lecture 7 equity valuation

8/7/2019 Lecture 7 Equity Valuation

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Business Valuation:

Equity Valuation


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Fundamental Stock Analysis:

Models of Equity Valuation Basic Types of Models

Balance Sheet Models

Dividend Discount Models

Price/Earning Ratios

Estimating Growth Rates and Opportunities


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Type of Equity Capital

Type of sharecapital

Security or votingright

Income Amount of capital

Ordinary shares

Have voting rightsin AGM.Rank after all

payables and

preference shares

in rights to assets

on liquidation

Dividends payablesat the discretion ofthe directors out of

undistributedprofits remaining

after senior claims

have been met.

Amounts availablefor dividends but

not paid out areretained in thecompany on behalf

of the ordinary

shareholders.

The right to allsurplus funds after

prior claims have

been met.


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Type of Equity Capital

Type of sharecapital

Security or votingright

Income Amount of capital

Non-cumulative

preference shares

Likely to have

some voting rights

at all times ratherthan in specified

circumstances as in

the case ofcumulative.

Rank as cumulative

in liquidation

A fixed amount per

year, as above.

Arrears do not

accumulate

A fixed amount per

share


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Balance Sheet Models

A common valuation measure is book value, whichis the net worth of a company as shown on thebalance sheet.

Book value cannot be a floor for the stock pricebecause there are always some firms selling theirstock below the book value.

A better measure is the firms liquidation value per

share. It is the amount that can be realized by selling the

assets of a firm and paying off the debt.


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Intrinsic Value and Market Price

Intrinsic Value

Self assigned Value

Variety of models are used for estimation

Market Price

Consensus value of all potential traders

Trading Signal

IV > MP Buy

IV < MP Sell or Short Sell

IV = MP Hold or Fairly Priced


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The return on a stock comprises cash dividends and capitalgain/losses

Example:

ABC stocks expected dividend per share (D1) is $4. Current price

(P0) is $48. Expected price at the end of year (P1) is $52

%7.16)r(E

48$

)48$52($4$)r(E

P

)PP(D)r(E

0

011

!

!

!


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According to CAPM, in equilibrium, if a stock ispriced correctly, its E(r) will equal the requiredreturn (k)

Assume Krf= 6%, (Km Krf) = 5% and = 1.20

%12K

%)`5(20.1%6K

!

!


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VD

k

o

t

tt

!!

g

( )11

V0 = Value of Stock

Dt = Dividend

k = required return

Dividend Discount Models:

General Model


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No Growth Model

VD

k

o !

Stocks that have earnings and dividends that areexpected to remain constant

Example: Preferred Stock


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Features of Preferred Stock

A hybrid security with both debt and equitycharacteristics.

Has priority over common stock in receipt ofdividends and in liquidation.

Dividends are fixed as a percentage of parvalue.

Only participating preferred stock (which israre) shares in the residual income with thecommon stockholders.


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Valuing Preferred Stock

V0 = Value of Preferred Stock

= PV ofALL dividends discounted at

investors Required Rate of Return

52 Weeks Yld Vol Net

Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg

s 42 29 QuakerOats OAT 1.14 3.3 24 5067 35 34 34 -s 36 25 RJR Nabisco RN .08p ... 12 6263 29 285/8 287/8 -

237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23 ...

7 5 RJR Nab pfC .60 9.4 ... 2248 6 6 63/8 -1/8

0 1 2 3 g

V0=23.75 D1=2.31 D2=2.31 D3=2.31 Dg=2.31

237

/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235

/8 23 ...


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V0 = + + +2.31

(1+ kp)2.31

(1+ kp)2

2.31(1+ kp)

3 g

52 Weeks Yld Vol Net

Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg


237

/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235

/8 23 ...7 5 RJR Nab pfC .60 9.4 ... 2248 6 6 63/8 -1/8

0 1 2 3 g

V0=23.75 D1=2.31 D2=2.31 D3=2.31 Dg=2.31

237

/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235

/8 23 ...


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V0 =Dk

=2.31.10

= $23.10

V0 = + + +2.31

(1+ kp)2.31

(1+ kp )2

2.31(1+ kp )

3 g

52 Weeks Yld Vol Net Hi Lo Stock Sym Div % PE 100s Hi Lo Close Chg


237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23 ...

7 5 RJR Nab pfC .60 9.4 ... 2248 6 6 63/8 -1/8

0 1 2 3 g

V0=23. =2.31 D2=2.31 D3=2.31 Dg=2.31

237/8 20 RJR Nab pfB 2.31 9.7 ... 966 24 235/8 23 ...


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VoD g

k g

o!

( )1

g = constant perpetual growth rate

Example: common stock

Constant Growth Model


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Characteristics of Common Stock

Dividends

Vary over time

Not guaranteed

Residual Claim

Voting Rights

Sometimes Preemptive Right to buy New

Stock


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Valuing Individual Shares of

Common StockV0 = PV ofALL expected dividends discounted at


Not like Preferred Stock since D0 = D1 = D2 = D3 = DN ,therefore the cash flows are no longer an annuity.Not like Preferred Stock since D0 = D1 = D2 = D3 = DN ,therefore the cash flows are no longer an annuity.

V0 = + + +gD1

(1+ ks )D2

(1+ ks )2

D3(1+ ks )

3

D1 D2 D3V0 Dg

0 1 2 3 g


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Valuing Individual Shares of

Common StockV0 = PV ofALL expected dividends discounted at


Investors donot know thevaluesofD1,D2,....,DN. Thefuture dividends mustbeestimated.

Investors donot know thevaluesofD1,D2,....,DN. Thefuture dividends mustbeestimated.

D1 D2 D3V0 Dg

0 1 2 3 g

V0 = + + +gD1

(1+ ks )D2

(1+ ks )2

D3(1+ ks )

3


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Requires

ks> g

Requires

ks> g

Reducesto:

V0 = + + ++D0 (1+ g)(1+ ks )

D0 (1+ g)2

(1+ ks )2

D0 (1+ g)3

(1+ ks )3 g

V0 = =D0(1+g)ks g

D1ks g

Assumethat dividends growataconstantrate (g).

D1=

D0 (

1+g)D0

D2=

D0 (

1+g)

2 D3=

D0 (

1+g)

3 Dg=

D0 (

1+g)

g

0 1 2 3 g


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Simplification of the Algebra

)1()k1()g1(

)k1()g1(

k1g1V

)k1(

)g1(V

)k1(

)g1(V

3

3

2

2

00

1tt

t

00

1tt

t

0

0

!

!

!

g

!

g

!

.


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00

2

2

00

D1g1

k1

)2(from)1(Subtract

)2(

)k1(

)g1(

k1

g11D

g1

k1

!

!

.


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gk

)g1(D

)g1(D)gk(

rearrange

)3(Dg1

gk

D)g1(

)g1()k1(

)2(equationrearrange,gkAssume

0

0

00

00

00

!

!

!

!

"


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P0 = = $30.501.14(1+.07)

.11 .07

What is the value of a share of common stock if themost recently paid dividend (D0) was $1.14 per share anddividends are expected to grow at a rate of 7%?Assume that you require a rate of return of 11%

on this investment.

P0 = =D0(1+g)ks g

D1ks g


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The Jackson Corporation has a required rate ofreturn of 16% and its current dividend is $3 pershare. if the current price of Jacksons stock is $55

per share, what is the growth rate of its dividend?

%10g

g3$3$g55$8.8$

)g1(3$)g%16(55$)g%16

)g1(3$55$

gk

)g1(DPV 0

00

!

!

!

!

!!


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The constant growth model is valid only wheng is less than k

The constant growth rate implies that a stock

value will be greater when: The expected dividend per share is larger

The market capitalization rate is lower

The expected growth rate of dividend is higher

The constant growth model assume that thestock price is expected to grow at the samerate as dividend.


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Example: ABC stocks expected dividend per share (D1) is $4.

Suppose that the stock is selling at its intrinsic value of$57.14. so that V0 = P0. The k is 12%

If the dividend is expected to grow at 5%, price should alsoincrease by 5%

14.57$ofpricecurrentthethan

higher%5iswhich

60$%5%12

20.4$

gk

D

P

20.4$)05.1(4$D

2

1

2

!

!

!

!!


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)g1(PP

g1

gk

DP

gk

)g1(D

gk

DP

01

1

1

12

1

!

!

!

!

If V0 = P0, then the expected rate of return equalsthe dividend yield plus the capital gain yield


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Stock Price and Investment

Opportunities No firm would grow in value if all earnings is

paid out as dividend (no earnings reinvestedin the firm)

A firm that retains or plowback some of itsearnings into highly profitable project canearn more rate of return to its shareholders.

A firm should reduce the dividend payoutratio to maintain a suitable plowback ratio (b).


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Life Cycle and Multistage Growth

Models In early year, payout ratios are low and

growth is correspondingly rapid.

In later years, the firm matures, so theydecide to increase the payout ratios. To valuecompanies with temporarily high growth,analysts use a multistage discount model

(Specified Holding Period Model)


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)1()1()1(

...2

2

1

1

0

k

PD

k

D

k

DV N

NN

!

PN = the expected sales price for the stock at time N

N = the specified number of years the stock isexpected to be held

Specified Holding Period Model


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Specified Holding Period Model: Example

1

ABC Company

Beta = 0.85, P0 = $32.50, Krf = 5%, g = 7%

Dividend 2005 = $1.25, Km Krf = 8%,

Year Dividend ($)2002 0.802003 0. 5200 1.10

2005 1.25


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Partitioning Value: Example 1

k = Krf+ (Km Krf)

= 5%+

0.85 (8%) = 11.8%

2001

V0 = ?

2002

$0.8

0

2003

$0.95

2004

$1.1

0

2005

$1.25


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865.27$%8.4

3375.1$P

%7%8.11

%)71(25.1P

gk)g1(DP

gk

DP

2005

2005

20052005

2006

2005

!!

!

!

!


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90.20V)8.111(

87.2725.1

)8.111(

10.1

)8.111(

95.0

)8.111(

80.0V

)k1()k1()k1()k1(V

2001

43212001

4

20052005

3

2004

2

2003

1

2002

2001

!

!

!

Since V0 = $20.90 is less than P0 = $32.50, thisstock is overvalued/overpriced. Overvalued stock isnot worth to buy.


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Investors require a 20 percent per year returnon the stock of Happy Corporation. YesterdayHappy Corporation paid a dividend of $2

(dividend are paid annually). The dividend isexpected to grow 30 percent per year for thenext two years and at 8 percent per yearthereafter. Assume that the stock is currentlyselling at $24 per share, should the investorsbuy the stock?


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In Example 1, the dividend for the respectiveyears have been given. In Example 2, weneed to determine the dividends for each

year first.D0 = $2 D1 D2 D3

D1 = 2 (1 + 30%) = 2.60

D2 = 2 (1 + 30%)2 = 3.38

D3 = 3.38 (1 + 8%) = 3.65


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Then, we can calculate the V0 for the stock at the

required rate of return of 20%.

D0 = $2 D1 D2 D3+ P2

64.25V

)201(

42.3038.3)201(

60.2V

)k1()k1(V

0

20

2221

0

!

!

!


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Since V0 = $25.64 is more than MP = $24,this stock is undervalued/underpriced.undervalued stock is worth to buy.


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Inflation and Equity Valuation

Inflation has an impact on equity valuations

Historical costs underestimate economiccosts

Empirical research shows that inflation hasan adverse effect on equity values

Research shows that real rates of return are lower

with high rates of inflation


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Potential Causes of Lower Equity

Values withInflation

Shocks cause expectation of lower earningsby market participants

Returns are viewed as being riskier withhigher rates of inflation

Real dividends are lower because of taxes

lecture 7 equity valuation

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