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r>;GE 7,N "4I@4J9< l9:>I
Cash flowsFirm: Pre-debt cash
flowEquity: After debtcash flows
Expected GrowthFirm: Growth inOperating EarningsEquity: Growth inNet Income/EPS
CF1 CF2 CF3 CF4 CF5
Forever
Firm is in stable growth:Grows at constant rateforever
Terminal Value
CFn.........
Discount RateFirm:Cost of Capital
Equity: Cost of Equity
ValueFirm: Value of Firm
Equity: Value of Equity
DISCOUNTED CASHFLOW VALUATIO
Length of Period of High Growth
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Free Cashflow to Firm
After-tax Operating Income- (Cap Ex - Depreciation)- Change in non-cash WC= Free Cashflow to firm
Cost of capital
Expected FCFF= Expected operatingincome * (1- Reinvestment rate)
Length of high growth period: PV of FCFF during highgrowth Stable Growth
When operating income andFCFF grow at constant rateforever.
Value of Operatng Assets+ Cash & non-operating assets- Debt= Value of equity
Weighted average ofcosts of equity anddebt
Expected growth inoperating ncome
Reinvestmentneeded to sustaingrowth
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Risk AdjustedCost of equity
Risk free rate in thecurrency of analysis
Relative risk of
company/equity inquestiion
Equity Risk Premium
required for average riskequity+ X=
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Black #: Total ERPRed #: Country risk premiumAVG: GDP weighted average
ERP:Jan2014
Angola 10.40% 5.40%Benin 13.25% 8.25%Botswana 6.28% 1.28%Burkina Faso 13.25% 8.25%Cameroon 13.25% 8.25%Cape Verde 13.25% 8.25%DR Congo 14.75% 9.75%Egypt 16.25% 11.25%Gabon 10.40% 5.40%Ghana 11.75% 6.75%Kenya 11.75% 6.75%Morocco 8.75% 3.75%Mozambique 11.75% 6.75%Namibia 8.30% 3.30%Nigeria 10.40% 5.40%Rep Congo 10.40% 5.40%Rwanda 13.25% 8.25%Senegal 11.75% 6.75%South Africa 7.40% 2.40%Tunisia 10.40% 5.40%Uganda 11.75% 6.75%Zambia 11.75% 6.75%Africa 10.04% 5.04%
Bangladesh 10.40% 5.40%Cambodia 13.25% 8.25%China 5.90% 0.90%Fiji 11.75% 6.75%Hong Kong 5.60% 0.60%India 8.30% 3.30%Indonesia 8.30% 3.30%Japan 5.90% 0.90%Korea 5.90% 0.90%Macao 5.90% 0.90%Malaysia 6.80% 1.80%Mauritius 7.40% 2.40%Mongolia 11.75% 6.75%Pakistan 16.25% 11.25%Papua New Guinea 11.75% 6.75%Philippines
8.30%
3.30%
Singapore 5.00% 0.00%Sri Lanka 11.75% 6.75%Taiwan 5.90% 0.90%Thailand 7.40% 2.40%Vietnam 13.25% 8.25%Asia 6.51% 1.51%
Australia 5.00% 0.00%Cook Islands 11.75% 6.75%New Zealand 5.00% 0.00%Australia & New
Zealand 5.00% 0.00%
Argentina 14.75% 9.75%Belize 18.50% 13.50%Bolivia 10.40% 5.40%Brazil 7.85% 2.85%Chile 5.90% 0.90%Colombia 8.30% 3.30%Costa Rica 8.30% 3.30%Ecuador 16.25% 11.25%El Salvador 10.40% 5.40%Guatemala
8.75%
3.75%
Honduras 13.25% 8.25%Mexico 7.40% 2.40%Nicaragua 14.75% 9.75%Panama 7.85% 2.85%Paraguay 10.40% 5.40%Peru 7.85% 2.85%Suriname 10.40% 5.40%Uruguay 8.30% 3.30%Venezuela 16.25% 11.25%Latin America 8.62% 3.62%
Albania 11.75% 6.75%Armenia 9.50% 4.50%Azerbaijan 8.30% 3.30%Belarus 14.75% 9.75%Bosnia and Herzegovina 14.75% 9.75%Bulgaria 7.85% 2.85%Croatia 8.75% 3.75%Czech Republic 6.05% 1.05%Estonia 6.05% 1.05%Georgia 10.40% 5.40%Hungary 8.75% 3.75%Kazakhstan 7.85% 2.85%Latvia 7.85% 2.85%Lithuania 7.40% 2.40%Macedonia 10.40% 5.40%Moldova 14.75% 9.75%Montenegro 10.40% 5.40%Poland 6.28% 1.28%Romania 8.30% 3.30%Russia 7.40% 2.40%Serbia 11.75% 6.75%Slovakia 6.28% 1.28%Slovenia 8.75% 3.75%Ukraine 16.25% 11.25%E. Europe & Russia 7.96% 2.96%
Abu Dhabi 5.75% 0.75%Bahrain 7.85% 2.85%Israel 6.05% 1.05%Jordan 11.75% 6.75%Kuwait 5.75% 0.75%Lebanon 11.75% 6.75%Oman 6.05% 1.05%Qatar 5.75% 0.75%Saudi Arabia 5.90% 0.90%United Arab Emirates 5.75% 0.75%Middle East 6.14% 1.14%
Canada 5.00% 0.00%United States of America 5.00% 0.00%North America 5.00% 0.00%
Andorra 6.80% 1.80% Liechtenstein 5.00% 0.00%Austria 5.00% 0.00% Luxembourg 5.00% 0.00%Belgium 5.90% 0.90% Malta 6.80% 1.80%Cyprus 20.00% 15.00% Netherlands 5.00% 0.00%Denmark 5.00% 0.00% Norway 5.00% 0.00%Finland 5.00% 0.00% Portugal 10.40% 5.40%France 5.60% 0.60% Spain 8.30% 3.30%Germany 5.00% 0.00% Sweden 5.00% 0.00%Greece 20.00% 15.00% Switzerland 5.00% 0.00%Iceland 8.30% 3.30% Turkey 8.30% 3.30%Ireland 8.75% 3.75% United Kingdom 5.60% 0.60%Italy 7.85% 2.85% Western Europe 6.29% 1.29%
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0.00%
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4.00%5.00%
6.00%
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1960
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ImpliedPremium
Year
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Beta of Firm (Unlevered Beta)
Beta of Equity (Levered Beta)
Nature of product orservice offered bycompany:Other things remaining equal,the more discretionary theproduct or service, the higherthe beta.
Operating Leverage (FixedCosts as percent of totalcosts):Other things remaining equalthe greater the proportion ofthe costs that are fixed, thehigher the beta of thecompany.
Financial Leverage:Other things remaining equal, thegreater the proportion of capital thata firm raises from debt,the higher itsequity beta will be
Implications1. Cyclical companies shouldhave higher betas than non-cyclical companies.2. Luxury goods firms should
have higher betas than basicgoods.3. High priced goods/servicefirms should have higher betasthan low prices goods/servicesfirms.4. Growth firms should havehigher betas.
Implications1. Firms with high infrastructureneeds and rigid cost structuresshould have higher betas thanfirms with flexible cost structures.
2. Smaller firms should have higherbetas than larger firms.3. Young firms should have higherbetas than more mature firms.
ImplciationsHighly levered firms should have highe betasthan firms with less debt.Equity Beta (Levered beta) =Unlev Beta (1 + (1- t) (Debt/Equity Ratio))
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ep : n e usness or us nesses a your rm opera es n.
Step 2: Find publicly traded firms in each of these businesses andobtain their regression betas. Compute the simple average acrossthese regression betas to arrive at an average beta for these publiclyra e rms. n ever s average e a usng e average e oequ y ra o across e pu c y ra e rms n e samp e.Unlevered beta for business = Average beta across publicly tradedfirms/ (1 + (1- t) (Average D/E ratio across firms))
If you can, adjust this beta for differencesbetween your firm and the comparablerms on opera ng everage an pro uc
characteristics.
Step 3: Estimate how much value your firm derives from each ofthe different businesses it is in.
e revenues or opera ng ncomeare o en use as weg s, s e erto try to estimate the value of eachbusiness.
Step 4: Compute a weighted average of the unlevered betas of theeren usnesses rom s ep usng e weg s rom s ep .
o om-up n evere e a or your rm = e g e average o eunlevered betas of the individual business
Step 5: Compute a levered beta (equity beta) for your firm, usingthe market debt to equity ratio for your firm.
evere o om-up e a = n evere e a + - e qu y
If you expect the business mix of yourrm o c ange over me, you can
c ange e weg s on a year- o-yearbasis.
I you expec your e o equ y ra o ochange over time, the levered beta willchange over time.
Possible Refinements
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Default spread over treasury
Rating 1-Jan-08 12-Sep-08 12-Nov-08 1-Jan-09 1-Jan-10 1-Jan-11
Aaa/AAA 0.99% 1.40% 2.15% 2.00% 0.50% 0.55%
Aa1/AA+ 1.15% 1.45% 2.30% 2.25% 0.55% 0.60%
Aa2/AA 1.25% 1.50% 2.55% 2.50% 0.65% 0.65%
Aa3/AA- 1.30% 1.65% 2.80% 2.75% 0.70% 0.75%
A1/A+ 1.35% 1.85% 3.25% 3.25% 0.85% 0.85%A2/A 1.42% 1.95% 3.50% 3.50% 0.90% 0.90%
A3/A- 1.48% 2.15% 3.75% 3.75% 1.05% 1.00%
Baa1/BBB+ 1.73% 2.65% 4.50% 5.25% 1.65% 1.40%
Baa2/BBB 2.02% 2.90% 5.00% 5.75% 1.80% 1.60%
Baa3/BBB- 2.60% 3.20% 5.75% 7.25% 2.25% 2.05%
Ba1/BB+ 3.20% 4.45% 7.00% 9.50% 3.50% 2.90%
Ba2/BB 3.65% 5.15% 8.00% 10.50% 3.85% 3.25%Ba3/BB- 4.00% 5.30% 9.00% 11.00% 4.00% 3.50%
B1/B+ 4.55% 5.85% 9.50% 11.50% 4.25% 3.75%
B2/B 5.65% 6.10% 10.50% 12.50% 5.25% 5.00%
B3/B- 6.45% 9.40% 13.50% 15.50% 5.50% 6.00%
Caa/CCC+ 7.15% 9.80% 14.00% 16.50% 7.75% 7.75%
ERP 4.37% 4.52% 6.30% 6.43% 4.36% 5.20%
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Cost of Capital = Cost of Equity (Equity/(Debt + Equity)) + Cost of Borrowing (1-t) (Debt/(Debt + Equity))
Cost of borrowing should be based upon(1) synthetic or actual bond rating
(2) default spreadCost of Borrowing = Riskfree rate + Default spread
Marginal tax rate, reflecting
tax benefits of debt
Weights should be market value weightsCost of equitybased upon bottom-upbeta
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Expected growth = Growth from new investments + Efficiency growth= Reinv Rate * ROC + (ROCt-ROCt-1)/ROCt-1
Assume that your cost of capital is 10%. As an investor, rank these
firms in the order of most value growth to least value growth.
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Year Revenues Change in revenue Sales/Capital Ratio Reinvestment Capital Invested Operating Income (Loss) Imputed ROC
Current $187 1,657$ -$787
1 $562 $375 1.50 $250 1,907$ -$1,125 -67.87%
2 $1,125 $562 1.50 $375 2,282$ -$1,012 -53.08%
3 $2,025 $900 1.50 $600 2,882$ -$708 -31.05%
4 $3,239 $1,215 1.50 $810 3,691$ -$243 -8.43%
5 $4,535 $1,296 1.50 $864 4,555$ $284 7.68%
6 $5,669 $1,134 1.50 $756 5,311$ $744 16.33%
7 $6,803 $1,134 1.50 $756 6,067$ $1,127 21.21%
8 $7,823 $1,020 1.50 $680 6,747$ $1,430 23.57%
9 $8,605 $782 1.50 $522 7,269$ $1,647 17.56%
10 $9,035 $430 1.50 $287 7,556$ $1,768 15.81%
Industry average Sales/Cap RatioCapital invested in year t+!=Capital invested in year t +
Reinvestment in year t+1
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Expected Growth Rate
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Equity Earnings Operating Income
HistoricalFundamentalsAnalysts HistoricalFundamentals
Stable ROE Changing ROE
ROE * Retention RatioROEt+1*Retention Ratio
+ (ROEt+1-ROEt)/ROEt
Stable ROC
ROC *Reinvestment Rate
Changing ROC
ROCt+1*Reinvestment Rate+ (ROCt+1-ROCt)/ROCt
Negative Earnings
1. Revenue Growth2. Operating Margins3. Reinvestment NeedsEarnings per share Net Income
Stable ROE Changing ROE
ROE * EquityReinvestment Ratio
ROEt+1*Eq. Reinv Ratio
+ (ROEt+1-ROEt)/ROEt
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t=N
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Terminal Value
LiquidationValue
Multiple Approach Stable GrowthModel
Most usefulwhen assetsare separableandmarketable
Easiest approach butmakes the valuationa relative valuation
Technically soundest,but requires that youmake judgments aboutwhen the firm will growat a stable rate which it
can sustain forever,and the excess returns(if any) that it will earnduring the period.
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Choose aCash Flow Dividends
Expected Dividends to
Stockholders
Cashflows to Equity
Net Income
- (1- !) (Capital Exp. - Deprecn)
- (1- !) Change in Work. Capital
= Free Cash flow to Equity (FCFE)
[! = Debt Ratio]
Cashflows to Firm
EBIT (1- tax rate)
- (Capital Exp. - Deprecn)
- 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
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Value of Operating Assets
+ Cash and MarketableSecurities
+ Value of Cross Holdings
+ Value of Other Assets
Value of Firm
- Value of Debt
= Value of Equity
- Value of Equity Options
= Value of Common Stock/ Number of shares
= Value per share
Operating versus Non-opeating cashShould cash be discounted for earning a low return?
How do you value cross holdings in other companies?What if the cross holdings are in private businesses?
What about other valuable assets?How do you consider under utlilized assets?
What should be counted in debt?Should you subtract book or market value of debt?What about other obligations (pension fund and health care?What about contingent liabilities?What about minority interests?
What equity options should be valued here (vested versus non-vested)?How do you value equity options?
Should you divide by primary or diluted shares?
Should you discount this value for opacity or complexity?How about a premium for synergy?
What about a premium for intangibles (brand name)?
Should there be a premium/discount for control?Should there be a discount for distress
Should there be a discount for illiquidity/ marketability?Should there be a discount for minority interests?
Since this is a discounted cashflow valuation, should there be a real optionpremium?
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Why a stable growth dividend discount model?1. Why stable growth: Company is a regulated utility, restricted from investing in new
growth markets. Growth is constrained by the fact that the population (and powerneeds) of its customers in New York are growing at very low rates.Growth rate forever = 2%2. Why equity: Companys debt ratio has been stable at about 70% equity, 30% debtfor decades.3. Why dividends: Company has paid out about 97% of its FCFE as dividends overthe last five years.
Riskfree rate4.10%
10-year T.Bond rate
Beta0.80
Beta for regulatedpower utilities
Equity RiskPremium
4.5%Implied Equity RiskPremium - USmarket in 8/2008
Cost of Equity = 4.1% + 0.8 (4.5%) = 7.70%
Value per share today= Expected Dividends per share next year / (Cost of equity - Growth rate)= 2.32 (1.021)/ (.077 - ,021) = $42.30
On August 12, 2008Con Ed was trading at $40.76.
Test 3: Is the firms risk and cost of equity consistent with a stable growith firm?Beta of 0.80 is at lower end of the range of stable company betas: 0.8 -1.2
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Valuepershare
Expected Growth rate
Con Ed: Value versus Growth Rate
Break even point: Value = Price
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Current Cashflow to FirmEBIT(1-t)= 5344 (1-.35)= 3474- Nt CpX= 350- Chg WC 691= FCFF 2433Reinvestment Rate = 1041/3474
Expected Growth inEBIT (1-t).30*.25=.0757.5%
Stable Growthg = 3%; Beta = 1.10;Debt Ratio= 20%; Tax rate=35%Cost of capital = 6.76%ROC= 6.76%;
3M: A Pre-crisis valuation
Reinvestment Rate30%
Return on Capital25%
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=29.97%Return on capital = 25.19% Reinvestment Rate=3/6.76=44%
Terminal Value5= 2645/(.0676-.03) = 70,409
Cost of Equity8.32%
Cost of Debt(3.72%+.75%)(1-.35)= 2.91%
WeightsE = 92% D = 8%
Op. Assets 60607+ Cash: 3253- Debt 4920=Equity 58400
Value/Share $ 83.55
Riskfree Rate:
Riskfree rate = 3.72% + Beta1.15 X
Risk Premium
4%
Unlevered Beta forSectors: 1.09
Term Yr$4,758$2,113$2,645
On September 12,2008, 3M wastrading at $70/share
First 5 years
D/E=8.8%
Cost of capital = 8.32% (0.92) + 2.91% (0.08) = 7.88%
Year 1 2 3 4 5EBIT (1-t) $3,734 $4,014 $4,279 $4,485 $4,619- Reinvestment $1,120 $1,204 $1,312 $1,435 $1,540 ,
= FCFF $2,614 $2,810 $2,967 $3,049 $3,079
Aswath Damodaran233
Current Cashflow to FirmEBIT(1-t)= 4810 (1-.35)= 3,180- Nt CpX= 350- Chg WC 691= FCFF 2139Reinvestment Rate = 1041/3180
Expected Growth inEBIT (1-t).25*.20=.055%
Stable Growthg = 3%; Beta = 1.00;; ERP =4%Debt Ratio= 8%; Tax rate=35%Cost of capital = 7.55%
3M: Post-crisis valuationReinvestment Rate25%
Return on Capital20%
Lowered base operating income by 10%
Reduced growthrate to 5%
Did not increase debtratio in stable growthto 20%
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=33%Return on capital = 23.06%
ROC= 7.55%;Reinvestment Rate=3/7.55=40%
Terminal Value5= 2434/(.0755-.03) = 53,481
Cost of Equity10.86%
Cost of Debt(3.96%+.1.5%)(1-.35)= 3.55%
WeightsE = 92% D = 8%
Op. Assets 43,975+ Cash: 3253- Debt 4920=Equity 42308
Value/Share $ 60.53
Riskfree Rate:
Riskfree rate = 3.96% + Beta1.15 XRisk Premium
6%
Unlevered Beta forSectors: 1.09
Term Yr$4,038$1,604$2,434
On October 16, 2008,MMM was trading at$57/share.
First 5 years
D/E=8.8%
Cost of capital = 10.86% (0.92) + 3.55% (0.08) = 10.27%
Year 1 2 3 4 5EBIT (1-t) $3,339 $3,506 $3,667 $3,807 $3,921- Reinvestment $835 $877 $1,025 $1,288 $1,558= FCFF $2,504 $2,630 $2,642 $ 2,519 $2,363
Increased risk premium to 6% for next 5 years
Higher default spread for next 5 years
Aswath Damodaran234
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