Value Line Investment Survey)
Websites for the companies analyzed in this chapter:
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Chapter Review, I.
Security Analysis: Be Careful Out There
The Dividend Discount Model
Constant Dividend Growth Rate Model
Constant Perpetual Growth
Applications of the Constant Perpetual Growth Model
The Sustainable Growth Rate
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Chapter Review, II.
The Two-Stage Dividend Growth Model
Discount Rates for Dividend Discount Models
Observations on Dividend Discount Models
Price Ratio Analysis
Price-Earnings Ratios
Price-Cash Flow Ratios
Price-Sales Ratios
Price-Book Ratios
Applications of Price Ratio Analysis
An Analysis of the McGraw-Hill Company
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Note: the % comes from a rule of thumb for the electric utility industry of adding 2% to the current 20-year . T-bond yield. At the time of this writing, that yield was about %. Although AEP has not increased its dividend since 1993, it would still be pessimistic to assume that AEP would never increase its dividend.
