Common Stock Valuation

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.

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:

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

T32 k1

D(T)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

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?

$515.42

0.081

$200

0.081

$200

0.081

$200V(0)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

32

32

Assume that the dividends will grow at a constant growth rate g. The dividend next period (t + 1) is:

For constant dividend growth, the DDM formula becomes:

g k if D(0) T V(0)

g k if k1

g11

gk

g)D(0)(1V(0)

T

g)(1g)(1D(0) g)(1 D(1) D(2) So,

g1tD1tD

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?

$243.86

1.08

1.101

.10.08

1.10$100V

g k if k1

g11

gk

g)D(0)(1V(0)

20

T

Assuming that the dividends will grow forever at a constant growth rate g.

For constant perpetual dividend growth, the DDM formula becomes:

k)g :(Important

gk

1D

gk

g10D0V

Think about the electric utility industry.

In 2009, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2.12.

Using D0 =$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.

What are the possible explanations for the difference?

$57.66

.02.05751.02$2.12

P0

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.

Return on Equity (ROE) = Net Income / Equity

Payout Ratio = Proportion of earnings paid out as dividends

Retention Ratio = Proportion of earnings retained for investment

Ratio) Payout - (1 ROE

Ratio Retention ROE Rate Growth eSustainabl

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:

Retention rate? Sustainable growth rate?

Payout ratio = $1.64 / $2.90 = .566 or 56.6%

So, retention ratio = 1 – .566 = .434 or 43.4%

Therefore, AEP’s sustainable growth rate = .10 .434 = .0434, or 4.34%

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.

What can we say about g and k in this example?

$121.36

.0434.0575

1.0434$1.64P

0

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: 2

2

T

1

T

1

1

1

gk

)g1)(0(D

k1

g1

k1

g11

gk

)g1)(0(D)0(V

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 MissMolly.com 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?

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.

$46.03.

$31.78 $14.25

0.040.10

0.04)$5.00(1

0.101

0.90

0.101

0.901

0.10)(0.10

)$5.00(0.90V(0)

gk

)gD(0)(1

k1

g1

k1

g11

gk

)gD(0)(1V(0)

55

2

2

T

1

T

1

1

1

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:

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) = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835

Year Total Dividend: (in $millions)

1 $5.00 x 1.30 = $6.50

2 $6.50 x 1.30 = $8.45

3 $8.45 x 1.30 = $10.985

Therefore, to determine the present value of the firm today, we need the present value of $120.835 and the present value of the dividends paid in the first 3 years:

million. $87.58

$69.93$6.36$5.87$5.42

0.201

$120.835

0.201

$10.985

0.201

$8.45

0.201

$6.50V(0)

k1

V(3)

k1

D(3)

k1

D(2)

k1

D(1)V(0)

332

332

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:

Discount rate = time value of money + risk premium

= U.S. T-bill rate + (stock beta x stock market risk premium)

T-bill rate: return on 90-day U.S. T-bills

Stock Beta: risk relative to an average stock

Stock Market Risk Premium: risk premium for an average stock

Constant Perpetual Growth Model:

Simple to compute

Not usable for firms that do not pay dividends

Not usable when g > k

Is sensitive to the choice of g and k

k and g may be difficult to estimate accurately.

Constant perpetual growth is often an unrealistic assumption.

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.

We have valued only companies that pay dividends.

But, there are many companies that do not pay dividends. What about them? It turns out that there is an elegant way to value these

companies, too.

The model is called the Residual Income Model (RIM).

Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends.

Inputs needed:

Earnings per share at time 0, EPS0 Book value per share at time 0, B0 Earnings growth rate, g Discount rate, k

There are two equivalent formulas for the Residual Income Model:

gk

gBEPSP

or

gk

kBg)(1EPSBP

010

0000

BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

National Beverage Corporation (FIZ)

It is July 1, 2005—shares are selling in the market for $7.98.

Using the RIM:

EPS0=$0.47 DIV = 0 B0=$4.271 g = 0.09 K = .103

What can we sayabout the marketprice of FIZ?

$9.84.$5.57$4.271P

.09.103

.103$4.271.09)(1$.47$4.271P

gk

kBg)(1EPSBP

0

0

0000

Using the information from the previous slide, what growth rate results in a FIZ price of $7.98?

8.42%. or .0842g

4.179g.3519

.0301.47g3.709g$.3820

.4399.47g.47g)(.103$3.709

g.103

.103$4.271g)(1$.47$4.271$7.98

gk

kBg)(1EPSBP 00

00

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)

Price-cash flow ratio (P/CF ratio)

Current stock price divided by current cash flow per share In this context, cash flow is usually taken to be net income

plus depreciation.

Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income.

Earnings and cash flows that are far from each other may be a signal of poor quality earnings.

Price-sales ratio (P/S ratio)

Current stock price divided by annual sales per share A high P/S ratio suggests high sales growth, while a low P/S

ratio suggests sluggish sales growth.

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 1.0 indicates that the firm is creating value for its stockholders.

Intel Corp (INTC) - Earnings (P/E) Analysis

5-year average P/E ratio 37.30Current EPS $1.16EPS growth rate 17.5%

Expected stock price = historical P/E ratio projected EPS

$50.84 = 37.30 ($1.16 1.175)

Mid-2005 stock price = $26.50

Intel Corp (INTC) - Cash Flow (P/CF) Analysis

5-year average P/CF ratio 19.75Current CFPS $1.94CFPS growth rate 13.50%

Expected stock price = historical P/CF ratio projected CFPS

$43.49 = 19.75 ($1.94 1.135)

Mid-2005 stock price = $26.50

Intel Corp (INTC) - Sales (P/S) Analysis

5-year average P/S ratio 6.77Current SPS $5.47SPS growth rate 10.50%

Expected stock price = historical P/S ratio projected SPS

$40.92 = 6.77 ($5.47 1.105)

Mid-2005 stock price = $26.50

The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.

Based on the CAPM, k = 3.1% + (.80 9%) = 10.3%

Retention ratio = 1 – $.66/$2.65 = .751

Sustainable g = .751 23% = 17.27%

Because g > k, the constant growth rate model cannot be used. (We would get a value of -$11.10 per share)

Let’s assume that “today” is January 1, 2005, g = 7%, and k = 10.3%.

Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below.

We use column one and our growth assumption for column three (CSR) of the table below.

2005 (time 0) 2006 (VL) 2006 (CSR)

Beginning BV per share NA 9.45 9.45

EPS 2.25 2.65 2.4075

DIV 0.66 0.66 1.7460

Ending BV per share 9.45 11.50 10.1115

1.072.25 1.079.45

9.45) - (10.1115-2.4075 Plug""

Using the CSR assumption:

Using Value Line numbers for EPS1=$2.65, B1=$11.50B0=$9.45; and using the actual change in book value instead of an estimate of the new book value, (i.e., B1-B0 is = B0 x k)

$52.91.P

.07.103

.103$9.45.07)(1$2.25$9.45P

gk

kBg)(1EPSBP

0

0

0000

$27.63P

.07.103

9.45)-($11.50$2.65$9.45P

gk

kBg)(1EPSBP

0

0

0000

Stock price at the time = $47.04.What can we say?

Quick calculations used: P/CF = P/E EPS/CFPS

P/S = P/E EPS/SPS

www.nyssa.org (the New York Society of Security Analysts)

www.aaii.com (the American Association of Individual Investors)

www.eva.com (Economic Value Added) www.valueline.com (the home of the Value Line

Investment Survey)

Websites for the companies analyzed in this chapter:• www.aep.com • www.americanexpress.com • www.pepsico.com • www.starbucks.com • www.sears.com • www.intel.com • www.disney.go.com • www.mcgraw-hill.com

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

The Two-Stage Dividend Growth Model

Discount Rates for Dividend Discount Models Observations on Dividend Discount Models

Residual Income Model (RIM)

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