Chapter 9Stocks and Their Valuation

Topics Covered•Common and Preferred Stock Properties•Valuing Preferred Stocks•Valuing Common Stocks - the Dividend

Growth Model▫No growth▫Constant growth▫Non-constant or supernormal growth

•Valuing the Entire Corporation – Free Cash Flow Approach

•Stock Market Equilibrium

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Facts about common stock

•Represents ownership•Ownership implies control•Stockholders elect directors•Directors elect management•Management’s goal: Maximize the stock

price

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Preferred Stock Characteristics•Unlike common stock, no ownership interest•Second to debt holders on claim on

company’s assets in the event of bankruptcy.•Annual dividend yield as a percentage of par

value•Preferred dividends must be paid before

common dividends• If cumulative preferred, all missed past

dividends must be paid before common dividends can be paid.

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Intrinsic Value and Stock Price•Outside investors, corporate insiders,

and analysts use a variety of approaches to estimate a stock’s intrinsic value (P0).

•In equilibrium we assume that a stock’s price equals its intrinsic value.▫Outsiders estimate intrinsic value to

help determine which stocks are attractive to buy and/or sell.

▫Stocks with a price below (above) its intrinsic value are undervalued (overvalued).

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Preferred Stock Valuation•Promises to pay the same dividend year

after year forever, never matures.•A perpetuity.•VP = DP/rP

•Expected Return: rP = DP/P0

•Example: GM preferred stock has a $25 par value with a 8% dividend yield. What price would you pay if your required return is 7%?

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What do investors in common stock want?•Periodic cash flows: dividends, and…•To sell the stock in the future at a higher

price•Management to maximize their wealth

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Stock Valuation: Dividend Growth Model

Stock Value = PV of Future Expected Dividends

r

D

r

D

r

D

r

DP

1. . .

111 33

22

11

0

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Stock Valuation: Dividend Patterns•For Valuation: we will assume stocks fall

into one of the following dividend growth patterns.▫Constant growth rate in dividends▫Zero growth rate in dividends, like

preferred stock▫Variable (non-constant) growth rate in

dividends

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Stock Valuation Case Study: Doh! Doughnuts•We have found the following information

for Doh! Doughnuts:•current dividend = $2.00 = Div0

•The current T-bill rate is 5% and investors demand an 9% market risk premium.

•Doh!’s beta = 1.2.

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Analysts Estimates for Doh! Doughnuts•NEDFlanders predicts a constant annual

growth rate in dividends and earnings of zero percent (0%)

•Barton Kruston Simpson predicts a constant annual growth rate in dividends and earnings of 10 percent (9%).

•Homer Co. expects a dramatic growth phase of 30% annually for each of the next 3 years followed by a constant 10% growth rate in year 4 and beyond.

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Our Task: Valuation Estimates

•What should be each analyst’s estimated value of Doh! Doughnuts?

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Valuing Common Stocks: No Growth

If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY.

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Perpetuity PDiv

rorEPS

r 0

1 1

Assumes all earnings are paid to shareholders.

Ned Flanders’ Valuation

•D0 = $2.00, rS = 15.8% or 0.158, g = 0%

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Constant Growth Valuation Model•Assumes dividends will grow at a constant rate

(g) that is less than the required return (rS )• If dividends grow at a constant rate forever,

you can value stock as a growing perpetuity, denoting next year’s dividend as D1:

grgr

g

SS

DDP -=

-

)+1(= 10

0

15Commonly called the Gordon growth model

Barton Kruston Simpson’s Valuation•D0 = $2.00, g = 9%, rS = 15.8%

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Expected Return of Constant Growth Stocks•Expected Rate of Return = Expected

Dividend Yield + Expected Capital Gains Yield

•D1/P0 = Expected Dividend Yield•g = Expected Capital Gains Yield•r = (D1/P0) + g = (D0(1+g)/P0) + g

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Example

•Burns International’s stock sells for $80 and their expected dividend is $4. The market expects a return of 15%.

•What constant growth rate is the market expecting for Burns International?

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Variable Growth Stock Valuation•Framework: Assume Stock has period of

non-constant growth in dividends and earnings and then eventually settles into a normal constant growth pattern (gc).

0 g1 1 g2 2 g3 3 gc 4 gc 5 gc ...

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D1 D2 D3

Non-constant Growth Period Constant Growth

Today’s agenda

•Supernormal (non-constant) dividend growth valuation

•Corporate value approach to stock valuation

•Stock Market Equilibrium

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Homer Co. Valuation

•Variable (non-constant) growth•Years 1-3 expect 30% growth•After year 3: constant growth of 10%

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Variable Growth Valuation Process3 Step Process• Estimate Dividends during non-constant

growth period.• Estimate Price, which is the PV of the

constant growth dividends, at the end of non-constant growth period which is also the beginning of the constant growth period. This is called the horizon or terminal value.

• Find the PV of non-constant dividends and horizon value. The total of these PVs = Today’s estimated stock value.

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Back to Homer Co’s Valuation: Step 1•D0 = $2.00, g = 30% or 0.3 for next 3

years

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Homer Co’s Valuation: Step 2

•Find Horizon Value which is the constant growth stock value at the end of year 3.

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Homer Co’s Valuation: Step 3

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rs = 15.8%

g = 30% g = 30% g = 30% gc = 10%

2.245

2.521

56.495

$61.26 = P0

^

0 1 2 3 4

PV(CF) 2.600 3.380 4.394

...

+83.334 87.728

Corporate value model

•Also called the free cash flow method. Suggests the value of the entire firm equals the present value of the firm’s free cash flows.

•Remember, free cash flow is the firm’s after-tax operating income less the net capital investment▫FCF = NOPAT – Net capital investment

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Applying the corporate value model•Find the market value (MV) of the firm,

by finding the PV of the firm’s future FCFs at the company’s weighted average cost of capital, WACC.

•Subtract MV of firm’s debt and preferred stock to get MV of common stock.

•Divide MV of common stock by the number of shares outstanding to get intrinsic stock price (value).

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Issues regarding the corporate value model•Often preferred to the dividend growth

model, especially when considering number of firms that don’t pay dividends or when dividends are hard to forecast.

•Similar to dividend growth model, assumes at some point free cash flow will grow at a constant rate.

•Terminal value (TVN) represents value of firm at the point that growth becomes constant.

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An Example: Advanced Micro Devices (AMD)

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AMD

• AMD’s debt market value is $692 million.

• No preferred stock• 486 million shares outstanding• Current free cash flow is $286

million.

Assume that AMD will experience 21% year 1, 19% year 2 and 18% FCF growth in year 3 and 11% constant annual growth thereafter.

AMD’s WACC is approximately 17%.

An Example: AMD Projected FCFs($millions)

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End of Year Growth Status

Growth Rate (%)

FCF Calculation

1 Variable 21 $286(1.21) = $346.1

2 Variable 19 $346.1 x (1.19) = $411.8

3 Variable 18 $411.8 x (1.18) = $485.9

4 Constant 11 $485.9 x (1.11) = $539.4

Use non-constant growth to estimate AMD’s corporate value.

AMD’s FCF Corporate Valuation ($millions)

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WACC=17%

gc = 11%

TV0.11

8989.8 3

539.4

0.17

295.8

300.8

303.4

5613.0

6513.0 = Firm Value^

0 1 2 3 4

346.1 411.8 485.9

...

539.4

AMD’s Stock Value per share

•MV of firm = $6513 million•MV of debt = $692 million•MV of equity (stock) = $6513 - $692 =

$5821 million•486 million shares outstanding•P0 = MV of equity/shares = $5821/486 =

$11.98•Recent price = $13.50

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Stock Market Equilibrium

• In equilibrium, stock prices are stable and there is no general tendency for people to buy versus to sell.

• In equilibrium, two conditions hold:▫The current market stock price equals its

intrinsic value (P0 = P0).▫Expected returns must equal required returns.

)br(r r r g PD

r RFMRFs0

1^

s

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How is market equilibrium established?

•If price is below intrinsic value …

▫The current price (P0) is “too low” and offers a bargain.

▫Buy orders will be greater than sell orders.

▫P0 will be bid up until expected return equals required return.

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Doh! In equilibrium?

•Doh! Doughnuts current stock price is $30.

•Required return = 5% + 9%(1.2) = 15.8%•Let’s assume the 2nd analyst is correct

and Doh! Has a constant growth rate of 9% and its current dividend is $2.

•Is Doh! Doughnuts’ current stock price in equilibrium?

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Expected Return of Constant Growth Stocks• Expected Rate of Return = Expected Dividend

Yield + Expected Capital Gains Yield• D1/P0 = D0(1+g)/P0 = Expected Dividend Yield• g = Expected Capital Gains Yield• From our example, D1=$2(1.09) = $2.18,

P0=$30, g = 9% or 0.09

%3.17%10%3.7%930$

18.2$

0

1^

gP

Dr s

36DOH! Doh! Doughnuts

The Effect On the Stock Price

0%5%

10%15%20%

0 0.2 0.4 0.6 0.8 1 1.2 1.4

• Expected Return needs to fall to the required return of 15.8%. This means the stock price must rise to the equilibrium price that yields the required return of 15.8%

• New Price = D1/(rs- g)=$2.18/(.158 - .09)= $32.06

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Stock Valuation Summary•Looked at Dividend Discount Model:

Value = PV of future expected dividends. All else equal:▫Higher interest rates (rs) yields lower stock

prices (inverse relationship)▫Higher growth rate yields higher stock

price.•Other Stock Valuation Methods

▫“Multiples” Method: P/E, P/CF, P/S ▫For example: Price Estimate = PE Ratio x

expected EPS

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