cost of capital slides
TRANSCRIPT
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Estimating Cost of Capital
Estimating Cost of Capital
Anders Vilhelmsson
Department of Business Administration, Lund University
September 2009
Cost of Capital
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Estimating Cost of Capital
Aim of the 2 lectures
I Cover chapter 10 in the book
I Cover relevant research, particularly from 2004 (when thebook was updated) until 2009
I Slides can be found after the lecture at www.nek.lu.se/nekavi
Cost of Capital
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Estimating Cost of Capital
Valuation
I Easy in theory, the total value of a company is the presentvalue of all future cash �ows
I V = CF11+k +
CF2(1+k )2
+ CF3(1+k )3
+ CF4(1+k )4
+ CF5(1+k )5
...
I However, k is unknown and may not be constant over time
Cost of Capital
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Estimating Cost of Capital
WACC
I WACC = DV kd (1� Tm) +
EV ke
D = Value of debtV = Enterprise valuekd = Current borrowing rate (tax deductible)Tm = Corporate (marginal) tax rate (e.g. 26.3% in Sweden)E = Value of equityke = Cost of equity
I Example 1 on the board
Cost of Capital
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Estimating Cost of Capital
WACC
I Why do we need 2 full lectures to do the above calculations?I kd and especially ke are unobservableI We need theory (models) to estimate kd and keI In practice it may also be non-trivial to calculate (target) DVand E
V
I We will put most e¤ort in estimating ke correctly since theuncertainty is largest in this number.
Cost of Capital
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Estimating Cost of Capital
Cost of debt
I Primary problem, non-�at term structure of interest ratesI In principle 1 year CF should be matched with 1 year debtrate, 2 year CF with 2 year rate and so on
I In practice match with the duration on the company�s CFsI Growth stocks, high duration, value stocks low durationI The book recommends about 10 years for all companies
Cost of Capital
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Estimating Cost of Capital
Duration
I Macaulay�s Duration:
D =n∑t=1
�t � PV (CFt )V
�=
n∑t=1
�t � CFt/(1+r )
t
V
�I V = Enterprise Value
I Do loan example on the boardI What happens with the sum is in�nite (e.g. CF from a stock)?
I D =n∑t=1
�t � PV (CFt )V
�+ (n+Dcv )
PV (CVn)V
I Dcv = 1r�g Duration of continuing value, derive on the board.
I Do stock example on the board
Cost of Capital
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Duration
Figure: Source: Own calculations
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Term structure of interest rates
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Estimating Cost of Capital
Estimate cost of debt
I Use Yield to maturity (YTM) on long term bondI YTM > kd but small di¤erence for BBB companies and betterI P = C
1+ytm +C
(1+ytm)2+ C(1+ytm)3
... C+P(1+ytm)n
I Solve for YTM but this is an n:th order equation (numericalsolution)
I Calculate YTM in Excel example
Cost of Capital
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Cost of debt vs YTM
00.05 0.10
0.150.20
0.250.30
0.350.40 0.45
0.50
0 .01
0.25
0.13
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Recovery rate
YTM as a function of Recovery rate and defualt prob. cost of debt is 6%
Default probability
YTM
Figure: Source: Own calculations
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Estimating Cost of Capital
Estimate cost of debt
I What to do with companies that only have untraded or shortdebt?
I Find credit ratingI Compare to traded long bonds with the same credit rating
I What to do with companies with <BBB rating?I Use BBB cost of debt and add 0.5% units (motivated by 0.1higher CAPM beta)
Cost of Capital
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Estimating Cost of Capital
Estimate cost of equity
I Estimating the cost of equity is the same thing as explainingthe cross section of stock returns
I Why do companies have di¤erent expected returns?I Theory: Because of di¤erent exposure to systematic riskfactor(s)
I CAPM, FF3, momentum, liquidity, risk aversion (APT)
Cost of Capital
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Estimating Cost of Capital
The CAPM
I Security market line (SML) E [Ri ] = rf + βi (E [Rm ]� rf )E [Ri ] = Expected return on asset irf = risk free rateE [Rm ] = Expected return on the market portfolioβi =
cov (Ri ,Rm )σ2m
systematic risk in asset i
I Problem: E [Ri ],E [Rm ] and βi are all unobservable and rfvaries with maturity
Cost of Capital
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Estimating Cost of Capital
Estimating the risk free rate
I Same thing as with the cost of debt (Match each cash �ow)I Make sure cash �ows and cost of capital uses the samecurrency
Cost of Capital
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Estimating Cost of Capital
Estimating the market risk premium
I Interesting working paper athttp://papers.ssrn.com/sol3/papers.cfm?abstract_id=1473225
I Compares the recommended market risk premium from 150di¤erent textbooks
I CAPM actually gives the market risk premium asE (Rm)� rf = γσ2m assuming CRRA utility
I σ2m can, at least historically, be observed but not γ (therelative risk aversion)
Cost of Capital
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Estimating the market risk premium
Figure: Source: Fernández (2009,WP)
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Estimating Cost of Capital
Estimating the market risk premium
Figure: Source: Fernández (2009,WP)
Cost of Capital
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Estimating Cost of Capital
Estimating Beta
I Lets look at the recommendations given by the bookI Use at least 60 data pointsI Use monthly dataI Use SP500 or MSCI world index as market portfolio
Cost of Capital
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Estimating Cost of Capital
At least 60 data points
I Number of data points is a trade o¤ betweenI Precision and possible time variationI If you think that beta is constant over time use all data youhave
I 60 data points in not a magic number, happens to be 5 yearsof monthly data
Cost of Capital
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Estimating Cost of Capital
Use monthly data
I Use monthly frequency - good idea if stock is very illiquid(traded infrequently)
I For e.g. the 30 stocks in Dow Jones you can use daily of evenintra-daily (15-30 minute data)
I Andersen et al. (2006) (Dow Jones 30 between 15 minutesand 1 day),
I Lewellen and Nagel (2006, JFE) daily and weekly on all NYSEstocks
I You can also adjust (Dimson 1979, JFE) for infrequent tradingI Bid ask Bounce can be �xed by calculating returns usingmidquotes instead of transaction prices(bid price + ask price)/2
I Currently there is a shift towards use of higher frequency inbeta estimation
Cost of Capital
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Estimating Cost of Capital
Use a broad market portfolio
I Use a broad value weighted stock index to calculate betas,otherwise their is no theoretical foundation.
I Never use a local market index, in e.g. Finland you wouldbasically measure a stock�s sensitivity towards Nokia
Cost of Capital
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Estimating Cost of Capital
Industry betas
I Idea: Improve precision in beta by using the mean beta of theindustry (adjusted for leverage)
I Assumes that companies in the same industry has the samesystematic operational risk
I Di¤erent betas within an industry is only due to di¤erentleverage
I Master thesis topic: How well does this assumption holdempirically?
Cost of Capital
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Estimating Cost of Capital
How to calculate an industry beta
I First compute betas for all companies in the industry withregression analysis
I Unleverage beta withVu
Vu+Vtxaβu +
VtxaVu+Vtxa
βtxa =D
D+E βd +E
D+E βe) βe = βu +
DE (βu � βd ) +
VtxaE (βtxa � βu)
assume βd = 0 and βu = βtxa) βe = βu(1+
DE )
I Do calculations on the board
Cost of Capital
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Estimating Cost of Capital
How to calculate an industry beta
I Average βu over all companiesI Relever to each companies target D
E ratioI Example on the board
Cost of Capital
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Estimating Cost of Capital
Other factor models
I Eugene Fama and Kenneth French 3 factor model FF3, Famaand French (1992, JoF)
E [Ri ] = rf + βi ,m (E [Rm ]� rf ) + βi ,smbE [SMB ] + βi ,HMLE [HML]SMB is the return on a small stock portfolio minus a big stockportfolio (small minus big)HML is the return on a high book to market minus a low book tomarket portfolio (high minus low)
I Is SMB and HML capturing risk exposure or misspricing?I Still open research question, enough papers to be the topic fora separate course
I Momentum, Jegadeesh and Titman (1993,RFS) and Liquidity,Amihud (2002) are other prominent factors
Cost of Capital
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Sample period is from March 1990 to April 2004
Panel A: 25 portfolios sorted on Book-to-market and size
λMKT λSMB λHML λMOM λMIMRA R2
CAPM -0.626 0.27
[-0.87]
CAPM+MIMRA -0.935 -0.020 0.64
[-1.51] [-2.07]
FF3 -1.602 0.141 0.353 0.60
[-2.92] [0.46] [1.24]
FF3+MIMRA -0.988 0.174 0.289 -0.023 0.66
[-1.41] [0.57] [1.03] [-2.61]
FF3+MOM+MIMRA -0.666 0.178 0.325 1.895 -0.025 0.68
[-0.83] [0.59] [1.16] [2.11] [-2.80]
Source: Nyberg and Wilhelmsson (forthcoming, The �nancialreview)
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Sample period is from March 1990 to April 2004
Panel B: 25 portfolios sorted on Book-to-market and size and 30 industry portfolios
λMKT λSMB λHML λMOM λMIMRA R2
CAPM -0.031 0.00
[-0.06]
CAPM+MIMRA -0.202 -0.012 0.15
[-0.41] [-1.23]
FF3 -0.144 0.110 0.033 0.03
[-0.29] [0.36] [0.11]
FF3+MIMRA 0.019 0.154 -0.008 -0.027 0.31
[0.04] [0.50] [-0.03] [-3.12]
FF3+MOM+MIMRA 0.176 0.141 0.013 1.211 -0.025 0.33
[0.31] [0.46] [0.04] [1.34] [-2.93]
Source: Nyberg and Wilhelmsson (forthcoming, The �nancialreview)
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Estimating Cost of Capital
In defence of beta
I Builds on solid theoryI Assumes multivariate normal distribution or investors withpreferences for only mean and variance (both assumptions arewrong)
I FF3 purely empirical evidence, no theory, size premiumvanishing
I rejecting FF3 does not really support CAPM we have morethan 2 competitors (evolution/creationism)
I CAPM may hold conditionally (beta should be forwardlooking)
I E¤ect is too small to save CAPM according to Lewellen andNagel (2006, JFE)
Cost of Capital
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Estimating Cost of Capital
Importance of model selection
I How important is the selection of factor model? Lets try to�nd out!
I Calculate cost of equity for J&J using CAPM and FF3 inExcel.
I Is the J&J results typical or not? Possible master thesis topic.
Cost of Capital
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Estimating Cost of Capital
Is the cost of equity time varying / are stock returnspredictable ?
I E [ri ]� rf = βi [E (Rm)� rf ]I E (Rm)� rf = γσ2m
I Three possible sources of time variationI Time varying betasI Time varying risk aversionI Time varying volatility
Cost of Capital
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Estimating Cost of Capital
Time varying betas
Figure: Source: Andersen et al. (2004) AA is Alcoa, ALD is Alliedcapital corporation, DD is DuPont, and DIS is WaltDisney.The samplecovers theperiod from 1962:3 through 1999:3.
Cost of Capital
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Estimating Cost of Capital
Time varying betas
Figure: Source: Andersen et al. (2004)
Cost of Capital
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Estimating Cost of Capital
Time varying betas
Figure: Source: Andersen et al. (2004) The sample covers the periodfrom 1993:2 through 1999:3. We calculate the realized quarterly betasfrom daily returns.
Cost of Capital
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Estimating Cost of Capital
Time varying betas
Figure: Source: Andersen et al. (2004) The sample covers the periodfrom 1993:2 through 1999:3. We calculate the realized quarterly betasfrom 15 minute returns.
I Conclusion - No consensus but tentative yesCost of Capital
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Estimating Cost of Capital
How important is the increased precision from 15 minutereturns?
I Daily sampling gives uncertainty (95% CI) of about 1, 15minute of about 0.2
I Simple illustration of e¤ect on valuation, sayE (Rm)� rf = 3%, rf = 2% Company with constant growthin dividends of 2%, last dividend 1$. Point estimate of beta1.5.
I Daily sampling gives beta between 1.0 and 2.0, 15 minutesampling gives beta between 1.4 and 1.6,
I How much will this e¤ect the equity value of a company witha constant growth of dividends of 2%, last dividend 1$.value = 1/(k � g)
Cost of Capital
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Estimating Cost of Capital
How important is the increased precision from 15 minutereturns?
I Daily beta Capital cost between 5% and 8%. Value between1/(k � g) = 1/(0.050� 0.02) : 33. 33$ and1/(0.080� 0.02) = 16. 67$
I 15 minute beta Capital cost between 6.2% and 6.8%. Valuebetween 1/(k � g) = 1/(0.062� 0.02) = 23. 81$ and1/(0.068� 0.02) = 20. 83$
Cost of Capital
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Estimating Cost of Capital
Time varying risk aversion
Figure: Source: Bollerslev et al. (2009, JEc)
Cost of Capital
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Estimating Cost of Capital
Time varying risk aversion
Figure: Source: Bollerslev et al. (2009, JEc)
I Conclusion - yes (not everyone agrees)
Cost of Capital
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Estimating Cost of Capital
Time varying variance
Figure: Variance from 1960-2000
I Conclusion - Yes clear consensus
Cost of Capital
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Estimating Cost of Capital
Stock return predictability
I Emerging consensus that stock returns are predictable (achange since the book was written)
I Taken as evidence of time varying risk premium, not asevidence against EMH
I Remember EMH says risk adjusted returns areunpredictable, not regular returns
I Conclusion: The cost of equity is time-varying but it isextremely hard to estimate over short periods of time so wemay be better of using a constant cost of equity
Cost of Capital
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Estimating Cost of Capital
Hybrid �nancing
I Mix of debt and equity such as convertible bonds, options,CDS instruments etc.
I Can be broken down to basic parts using replicating portfoliosI E.g. Convertible bond = Corporate bond + Call option, Calloption = Risk free bond + company stock
I More on this on the real option lectures
Cost of Capital