Equity Valuation

15.1 VALUATION BY COMPARABLES

Basic Types of Models◦ Balance Sheet Models◦ Dividend Discount Models◦ Price/Earnings Ratios

Valuation models use comparables◦ Look at the relationship between price and

various determinants of value for similar firms

Book value ◦ Based on historical values◦ Not the floor

Can book value represent a floor value? Better approaches

◦Liquidation value If below, attractive

◦Replacement cost Tobin’s q (ratio of market price to replacement cost)

14.2 INTRINSIC VALUE VERSUS MARKET PRICE

• Example (1-year horizon), whether the price today is attractively priced given your forecast of next year’s price and dividend

• Rf=6%, beta=1.2 Rm=11%

0 1 148, 52, 4P E P E D

compare expected HPR and required return expected HPR

◦ The return on a stock investment comprises cash dividends and capital gains or losses Assuming a one-year holding period 1 1 0

0

( ) ( )Expected HPR= ( )

E D E P PE r

P

16.7%E r

required return CAPM gave us required return:

If the stock is priced correctly◦ Required return should equal expected

return

( )f M fk r E r r

6% 1.2*5% 12%k

Intrinsic value ◦ The present value of all cash payments

to the investor, including dividends and proceeds from the ultimate sale of the stock, discounted at the appropriate risk-adjusted interest rate, k

Example:

50>48, undervalued

0V

1 10

52 450

1 1 12%

E D E PV

k

Market Price◦ Consensus value of all potential traders◦ Current market price will reflect intrinsic value

estimates◦ This consensus value of the required rate of

return, k, is the market capitalization rate Trading Signal

◦ IV > MP Buy◦ IV < MP Sell or Short Sell◦ IV = MP Hold or Fairly Priced

14.3 DIVIDEND DISCOUNT MODELS

1 10 1

D PV

k

2 21 1

D PP

k

1 2 20 2

1 2 20 2

1 1

1 1 1H H

H

D D PV

k k

D D P D PV

k k k

DDM◦ Stock price should equal the present value

of all expected future dividends into perpetuity

VDk

ot

tt

( )11

VDk

ot

tt

( )11

V0 = Value of StockDt = Dividendk = required return

Constant Growth Model ◦Assuming dividends are trending upward at a stable growth rate g

g = constant perpetual growth rate

VoD g

k g

o

( )1

Constant growth DDM

A Stock’s price will be greater ◦Larger its expected dividend per share

◦Lower k◦Higher g

0 10

1D g DP

k g k g

Stock price is expected to grow at the same rate as dividends

If market price equals its intrinsic value, expected HPR will be equal to required return

121 0

11

D gDP P g

k g k g

1 01 1

0 0 0

P PD DE r g k

P P P

VoD g

k g

o

( )1

E1 = $5.00 b = 40% k = 15%

(1-b) = 60% D1 = $3.00 g = 8%

V0 = 3.00 / (.15 - .08) = $42.86

VD

ko

g=0

Stocks that have earnings and dividends that are expected to remain constant◦ Preferred Stock

VoD g

k g

o

( )1

E1 = D1 = $5.00

k = 12.5%V0 = $5.00 / .125 = $40

VD

ko

Consider two companies◦ Cash Cow, Inc◦ Growth Prospects

k=12.5% IF pay out all as dividends (payout ratio =100%),

perpetual dividend=5 Both valued at 5/12.5%=40, neither firm will grow in

value GP, project’s ROE=15%, what should be GP’s dividend

policy ? investment=$100 million, 3 million shares outstanding,

expected earnings in coming year (EPS)=$100*15%/3= $5

Suppose, Growth Prospects lower payout ratio (40%) Earnings retention ratio b=1-40%=60% Total earning=$100*15%=$15 million Reinvestment=$15*60%=$9 million (capital increase

9/100=9%) 9% more capital, 9% more income, 9% higher dividend

Low-reinvestment-rate plan, pay higher initial dividends, but result in a lower dividend growth rate

High-reinvestment-rate, lower initial dividends, but result in higher dividend growth

g ROE b

g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate

= (1- dividend payout percentage rate)

g=15%*60%=9%

The project’s ROE >required rate (the project has positive NPV), reduce dividend payout ratio and reinvest in the positive NPV project.

The firm’s value rises by the NPV of the project PVGO: net present value of growth opportunities

10

5*40%57.14

12.5% 9%

DP

k g

Value of the firm rises by the NPV of the investment opportunities

Price = No-growth value per share (NGV) +present value of growth opportunities (PVGO)

PVGO=57.14-40=17.14 Where: E1 = Earnings Per Share for period 1

and

10

EP PVGO

k

0 1(1 )

( )

D g EPVGO

k g k

Growth enhance company value only if it is achieved by investment in projects with attractive profit opportunities (ROE>k)

If the project’s ROE=12.5%=k, lower the dividend payout ratio (40%)

Then stock price=?

g= ROE*b=12.5%*60%=7.5%

No different from no-growth strategy To justify reinvestment, the firm must

engage in projects with better prospective returns than those shareholders can find elsewhere

If ROE=k, no advantage to reinvestment

10

5*40%40

12.5% 7.5%

DP

k g

ROE = 20% d = 60% b = 40%

E1 = $5.00 D1 = $3.00 k = 15%

g = .20 x .40 = .08 or 8%

P

NGV

PVGO

o

o

3

15 0886

5

1533

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

Partitioning Value: ExamplePartitioning Value: Example

PPoo = price with growth = price with growth

NGVNGVoo = no growth component value = no growth component value

PVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities

Constant-growth DDM◦ Assume dividend growth rate be constant

In fact, different dividend profiles in different phases◦ In early years, high return, high reinvestment,

high growth◦ In later years, low return, low reinvestment, low

growth, as mature companies Multistage version of DDM

P Dg

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

11

1

2

2

g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1

D0 = $2.00 g1 = 20% g2 = 5% k = 15% T = 3 D1 =2*1.2= 2.40 D2 = 2.4*1.2=2.88 D3 =2.88*1.2= 3.46 D4 =3.46*1.05= 3.63 V0 = D1/(1.15) + D2/(1.15)2 + D3/(1.15)3 +

D4 / (.15 - .05) ( (1.15)3

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

14.4 PRICE-EARNINGS RATIOS

Used to assess the valuation of one firm versus another based on a fundamental indicator such as earnings.

Price-to-earnings multiple Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio

P/E Ratios are a function of two factors◦ Required Rates of Return (k)◦ Expected growth in Dividends

Uses◦ Relative valuation◦ Extensive use in industry

Useful indicator of expectations of growth opportunities

Ratio of PVGO/(E/k), component of firm value due to growth opportunities to the component of value due to assets already in place

High P/E ratio indicates ample growth opportunities◦ GROWTH PROSPECT, 57.14/5=11.4◦ CASH COW, 40/5=8

0

1

11

P PVGOEE kk

Investor may well pay a higher price per dollar of current earnings if he or she expects that earnings stream to grow more rapidly

P/E ratio a reflection of the market’s optimism concerning a firm’s growth prospects, but whether they are more of less optimistic than the market ?

PE

kP

E k

01

0

1

1

E1 - expected earnings for next year◦ E1 is equal to D1 under no growth

k - required rate of return

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

b = retention rationROE = Return on Equity

Higher ROE, higher P/E Higher b, higher P/E, only if ROE>k

E0 = $2.50 k = 12.5%, ROE=15%,

No growth: g=0 P/E=?With growth: payout ratio=40%,

P/E=?

E0 = $2.50 g = 0 k = 12.5%

P0 = D/k = $2.50/.125 = $20.00

P/E = 1/k = 1/.125 = 8

b = 60% ROE = 15% (1-b) = 40%g = (.6)(.15)= 9%E1 = $2.50 (1 +9%) = $2.73D1 = $2.73 (1-.6) = $1.09k = 12.5% g = 9%P0 = 1.09/(.125-.09) = $31.14P/E = 31.14/2.73 = 11.4P/E = (1 - .60) / (.125 - .09) = 11.4

Holding all else equal◦Riskier stocks will have lower P/E multiples

◦Higher values of k; therefore, the P/E multiple will be lower

1P b

E k g

Use of accounting earnings◦ Influenced by somewhat arbitrary accounting rules , use

of historical cost in depreciation and inventory valuation (earnings management)

Inflation◦ P/E ratio have tended to be lower when inflation has been

higher ◦ Market’s assessment that earnings in these periods are of

lower quality Reported earnings fluctuate around the business cycle No way to say P/E is overly high or low without referring to

the company’s long-run growth and current EPS relative to the long-run trend line

Price-to-book ratio Price-to-cash-flow ratio Price-to-sales ratio Creative: price-to-hits ratio for retail

internet firms

14.5 FREE CASH FLOW VALUATION APPROACHES

Discount the free cash flow for the firm

Discount rate is the firm’s cost of capital

Components of free cash flow◦After tax EBIT◦Depreciation◦Capital expenditures◦Increase in net working capital

discount FCFF at the weighted-average cost of capital , Subtract existing value of debtFCFF = EBIT (1- tc) + Depreciation – Capital

expenditures – Increase in NWC where:

EBIT = earnings before interest and taxestc = the corporate tax rate

NWC = net working capital

Another approach focuses on the free cash flow to the equity holders (FCFE) and discounts the cash flows directly at the cost of equity

FCFE = FCFF – Interest expense (1- tc) + Increases in net debt

Free cash flow approach should provide same estimate of IV as the dividend growth model

In practice the two approaches may differ substantially◦ Simplifying assumptions are used