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
Copyright ©1998 Ian H. Giddy Equity Valuation 3
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
Copyright ©1998 Ian H. Giddy Equity Valuation 4
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
Copyright ©1998 Ian H. Giddy Equity Valuation 5
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
Copyright ©1998 Ian H. Giddy Equity Valuation 6
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
Copyright ©1998 Ian H. Giddy Equity Valuation 7
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
Copyright ©1998 Ian H. Giddy Equity Valuation 8
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.
Copyright ©1998 Ian H. Giddy Equity Valuation 9
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
Copyright ©1998 Ian H. Giddy Equity Valuation 10
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.
Copyright ©1998 Ian H. Giddy Equity Valuation 11
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)
Copyright ©1998 Ian H. Giddy Equity Valuation 12
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
Copyright ©1998 Ian H. Giddy Equity Valuation 13
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
Copyright ©1998 Ian H. Giddy Equity Valuation 14
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
Copyright ©1998 Ian H. Giddy Equity Valuation 15
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?
Copyright ©1998 Ian H. Giddy Equity Valuation 16
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?
Copyright ©1998 Ian H. Giddy Equity Valuation 17
Fundamental Stock Analysis: Models of Equity Valuation
Basic Types of ModelsBalance Sheet ModelsDividend Discount ModelsPrice/Earning Ratios
Estimating Growth Rates and Opportunities
Copyright ©1998 Ian H. Giddy Equity Valuation 18
Equity Valuation: From the Balance Sheet
Value of Assets Book Liquidation Replacement
Value of Liabilities
Book Market
Value of Equity
Copyright ©1998 Ian H. Giddy Equity Valuation 19
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?
Copyright ©1998 Ian H. Giddy Equity Valuation 20
Dividend Discount Models:General Model
VD
ko
t
tt
( )11
VD
ko
t
tt
( )11
V0 = Value of Stock Dt = Dividend k = required return
Copyright ©1998 Ian H. Giddy Equity Valuation 21
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
Copyright ©1998 Ian H. Giddy Equity Valuation 22
No Growth Model
VD
ko
Stocks that have earnings and dividends that are expected to remain constant
Preferred Stock
Copyright ©1998 Ian H. Giddy Equity Valuation 23
No Growth Model: Example
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
VD
ko
Copyright ©1998 Ian H. Giddy Equity Valuation 24
Constant Growth Model
VoD g
k g
o
( )1Vo
D g
k g
o
( )1
g = constant perpetual growth rate
Copyright ©1998 Ian H. Giddy Equity Valuation 25
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
Copyright ©1998 Ian H. Giddy Equity Valuation 26
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)
Copyright ©1998 Ian H. Giddy Equity Valuation 27
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
Copyright ©1998 Ian H. Giddy Equity Valuation 28
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
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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
Copyright ©1998 Ian H. Giddy Equity Valuation 30
Partitioning Value: Example
ROE = 20% d = 60% b = 40%
E1 = $5.00 D1 = $3.00 k = 15%
g = .20 x .40 = .08 or 8%
Copyright ©1998 Ian H. Giddy Equity Valuation 31
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
Copyright ©1998 Ian H. Giddy Equity Valuation 32
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
Copyright ©1998 Ian H. Giddy Equity Valuation 33
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
Copyright ©1998 Ian H. Giddy Equity Valuation 34
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
Copyright ©1998 Ian H. Giddy Equity Valuation 35
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
Copyright ©1998 Ian H. Giddy Equity Valuation 36
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
Copyright ©1998 Ian H. Giddy Equity Valuation 37
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
Copyright ©1998 Ian H. Giddy Equity Valuation 38
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
Copyright ©1998 Ian H. Giddy Equity Valuation 39
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
Copyright ©1998 Ian H. Giddy Equity Valuation 40
Copyright ©1998 Ian H. Giddy Equity Valuation 41
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