CHAPTER 9

STOCK VALUATION

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KEY CONCEPTS AND SKILLS

• Understand how stock prices depend on

future dividends and dividend growth
• Be able to compute stock prices using the
dividend growth model
• Understand valuation comparables
• Understand the basics of the stock market

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 CHAPTER OUTLINE

9.1 The Present Value of Common Stocks

9.2 Estimates of Parameters in the Dividend Discount Model
9.3 Comparable
9.4 Valuing Stocks Using Free Cash Flows
9.5 The Stock Markets

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THE PRESENT VALUE OF COMMON
STOCKS

• The value of any asset is the present value of its expected

future cash flows.
• Stock ownership produces cash flows from:
• Dividends
• Capital Gains

• Valuation of Different Types of Stocks

• Zero Growth
• Constant Growth
• Differential Growth

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 EXAMPLE 1

In this dividend discount model example, assume that you are considering
the purchase of a stock which will pay dividends of $20 (Dividend 1) next
year and $21.6 (Dividend 2) the following year. After receiving the second
dividend, you plan on selling the stock for $333.3. What is the intrinsic value
of this stock if your required return is 15%? 

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 DDM

• DDM stands for Dividend Discount Model.

• It is a valuation method used to estimate the intrinsic value
of a stock based on the present value of the expected future
dividends.
• The model assumes that the stock's value is equal to the
present value of all future dividends it is expected to pay,
discounted back to their present value using a discount rate.

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 CASE 1: ZERO GROWTH

• Assume that dividends will remain at the same level

forever

· Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:

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9-7
 EXAMPLE 2

• If a preferred share of stock pays dividends of $1.80 per

year, and the required rate of return for the stock is 8%, then
what is its intrinsic value?
• 1.80/8%

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 CASE 2: CONSTANT GROWTH

Assume that dividends will grow at a constant rate, g,

forever, i.e.,

Since future cash flows grow at a constant rate forever,

the value of a constant growth stock is the present value
of a growing perpetuity:

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 CONSTANT GROWTH
EXAMPLE

• Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase

its dividend by 2% per year. If the market requires a return of 15% on
assets of this risk level, how much should the stock be selling for?
• P0 = .50(1 + .02) / (.15 – .02) = $3.92

• Self Learn: If a stock pays a $4 dividend this year, and the dividend
has been growing 6% annually, what will be the stock’s intrinsic value,
assuming a required rate of return of 12%?

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VARIABLE-GROWTH RATE DDM MODEL (MULTI-
STAGE DIVIDEND DISCOUNT MODEL)

• The variable-growth rate dividend discount model or DDM

Model is much closer to reality than the other two types of
dividend discount models. This model solves the problems
related to unsteady dividends by assuming that the company
will experience different growth phases.
1. An initial high rate of growth.
2. A transition to slower growth.
3. A sustainable, steady rate of growth.

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 TWO-STAGE DDM
(TWO GROWTH RATES)
• This model is designed to value the equity in a firm with
two stages of growth, an initial period of higher growth and
a subsequent period of stable growth.
• Check Mate forecasts that its dividend will grow at 20%
per year for the next four years before settling down at a
constant 8% forever. Dividend (current year,2016) =
$12; expected rate of return = 15%. What is the value of
the stock now?

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THREE STAGE DIVIDEND DISCOUNT MODEL
DDM

One improvement that we can make to the two-stage DDM model is to

allow the growth rate to change slowly rather than instantaneously.
The three-stage dividend discount model or DDM model is given by: –
• First phase: There is a constant dividend growth (g1) or with no
dividend.
• Second phase: There is a gradual dividend decline to the final level.
• Third phase: There is a constant dividend growth again (g3), i.e., the
growth company opportunities are over.

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 A DIFFERENTIAL GROWTH
EXAMPLE
• Find the Value of company which has declared Rs. 12 per share as annual
dividend this year. The dividend is expected to grow at an annual growth
rate of 10% each year for the next three years, followed by 12% for the
next four years and then grow by 6% after that till perpetuity.

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9-14
 ESTIMATES OF PARAMETERS IN THE
DIVIDEND DISCOUNT MODEL

• The value of a firm depends upon its growth rate, g, and its discount rate, R.

• Where does g come from? g = Retention ratio × Return on retained earnings.

• Page master Enterprises just reported earnings of $2 million. The firm plans that
60 percent of earnings will be paid out as dividends. The ratio of dividends to
earnings is often called the payout ratio, so the payout ratio for Page master is
60 percent. The historical return on equity (ROE) has been .16, a figure expected
to continue into the future. How much will earnings grow over the coming year?

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9-15
 WHERE DOES R COME FROM?

• The required rate of return (RRR) is the minimum return an investor will accept for
owning a company's stock, as compensation for a given level of risk associated with
holding the stock.
• The discount rate can be broken into two parts.
• The dividend yield.
• The growth rate (in dividends).

• In practice, there is a great deal of estimation error involved in estimating R.

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9-16
 USING THE DGM TO FIND R

• Start with the DGM:

Rearrange and solve for R:

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9-17
 COMPARABLES

• Comparable company analysis (or “comps” for short) is a valuation

methodology that looks at ratios of similar public companies and uses them to
derive the value of another business. Comps is a relative form of valuation,

• Common multiples include:

• Price-Earnings Ratios
• Enterprise Value Ratios

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9-18
 PRICE-EARNINGS RATIO

• The price-earnings ratio is calculated as the current stock price

divided by annual EPS.
• The Wall Street Journal uses last four quarters’ earnings

Price per share

P/E ratio 
EPS
• For example, if the stock of Sun Aerodynamic Systems (SAS) is selling at $27.00 per
share and its earnings per share over the last year was $4.50, SAS’s PE ratio would be 6.

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 PE RATIO EXAMPLE

Stock Valuation and PE Ramsay Corp. currently has an EPS of $3.10, and
the benchmark for the company is 21. Earnings are expected to grow at 6
percent per year.
• a. What is your estimate of the current stock price?
• b. What is the target stock price in one year?
• c. Assuming the company pays no dividends, what is the implied return
on the company’s stock over the next year? What does this tell you about
the implicit stock return using PE valuation?

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 ENTERPRISE VALUE RATIOS

• The PE ratio focuses on equity, but what if we want the value of

the firm?
• Use enterprise value:
• EV = market value of equity + market value of debt – cash

• Like PE, we compare the value to a measure of earnings. From a

firm level, this is EBITDA, or earnings before interest, taxes,
depreciation, and amortization.
• EBITDA represents a measure of total firm cash flow

• The Enterprise Value Ratio = EV / EBITDA

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 The EV to EBITDA ratio is 5
( 1 billion/200 million).

 As with PE ratios, it is generally assumed that similar firms have similar EV

to EBITDA ratios.

 Companies in the same industry may differ by leverage, i.e., the ratio of debt
to equity.

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 MARKET AND LIMIT ORDERS

• Market orders:
• You specify ticker and quantity
• Immediate execution at best available price
• Market buy will be executed at lowest ask
• Market sell will be executed at highest bid
• Limit orders:
• You specify ticker, quantity, and price
• The order will be executed only if trade can be made at the limit price or better
• Limit buy can only be executed at limit price or lower
• Limit sell can only be executed at limit price or higher
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 SELF LEARNING

• Free Cashflow in Valuation.

• BMC Certification (ICA)
• Next Class Quiz 10 Marks.

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