Chapter 13

Equity Valuation

Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

13-2

Fundamental Stock Analysis: Models of Equity Valuation

• Basic Types of Models– Balance Sheet Models– Dividend Discount Models– Price/Earnings Ratios– Free Cash Flow Models

13-3

Models of Equity Valuation

• Valuation models using comparables– Look at the relationship between price and various

determinants of value for similar firms

• The internet provides a convenient way to access firm data. Some examples are:– EDGAR Electronic Data-Gathering, Analysis, and Retrieval system

– Finance.yahoo.com– Factset, Reuters (Thompson), Bloomberg, etc

Aside) 10-K, 10-Q

13-4

Table 13.1 Microsoft Corporation Financial Highlights 2009

13-5

Valuation Methods

• Book value – Value of common equity on the balance sheet– Based on historical values of assets and

liabilities, which may not reflect current values– Some assets such as brand name or

specialized skills are not on a balance sheet

13-6

Valuation Methods

• Market value– Current market value of assets minus current

market value of liabilities• Market value of assets may be difficult to ascertain

– Market value based on stock price => basically, price rather than value

– Better measure than book value of the worth of the stock to the investor.

13-7

Valuation Methods (Other Measures)

• Liquidation value – Net amount realized from sale of assets and

paying off all debt

– Firm becomes a takeover target if market value stock falls below this amount, so liquidation value may serve as floor to value

13-8

Valuation Methods (Other Measures)

• Replacement cost – Replacement cost of the assets less the

liabilities

– May put a ceiling on market value in the long run because values above replacement cost will attract new entrants into the market.

– Tobin’s Q = Market Value / Replacement Cost; should tend toward 1 over time.

13-9

13.2 Intrinsic Value Versus Market Price

13-10

Expected Holding Period Return

1 1 0

0

( ) ( )Expected HPR= ( )

E D E P PE r

P

• The return on a stock investment comprises cash dividends and capital gains or losses

– Assuming a one-year holding period

13-11

Required Return• CAPM gave us required

return, call it k:• k = market capitalization

rate

• If the stock is priced correctly (EMH)– Required return should

equal expected return 1 1 0

0

( ) ( )Expected HPR= ( )

E D E P PE r

P

=

( )f M fk r E r r

13-12

Intrinsic Value

Intrinsic Value• The present value of a firm’s expected future net cash

flows discounted by an “appropriate” risk adjusted required rate of return (e.g., CAPM).

• The cash flows on a stock are?

– Dividends (Dt)

– Sale price (Pt)

• Intrinsic Value today (time 0) is denoted V0 and for a one year holding period may be found as:

k1

)P(E)D(EV 11

0

13-13

Intrinsic Value and Market Price

• Market Price– Consensus value of all traders– Given to small investors like you and me– In equilibrium, the current market price will

equal intrinsic value (EMH)

• Trading Signals– If V0 > P0

– If V0 < P0

– If V0 = P0

Buy for me. But then what happens?

Sell or Short Sell for me. But then?

Indifferent at it is fairly priced

13-14

Basic Dividend Discount Model

Intrinsic value of a stock can be found from the following:

What happened to the expected sale price in this formula?

• Why is this an infinite sum?• Is stock price independent of the investor’s

holding period?

1tt

t0 )k1(

DV

V0 = Intrinsic Value of Stock

Dt = Dividend in time t

k = required return

13-15

Basic Dividend Discount Model

Intrinsic value of a stock can be found from the following:

• This equation is not useable because it is an infinite sum of variable cash flows.

• Therefore we have to make assumptions about the dividends to make the model tractable.

1tt

t0 )k1(

DV

13-16

No Growth Model• Use: Stocks that have earnings and

dividends that are expected to remain constant over time (zero growth)

– Preferred Stock• A preferred stock pays a $2.00 per share dividend and

the stock has a required return of 10%. What is the most you should be willing to pay for the stock?

k

DV0

00.20$0.10

$2.00V0

13-17

Constant Growth Model• Use: Stocks that have earnings and dividends

that are expected to grow at a constant rate forever

• A common stock share just paid a $2.00 per share dividend and the stock has a required return of 10%. Dividends are expected to grow at 6% per year forever. What is the most you should be willing to pay for the stock?

dividendsin rategrowth perpetual;g-k

DV 1

0 g

00.53$0.06-0.10

1.06$2.00V0

13-18

Comparing Value and Returns• Why do you have to pay more for the

constant growth stock?– Must pay for expected growth

• What is the one year rate of return for each stock?

No Growth Stock

V0 = $20.00; D = $2.00

E(V1)=

%1020$

2$20$20$)(

ROIE

Constant Growth Stock

V0 = $53.00; D0 = $2.00

18.56$0.06-0.10

1.06$2.00)E(V

2

1

%1053$

12.2$53$18.56$)(

ROIE

$2.00 / 0.10 = $20.00

13-19

Comparing Value and Returns

• Both stocks give an investor a pre-tax return of 10%.

• Is one stock a better buy than the other?– Not if both are actually priced at their intrinsic

value (ignoring taxes).

13-20

Stock Prices and Investment Opportunities

• g = growth rate in dividends is a function of two variables:– ROE = Return on Equity for the firm

– b = plowback or retention percentage rate = (1- dividend payout percentage rate)

• g increases if a firm increases its retention ratio and/or its ROE

bROEg

13-21

Value of Growth Opportunities

Cash Cow, Inc.(CC)E1 = $5, ROE=12.5%

D1 = $5

b = ; therefore g =

k = 12.5% ; Find VCC

Growth Prospects(GP)E1 = $5, ROE=15%

D1 = $5

b =0; therefore g = 0

k = 12.5%, Find VGP

00

40$0.125

$5.00VCC 40$

0.125

$5.00VGP

Should either or both firms retain some earnings?

bROEg Value with 100% dividend payout

13-22

Value of Growth Opportunities

Cash Cow, Inc.(CC)

E1 = $5, ROE=12.5%

b = 60%; therefore g =

D1 = 0.40 x $5 = $2.00

k = 12.5%; Find VCC

CC value is the same, why?

Growth Prospects (GP)

E1 = $5, ROE=15%

b = 60%; therefore g = 9%

D1 = 0.40 x $5 = $2.00

k = 12.5%; Find VGP

GP Value has increased, why?

7.5%

40$0.075-0.125

$2.00VCC 14.57$

0.09 - 0.125

$2.00VGP

bROEg Value with 40% dividend payout

13-23

Value of Growth Opportunities

Value of assets in place for GP = $40.00 (value with all dividends paid out, with ROE = 12.5%)

Value of growth opportunities with ROE = 15% may be inferred from the difference between the new VGP = $57.14 and the no growth value of $40.00

Thus the present value of growth opportunities (PVGO) = $57.14 - $40.00 = $17.14

0 1(1 )

( )

D g EPVGO

k g k

In general:

13-24

Figure 13.1 Dividend Growth for Two Earnings Reinvestment

Policies

(for a given ROE)

High reinvestment increases stock price only if ROE > k

13-25

Multistage Growth Models

• As firms progress through their industry life cycle, earnings and dividend growth rates (ROE) are likely to change.

• A two stage growth model:

• g1 = first growth rate

• g2 = second growth rate

• T = number of periods of growth at g1

T2

2TT

1tt

t1

00 k))(1g(k

)g(1D

k)(1

)g(1DV

13-26

Multistage Growth Rate Model: Example

• D0 = $2.00 g1 = 20% g2 = 5% • k = 15% T = 3 • D1 = 2.40 D2 = 2.88 D3 = 3.46 D4 = 3.63

• V0 = 2.09 + 2.18 + 2.27 + 23.86 = $30.40

3320 )15.1)(05.015.0(

63.3$

15.1

46.3$

15.1

88.2$

15.1

40.2$V

13-27

Two Stage DDM for Honda

Dividends:

Assume the dividend growth rate will be steady beyond 2012. Value Line forecasts b = 70% and ROE of 11%. What should be the long term growth rate?

Year Dividend

2009 0.90

2010 0.98

2011 1.06

2012 1.15

bROEg %7.77.0%11 g

From Value Line

13-28

Two Stage DDM for Honda

The required rate of return:

Honda = 1.05

Rf in 2008 = 3.5%

Market risk premium=historical average of 8%

HondafMfHonda )RR(Rk %9.1105.1%8%5.3 Hondak

From Value Line

13-29

Two Stage DDM for Honda

k = 11.90%

g = 7.70%

Find the intrinsic value

Value Line reported the actual price = $21.37, so Honda was undervalued by $0.51 or about 2.4%.

44320 )119.1)(077.0119.0(

077.115.1$

119.1

15.1$

119.1

06.1$

119.1

98.0$

119.1

90.0$V

Year Dividend

2009 0.90

2010 0.98

2011 1.06

2012 1.15

88.21$V0

13-30

Two Stage DDM for HondaShould we trust the valuation result?

What if the beta is slightly incorrect, suppose it is 1.10 (< 5% error) rather than 1.05?

Now k = 12.3% and the intrinsic value estimate V0= $19.98, reversing our conclusion that Honda is undervalued

Recall that the actual price = $21.37

13-31

13.4 Price-Earnings (P/E) Ratios

13-32

P/E Ratio and Growth Opportunities

• P/E Ratios are a function of two factors– Required Rates of Return (k) (inverse relationship)– Expected Growth in Dividends (direct relationship)

• Uses– Estimate intrinsic value of stocks

• Conceptually equivalent to the constant growth DDM– Extensively used by analysts and investors

Aside) k = required r/r, discount rate, opportunity, can be given, or needs to be estimated. As k increases, the (present) value decreases.

13-33

P/E, ROE and Growth

With positive growth:

With zero growth:

If b = 0 then g should = 0 and the ratio simplifies to:

bROEg

gk

b

E

P

)1(

1

0

k

1

E

P

1

0

The P/E here is not the actual P/E you get with P0 and trailing EPS. The elements of the V0/E1 ratio here (theoretical P/E) are similar to the constant growth DDM.

13-34

Numerical Example: No Growth• E(E1)= $2.50 g = 0 k = 12.5%; Find P/E and

V0

• P/E = 1/k = 1/.125 = 8• V0 = P/E x E(E1)= 8 x $2.50 = $20.00 or

= $2.50/(.125-0)= $20.00

Then, the theoretical P/E= $20/$2.5= 8

• V0 = P/E x E(E1) is called P/E multiple. Typically, we use current industry P/E and projected E(EPS1) of the firm instead of this hypothetcal situation.

13-35

Numerical Example with Growth• b = 60% ROE = 15%; k = 12.5% (1-b) = 40%, E0 = $2.50

• Find the P/E and V0:

• g = ROE x b = 15% x 60% = 9%

• E(E1)= $2.50 (1.09) = $2.725, E(D1)=$2.725 (0.4) = $1.09

• P/E = (1 - 0.60) / (0.125 - 0.09) = 11.4

• V0 = P/E x E(E1)= 11.4 x $2.73 = $31.14 or

= $1.09/(.125 - .09) = $31.14

Then => the theoretical P/E = 31.14/2.725 = 11.4

• Again, V0 = P/E x E(E1) Is using data (current industry P/E from Yahoo Finance! and the projected E(E1) from I/B/E/S or pro forma I/S)

13-36

ROE and b and growth and P/E

13-37

P/E Ratios and Stock Risk

• Riskier firms will have higher required rates of return (higher values of k)

• Riskier stocks will have lower P/E multiples

gk

b

E

P

)1(

1

0

13-38

Pitfalls in Using Actual P/E1 Ratios• Not often, but E(EPS1) can be negative,• Earnings management is a serious problem,• E(EPS1) should be calculated using pro forma

earnings, or obtained from data services which provides analysts’ forecasts (I/B/E/S),

• A high P/E implies high expected growth, but not necessarily high stock returns,

• It assumes that the future P/E will be steady. If the expected growth in earnings fails to materialize, the P/E will fall and investors may incur (large) losses.

13-39

Figure 13.3 Actual P/E Ratios and Inflation

13-40

Figure 13.4 Earnings Growth for Two Companies

13-41

Figure 13.5 Price-Earnings Ratios

13-42

Figure 13.6 P/E Ratios

13-43

Other Comparative Valuation Ratios

• Price-to-book– High ratio indicates a large premium over book value,

and a ‘floor’ value that is often far below market price• Price-to-cash flow

– P/Cash Flow instead of P/E; less subject to accounting manipulation

• Price-to-sales– Useful for firms with low or negative earnings in early

growth stage• Be creative

13-44

Figure 13.7 Valuation Ratios for the S&P 500

13-45

Free Cash Flow Valuation Approach

• Capitalize or discount the free cash flow for the firm (FCFF) at the weighted-average cost of capital and then subtract the existing (market) value of debt– Useful for firms that don’t pay dividends, – Helpful to understand sources and uses of cash

– where:• EBIT = earnings before interest and taxes

• Tc = the corporate tax rate

• NWC = net working capital

NWCin IncreaseesExpenditur CapitalonDepreciati)TEBIT(1FCFF C

13-46

FCFF, Firm Value & Equity ValueThe free cash flow methods discount year to year cash flows plus some estimate of the terminal value PT where

WACC = Weighted average cost of capital

g = estimate of long run growth in free cash flow

T = time period when the firm approaches constant growth

Equity value =

gWACC

FCFFP 1T

T

TT

T

tt

t

WACC

P

WACC

FCFFValueFirm

)1()1(

1

Firm Value – Market Value of Debt

13-47

Free Cash Flow (cont.)• Another approach calculates the free cash flow

to the equity holders (FCFE) and discounts the cash flows directly at the cost of equity, kE.

• Equity value can then be estimated as:

Debt Net in Increase)TExpense(1 InterestFCFFFCFE C

gk

FCFEP

E

1TT

T

E

TT

1tt

E

t

)k1(

P

)k1(

FCFEValuequity E

13-48

FCF Valuation Example

13-49

Comparing the Valuation Models

• In theory free cash flow approaches should provide the same estimate of intrinsic value as the dividend growth model

• In practice the various approaches often differ substantially– Simplifying assumptions are used in all models– The models establish ranges of likely intrinsic value– Using multiple models forces rigorous thinking about the

inputs

13-50

13.6 The Aggregate Stock Market

13-51

Earnings Multiplier Approach

1. Forecast corporate profits for the coming period for an index such as the S&P 500.

2. Derive an estimate for the aggregate P/E ratio using long-term interest rates– Based on the relationship between the ‘earnings

yield’ or E/P ratio for the S&P 500 and the yield on 10 year Treasuries

3. Product of the two forecasts is the estimate of the end-of-period level of the market

13-52

Figure 13.8 Earnings Yield of the S&P 500 Versus 10-year Treasury Bond Yield

13-53

Earnings Multiplier Approach2009 Data: Starting S&P500 level = 900

Treasury yield = 3.2%

Implied Earnings Yield = 2.5% + 3.2% = 5.7%

If E/P = 5.7% then P/E = 1 / 0.057 = 17.54

If forecast EPS = $55 what is the expected forecast for the S&P500 one year later and the % gain or loss?

2.5% spreadTreasury yr10 – P500&S yieldEarnings Expected

7.2%900

900965turnExpectedRe

9655517.54P500&S 1

13-54

Table 13.4 S&P 500 Index Forecasts