Chapter #7 - Stock Valuation
7.1 – Common Stock Valuation
Our goal commonly used by financial analysts to assess the economic value of common stocks.
These methods are grouped into four categories:
Dividend discount models
Residual Income model
Free Cash Flow model
Price ratio models
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.
7.2 – The Dividend Discount Model
the fundamental principle of finance holds that the economic value of a security is properly measured by the sum
of its future cash flows, where the cash flows are adjusted for risk and the time value of money.
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 basic DDM equation is:
D1 D2 D3 DT
P0= 1+k + 2+ 3+ T
( ) (+k) ( 1+k) (1+k)
In the DDM equation:
P 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
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?
P = D1 + D2 + D3
0 (+k) (+k)2(1+k)
P0= $200 + $2002+ $2003=$515.42
(+0.0) (+0.) (1+0.0)
Constant Perpetual Growth
Constant Perpetual Growth Model – a version of the dividend discount model in which dividends grow forever at
a constant rate, and the growth rate is strictly less than the discount rate
Assuming that the dividends will grow forever at a constant growth rate
D0× (+g) D1
P0= k−g =k−g (Important: g< k)
The formula is not valid because the perpetual dividend growth rate greater than a discount rate implies an infinite
value since the present value of the dividends keeps getting bigger and bigger
Example: Constant Perpetual Growth Model
Think about the electric utility industry.
In 2009, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2.12.
Using 0 =$2.12, k = 5.75%, and g = 2%, calculate an estimated value for DTE.
Note: the actual mid-2009 stock price of DTE was $40.29
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? D (1+g) 1+gT
P0= 0 1− ÷
k −g 1+k
P0= .08−.101−1.08 =$243.86
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.
The Historical Average Growth Rate
Geometric Average Dividend Growth Rate – a dividend growth rate based on a geometric average of historical
Arithmetic Average Dividend Growth Rate – a dividend growth rate based on an arithmetic average of historical
Both have different results – geometric approach is preferred
Suppose the Broadway Joe Company paid the following dividends:
2005: $1.50 2008: $1.80
2006: $1.70 2009: $2.00
2007: $1.75 2010: $2.20
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric
Year: Dividend:Pct. Chg:
2010 $2.20 10.00%
2009 $2.00 11.11%
2008 $1.80 2.86% Grown at
2007 $1.75 2.94% Year: 7.96%:
2006 $1.70 13.33% 2005 $1.50
2005 $1.50 2006 $1.62
Arithmetic Aver8.05% 2008 $1.89
Geometric Avera7.96% 2010 $2.20
The Sustainable Growth Rate
Sustainable Growth Rate = ROE × Retention Ratio
= ROE × (1 - Payout Ratio)
Sustainable Growth Rate – a dividend growth rate that can be sustained by a company’s earnings
Limitation of the constant perpetual growth model is that it should be applied only to companies with stable
dividend and earnings growth
A company’s earnings can be paid out as dividends to its shareholders or kept as retained earnings
Retained Earnings – earnings retained within the firm to finance growth
Payout Ratio – proportion of earnings paid out as dividends
Retention ratio – proportion of earnings retained for reinvestment
Return on Equity (ROE) = Net Income / Equity
A common problem with SGR is that they are sensitive to year-to-year fluctuations in earnings
Security analysts routinely adjust SGR estimates to smooth out the effects of earnings variations
Example: Calculating and Using the Sustainable Growth Rate
In 2009, American Electric Power (AEP) had an ROE of 10%, projected earnings per share of $2.90, and a per-
share dividend of $1.64. What was AEP’s:
Sustainable growth rate?
Payout ratio = $1.64 / $2.90 = .566 or 56.6%
Retention ratio = 1 – .566 = .434 or 43.4% Therefore, AEP’s sustainable growth rate = .10 ´ .434 = .0434, or 4.34%
Example: Calculating and Using the Sustainable Growth Rate
What is the value of AEP stock using the perpetual growth model and a discount rate of 5.75%?
The actual late-2009 stock price of AEP was $31.83.
In this case, using the sustainable growth rate to value the stock gives a reasonably poor estimate.
To estimate a sustainable growth rate, you need the (relatively stable) dividend payout ratio and ROE.
Changes in sustainable growth rate likely stem from changes in ROE.
The DuPont formula separates ROE into three parts (profit margin, asset turnover, equity multiplier)
Net Income Net IncomeSales Assets
=ROE = × ×
Equity Sales Assets Equity
Managers can increase the sustainable growth rate by:
Decreasing the dividend payout ratio
Increasing profitability (Net Income / Sales)
Increasing asset efficiency (Sales / Assets)
Increasing debt (Assets / Equity)
7.3 - The Two-Stage Dividend Growth Model
The two-stage dividend growth model - assumes that a firm will initially grow at a rate g for T years, and
thereafter, it will grow at a 2ate g < k during a perpetual second stage of growth.
The Two-Stage Dividend Growth Model formula is:
D0(1+g1) 1+g 1 1+g1 D 01+g 2
P0= 1− ÷+ ÷
k−g1 1+k 1+k k−g 2
Using the Two-Stage Dividend Growth Model
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
Part 2 is the present value of all subsequent dividends.
Suppose MissMolly.com has a current dividend of
D0= $5, which is expected to shrink at the rate1 g = 10%, for 5 years but grow at the ra2e, g = 4%, forever.
With a discount rate of k = 10%, what is the present value of the stock?
D (1+g ) 1+g 1+g D (1+g )
P0= 0 1 − 1÷+ 1÷ 0 2
k−g1 1+k 1+k k−g2
P0= $5.00(0.9− 0.90 ÷+ 0.90÷ $5.00(1+0.04)
0.10−(−0.1) 1+0.10 1+0.10 0.10−0.04
= $14.25 + $31.78
The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present
value of all subsequent dividends.
Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth
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.?
First, calculate the total dividends over the “supernormal” growth period:
Yea Total Dividend: (in
1 $5.00 x 1.30 = $6.50
2 $6.50 x 1.30 = $8.45
3 $8.45 x 1.30 = $10.985 Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as:
P3= [D3x (1 + g)] / (k – g)
P3= [$10.985 x 1.10] / (0.20 – 0.10) = $120.835
To determine t