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Ian H. Giddy Valuation-1
Prof. Ian GiddyNew York University
Equity Valuation
Copyright ©2001 Ian H. Giddy Valuation 2
Valuing a Firm with DCF: An Illustration
Historical financial results
Adjust for nonrecurring aspects
Gauge future growth
Adjust for noncash items
Projected sales and operating profits
Projected free cash flows to the firm (FCFF)
Year 1 FCFF
Year 2 FCFF
Year 3 FCFF
Year 4 FCFF
Terminal year FCFF
Stable growth model or P/E comparable
Present value of free cash flows
+ cash, securities & excess assets
- Market value of debt
Value of shareholders equity
…
Discount to present using weighted average cost of capital (WACC)
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The Cost of Capital
Choice Cost1. Equity Cost of equity- Retained earnings - depends upon riskiness of the stock- New stock issues - will be affected by level of interest rates- Warrants
Cost of equity = riskless rate + beta * risk premium
2. Debt Cost of debt- Bank borrowing - depends upon default risk of the firm- Bond issues - will be affected by level of interest rates
- provides a tax advantage because interest is tax-deductible
Cost of debt = Borrowing rate (1 - tax rate)
Debt + equity = Cost of capital = Weighted average of cost of equity andCapital cost of debt; weights based upon market value.
Cost of capital = kd [D/(D+E)] + ke [E/(D+E)]
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Valuation: The Key Inputs
l A publicly traded firm potentially has an infinite life. The value is therefore the present value of cash flows forever.
l 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)Nt =1
t =N∑
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Stable Growth and Terminal Value
l 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
l 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.
l While companies can maintain high growth rates for extended periods, they will all approach “stable growth” at some point intime.
l When they do approach stable growth, the valuation formula above can be used to estimate the “terminal value” of all cash flows beyond.
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Growth Patterns
l A key assumption in all discounted cash flow models is the period of high growth, and the pattern of growth during that period. Ingeneral, we can make one of three assumptions:u there is no high growth, in which case the firm is already in
stable growthu there will be high growth for a period, at the end of which the
growth rate will drop to the stable growth rate (2-stage)u 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)
l The assumption of how long high growth will continue will dependupon several factors including:u the size of the firm (larger firm -> shorter high growth periods)u current growth rate (if high -> longer high growth period)u barriers to entry and differential advantages (if high -> longer
growth period)
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Length of High Growth Period
l Assume that you are analyzing two firms, both of which are enjoying high growth. The first firm is EarthlinkNetwork, 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?
o Earthlink Networko Biogeno Both are well managed and should have the same high
growth period
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Choosing a Growth Pattern: Examples
Company Valuation in Growth Period Stable GrowthDisney 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
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The Building Blocks of Valuation
Choose aCash Flow Dividends
Expected Dividends to
Stockholders
Cashflows to Equity
Net Income
- (1- δ) (Capital Exp. - Deprec’n)
- (1- δ) Change in Work. Capital
= Free Cash flow to Equity (FCFE)
[δ = 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 + Σ 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
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Dividend Discount Models:General Model
VD
ko
t
tt
=+=
∞
∑( )11
lV0 = Value of StocklDt = Dividendlk = required return
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Specified Holding Period Model
01
12
2
1 1 1V D
kD
kD P
kN N
N= + +
+
+ + +( ) ( ) ( )...
l PN = the expected sales price for the stock at time N
l N = the specified number of years the stock is expected to be held
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No Growth Model
VD
ko =
l Stocks that have earnings and dividends that are expected to remain constant
l Preferred Stock
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No Growth Model: Example
E1 = D1 = $5.00k = .15
V0 = $5.00 / .15 = $33.33
VD
ko =
n Burlington Power & Light has earnings of $5 per share and pays out 100% dividend
n The required return that shareholders expect is 15%
n The earnings are not expected to grow but remain steady indefinitely
n What’s a BPL share worth?
n Burlington Power & Light has earnings of $5 per share and pays out 100% dividend
n The required return that shareholders expect is 15%
n The earnings are not expected to grow but remain steady indefinitely
n What’s a BPL share worth?
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Constant Growth Model
VoD g
k g
o=
+−
( )1
lg = constant perpetual growth rate
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Constant Growth Model: Example
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
n Motel 6 has earnings of $5 per share. It reinvests 60% and pays out 40%dividend
n The required return that shareholders expect is 15%
n The earnings are expected to grow at 8% per annum
n What’s an M6 share worth?
n Motel 6 has earnings of $5 per share. It reinvests 60% and pays out 40%dividend
n The required return that shareholders expect is 15%
n The earnings are expected to grow at 8% per annum
n What’s an M6 share worth?
Plowback rate
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Estimating Dividend Growth Rates
g ROE b= ×
l g = growth rate in dividendsl ROE = Return on Equity for the firml b = plowback or retention percentage rate
i.e.(1- dividend payout percentage rate)
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Shifting Growth Rate Model
V Dg
k
D g
k g ko o
t
tt
TT
T=++
++
− +=∑( )
( )
( )
( )( )
1
1
1
1
1
1
2
2
lg1 = first growth ratelg2 = second growth ratelT = number of periods of growth at
g1
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n Mindspringpays dividends $2 per share. The required return that shareholders expect is 15%
n The dividends are expected to grow at 20% for 3 years and 5% thereafter
n What’s a Mindspringshare worth?
n Mindspringpays dividends $2 per share. The required return that shareholders expect is 15%
n The dividends are expected to grow at 20% for 3 years and 5% thereafter
n What’s a Mindspringshare worth?
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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Ratios Do Have Meaning
l Gordon Growth Model:l Dividing both sides by the earnings,
l Dividing both sides by the book value of equity,
l If the return on equity is written in terms of the retention ratio and the expected growth rate
l Dividing by the Sales per share,
P 0 =DPS1
r − gn
P 0
EPS 0
= PE = Payout Ratio * (1 + g n )
r-gn
P 0
BV 0
= PBV = ROE - gn
r-gn
P 0
BV 0= PBV =
ROE * Payout Ratio * (1 + g n )
r-g n
P 0
Sales 0= PS =
Profit Margin * Payout Ratio * (1 + g n )
r-gn
Equity Valuation:Spreadsheet Application
Prof. Ian GiddyNew York University
Ian H. Giddy Valuation-11
Equity Valuation:Application to M&A
Prof. Ian GiddyNew York University
Equity Valuation:Application to M&A
Prof. Ian GiddyNew York University
OptikaSchirnding
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How Much Should We Pay?
Applying the discounted cash flow approach, we need to know:
1.The incremental cash flows to be generated from the acquisition, adjusted for debt servicing and taxes
2.The rate at which to discount the cash flows (required rate of return)
3.The deadweight costs of making the acquisition (investment banks' fees, etc)
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Application
l Fakawi Navigation plans to acquire Feng-ShuiCompass Co. This would result in $25 million of incremental operating revenues in each of the first 5 years, and in $15 million of additional debt servicing costs per annum, as well as $5 million in tax shields.Fakawi expects to divest the target in year 6 for $100 million. The Treasury note rate is 6%, and the S&P return is 16%. Fakawi's advisors estimate that Feng-Shui has a beta of 1.3. For this advice they are charging 2% of the acquisition price.
l What is the maximum price that Fakawi should offer for Feng-Shui?
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Framework for Assessing RetructuringOpportunities
RestructuringFramework
1
2
CurrentMarketValue
3
Totalrestructuredvalue
Potentialvalue withinternal+ externalimprovements
Potentialvalue withinternalimprovements
Company’sDCF value
Maximumrestructuringopportunity
Financialstructureimprovements
4
Disposal/Acquisitionopportunities
Operatingimprovements
Current marketoverpricing orunderpricng
5
(Eg Increase D/E)
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Equity Valuation in Practice
l Estimating discount rate
l Estimating cash flowsl Application to Optika
l Application in M&A: Schirnding-Optika
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Estimating Future Cash Flows
n Dividends?n Free cash
flows to equity?
n Free cash flows to firm?
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Optika OptikaGrowth 5%Tax rate 35%Initial Revenues 3125COGS 89%WC 10%Equity Market Value 1300Debt Market Value 250Beta 1Treasury bond rate 7%Debt spread 1.5%Market risk premium 5.50%
T+1Revenues 3281-COGS 2920-Depreciation 74=EBIT 287EBIT(1-Tax) 187-Change in WC 16=Free Cash Flow to Firm 171Cost of Equity (from CAPM) 12.50%Cost of Debt (after tax) 5.53%WACC 11.38%
Firm Value 2278
CAPM:7%+1(5.50%)
Debt cost(7%+1.5%)(1-.35)
WACC:ReE/(D+E)+RdD/(D+E)
Value:FCFF/(WACC-growth rate)
Equity Value:Firm Value - Debt Value = 2278-250 = 2028
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Optika & SchirndingSchirnding-Optika
Optika Schirnding CombinedGrowth 5% 5% 5%Tax rate 35% 35% 35%Initial Revenues 3125 4400 7525COGS 89% 87.50%WC 10% 10% 10%Equity Market Value 1300 2000 3300Debt Market Value 250 160 410Beta 1 1 1Treasury bond rate 7% 7% 7%Debt spread 1.5% 1.5% 1.5%Market risk premium 5.50% 5.50% 5.50%
T+1 T+1Revenues 3281 4620 7901-COGS 2920 4043 6963-Depreciation 74 200 274=EBIT 287 378 664EBIT(1-Tax) 187 245 432-Change in WC 16 22 38=Free Cash Flow to Firm 171 223 394Cost of Equity (from CAPM) 12.50% 12.50% 12.50%Cost of Debt (after tax) 5.53% 5.53% 5.53%WACC 11.38% 11.98% 11.73%
Firm Value 2278 3199 5859
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Optika-Schirnding with SynergySchirnding-Optika
Optika Schirnding Combined SynergyGrowth 5% 5% 5% 5%Tax rate 35% 35% 35% 35%Initial Revenues 3125 4400 7525 7525COGS 89% 87.50% 86.00%WC 10% 10% 10% 10%Equity Market Value 1300 2000 3300 3300Debt Market Value 250 160 410 410Beta 1 1 1 1Treasury bond rate 7% 7% 7% 7%Debt spread 1.5% 1.5% 1.5% 1.5%Market risk premium 5.50% 5.50% 5.50% 5.50%
T+1 T+1 T+1Revenues 3281 4620 7901 7901-COGS 2920 4043 6963 6795-Depreciation 74 200 274 274=EBIT 287 378 664 832EBIT(1-Tax) 187 245 432 541-Change in WC 16 22 38 38=Free Cash Flow to Firm 171 223 394 503Cost of Equity (from CAPM) 12.50% 12.50% 12.50% 12.50%Cost of Debt (after tax) 5.53% 5.53% 5.53% 5.53%WACC 11.38% 11.98% 11.73% 11.73%
Firm Value 2278 3199 5859 7479Increase 1620