equity valuation prof. ian giddy new york university stern school of business

Equity Valuation

Prof. Ian GiddyNew York University

New York University

Stern School of Business

Copyright ©1998 Ian H. Giddy Equity Valuation 2

First Principles

Invest in projects that yield a return greater than the minimum acceptable hurdle rate.The hurdle rate should be higher for riskier projects and reflect the

financing mix used - owners’ funds (equity) or borrowed money (debt)

Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.

Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.

If there are not enough investments that earn the hurdle rate, return the cash to stockholders. The form of returns - dividends and stock buybacks - will depend

upon the stockholders’ characteristics.

Objective: Maximize the Value of the Firm


Discounted Cashflow Valuation: Basis for Approach

where, n = Life of the asset CFt = Cashflow in period t r = Discount rate reflecting the

riskiness of the estimated cashflows

Value = CFt

(1+ r)tt =1

t = n


Equity Valuation versus Firm Valuation

value just the equity stake in the business

value the entire firm, which includes, besides equity, the other claimholders in the firm


I.Equity Valuation

The value of equity is obtained by discounting expected cashflows to equity, i.e., the residual cashflows after meeting all expenses, tax obligations and interest and principal payments, at the cost of equity, i.e., the rate of return required by equity investors in the firm.

where,

CF to Equityt = Expected Cashflow to Equity in period t

ke = Cost of Equity The dividend discount model is a specialized case of equity

valuation, and the value of a stock is the present value of expected future dividends.

Value of Equity = CF to Equityt

(1+ ke )tt=1

t=n


II. Firm Valuation

The value of the firm is obtained by discounting expected cashflows to the firm, i.e., the residual cashflows after meeting all operating expenses and taxes, but prior to debt payments, at the weighted average cost of capital, which is the cost of the different components of financing used by the firm, weighted by their market value proportions.

where,

CF to Firmt = Expected Cashflow to Firm in period t

WACC = Weighted Average Cost of Capital

Value of Firm = CF to Firmt

(1+ WACC)tt=1

t=n


Equity versus Firm Valuation

It is often argued that equity valuation requires more assumptions than firm valuation, because cash flows to equity require explicit assumptions about changes in leverage whereas cash flows to the firm are pre-debt cash flows and do not require assumptions about leverage. Is this true?

Yes No


First Principle of Valuation

Never mix and match cash flows and discount rates.

The key error to avoid is mismatching cashflows and discount rates, since discounting cashflows to equity at the weighted average cost of capital will lead to an upwardly biased estimate of the value of equity, while discounting cashflows to the firm at the cost of equity will yield a downward biased estimate of the value of the firm.


Valuation: The Key Inputs

A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever.

Since we cannot estimate cash flows forever, we estimate cash flows for a “growth period” and then estimate a terminal value, to capture the value at the end of the period:

Value = CF

t

(1+ r)tt = 1

t =

Value = CFt

(1 + r)t

Terminal Value

(1 + r)N

t = 1

t = N


Stable Growth and Terminal Value

When a firm’s cash flows grow at a “constant” rate forever, the present value of those cash flows can be written as:Value = Expected Cash Flow Next Period / (r - g)

where,

r = Discount rate (Cost of Equity or Cost of Capital)

g = Expected growth rate This “constant” growth rate is called a stable growth rate and

cannot be higher than the growth rate of the economy in which the firm operates.

While companies can maintain high growth rates for extended periods, they will all approach “stable growth” at some point in time.

When they do approach stable growth, the valuation formula above can be used to estimate the “terminal value” of all cash flows beyond.


Growth Patterns

A key assumption in all discounted cash flow models is the period of high growth, and the pattern of growth during that period. In general, we can make one of three assumptions:there is no high growth, in which case the firm is already in stable

growththere will be high growth for a period, at the end of which the growth

rate will drop to the stable growth rate (2-stage)there will be high growth for a period, at the end of which the growth

rate will decline gradually to a stable growth rate(3-stage) The assumption of how long high growth will continue will

depend upon several factors including:the size of the firm (larger firm -> shorter high growth periods)current growth rate (if high -> longer high growth period)barriers to entry and differential advantages (if high -> longer growth

period)


Length of High Growth Period

Assume that you are analyzing two firms, both of which are enjoying high growth. The first firm is Earthlink Network, an internet service provider, which operates in an environment with few barriers to entry and extraordinary competition. The second firm is Biogen, a bio-technology firm which is enjoying growth from two drugs to which it owns patents for the next decade. Assuming that both firms are well managed, which of the two firms would you expect to have a longer high growth period?

Earthlink Network Biogen Both are well managed and should have the same high

growth period


Choosing a Growth Pattern: Examples

Company Valuation in Growth PeriodStable Growth

Disney Nominal U.S. $ 10 years 5%(long term Firm (3-stage) nominal growth rate

in the U.S. economy

Aracruz Real BR 5 years 5%: based upon Equity: FCFE (2-stage) expected long term

real growth rate for Brazilian economy

Deutsche Bank Nominal DM 0 years 5%: set equal to Equity: Dividends nominal growth rate in the world economy


The Building Blocks of Valuation

Choose aCash Flow Dividends

Expected Dividends to

Stockholders

Cashflows to Equity

Net Income

- (1- ) (Capital Exp. - Deprec’n)

- (1- ) Change in Work. Capital

= Free Cash flow to Equity (FCFE)

[ = Debt Ratio]

Cashflows to Firm

EBIT (1- tax rate)

- (Capital Exp. - Deprec’n)

- Change in Work. Capital

= Free Cash flow to Firm (FCFF)

& A Discount Rate Cost of Equity

Basis: The riskier the investment, the greater is the cost of equity.

Models:

CAPM: Riskfree Rate + Beta (Risk Premium)

APM: Riskfree Rate + Betaj (Risk Premiumj): n factors

Cost of Capital

WACC = ke ( E/ (D+E))

+ kd ( D/(D+E))

kd = Current Borrowing Rate (1-t)

E,D: Mkt Val of Equity and Debt

& a growth pattern

t

g

Stable Growth

g

Two-Stage Growth

|High Growth Stable

g

Three-Stage Growth

|High Growth StableTransition


Value is Not Price

What is Intrinsic Value?Self assigned ValueVariety of models are used for estimation

Market PriceWhat stock can be sold for or bought at

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

More, less, or same as market portfolio?


Value is Not Price

What is Intrinsic Value?Self assigned ValueVariety of models are used for estimation

Market PriceWhat stock can be sold for or bought at

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

More, less, or same as market portfolio?

When are a company’s shares undervalued?


Fundamental Stock Analysis: Models of Equity Valuation

Basic Types of ModelsBalance Sheet ModelsDividend Discount ModelsPrice/Earning Ratios

Estimating Growth Rates and Opportunities


Equity Valuation: From the Balance Sheet

Value of Assets Book Liquidation Replacement

Value of Liabilities

Book Market

Value of Equity


Equity Valuation: From the Balance Sheet

Value of Assets Book Liquidation Replacement

Value of Liabilities

Book Market

Value of Equity

Book ValueLiquidation

ValueReplacement

ValueTobin’s Q:

Market/Replacement tends to 1?


Dividend Discount Models:General Model

VD

ko

t

tt

( )11

VD

ko

t

tt

( )11

V0 = Value of Stock Dt = Dividend k = required return


Specified Holding Period Model

01

12

2

1 1 1V D

kD

kD P

kN N

N

( ) ( ) ( )...

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

N = the specified number of years the stock is expected to be held


No Growth Model

VD

ko

Stocks that have earnings and dividends that are expected to remain constant

Preferred Stock


No Growth Model: Example

E1 = D1 = $5.00

k = .15

V0 = $5.00 / .15 = $33.33

VD

ko


Constant Growth Model

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

g = constant perpetual growth rate


Constant Growth Model: Example

VoD g

k g

o

( )1Vo

D g

k g

o

( )1

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

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

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


Estimating Dividend Growth Rates

g ROE b g ROE b

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

i.e.(1- dividend payout percentage rate)


Shifting Growth Rate Model

V Dg

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2V D

g

k

D g

k g ko o

t

tt

TT

T

( )

( )

( )

( )( )

1

1

1

1

1

1

2

2

g1 = first growth rate

g2 = second growth rate

T = number of periods of growth at g1


Shifting 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 = 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


Partitioning Value: Growth and No Growth Components

VE

kPVGO

PVGOD g

k g

E

k

o

o

1

11( )

( )

VE

kPVGO

PVGOD g

k g

E

k

o

o

1

11( )

( )

PVGO = Present Value of Growth Opportunities

E1 = Earnings Per Share for period 1


Partitioning Value: Example

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

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

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


V

NGV

PVGO

o

o

3

15 0886

5

1533

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

V

NGV

PVGO

o

o

3

15 0886

5

1533

86 33 52

(. . )$42.

.$33.

$42. $33. $9.

Partitioning Value:: Example

Vo = value with growth

NGVo = no growth component value

PVGO = Present Value of Growth Opportunities


Price Earnings Ratios

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

UsesRelative valuationExtensive Use in industry


P/E Ratio: No expected growth

PE

kP

E k

01

0

1

1

PE

kP

E k

01

0

1

1

E1 - expected earnings for next yearE1 is equal to D1 under no growth

k - required rate of return


P/E Ratio with Constant Growth

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

PD

k g

E b

k b ROE

P

E

b

k b ROE

01 1

0

1

1

1

( )

( )

( )

Where b = retention ratio ROE = Return on Equity


Numerical Example: No Growth

E0 = $2.50 g = 0 k = 12.5%

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

PE = 1/k = 1/.125 = 8


Numerical Example with Growth

b = 60% ROE = 15% (1-b) = 40%

E1 = $2.50 (1 + (.6)(.15)) = $2.73

D1 = $2.73 (1-.6) = $1.09

k = 12.5% g = 9%

P0 = 1.09/(.125-.09) = $31.14

PE = 31.14/2.73 = 11.4

PE = (1 - .60) / (.125 - .09) = 11.4


Valuation and M&A

Rationale: Firm A should merge with Firm B if

[Value of AB > Value of A + Value of B + Cost of transaction]

Synergy Gain market power Discipline Taxes Financing


Goals of Acquisitions

Rationale: Firm A should merge with Firm B if

[Value of AB > Value of A + Value of B + Cost of transaction] Synergy

Eg Martell takeover by Seagrams to match name and inventory with marketing capabilities

Gain market power Eg Atlas merger with Varity. (Less important with open borders)

Discipline Eg Telmex takeover by France Telecom & Southwestern Bell

(Privatization) Eg RJR/Nabisco takeover by KKR (Hostile LBO)

Taxes Eg income smoothing, use accumulated tax losses, amortize goodwill

Financing Eg Korean groups acquire firms to give them better access to within-group

financing than they might get in Korea's undeveloped capital market


Value Changes In An Acquisition

175

250

75

5050

30 30

10

Final value ofcombined company

Initial valueplus gains

Financial structure improvements

Profit on saleof assets

Synergies and/or operatingimprovements

Value ofacquired company asa separateentity

Value ofacquiringcompanywithoutacquisition

Gain inshareholdervalue

Takeover premium & costs

Taxes on sale of assets10


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