Cost Of Capital Slides

Estimating Cost of Capital

Estimating Cost of Capital Anders Vilhelmsson Department of Business Administration, Lund University

September 2009

Cost of Capital

Estimating Cost of Capital

Aim of the 2 lectures

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Cover chapter 10 in the book

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Cover relevant research, particularly from 2004 (when the book was updated) until 2009

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Slides can be found after the lecture at www.nek.lu.se/nekavi

Cost of Capital

Estimating Cost of Capital

Valuation

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Easy in theory, the total value of a company is the present value of all future cash ‡ows

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V =

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However, k is unknown and may not be constant over time

CF 1 1 +k

+

CF 2 (1 +k )2

+

CF 3 (1 +k )3

+

CF 4 (1 +k )4

+

Cost of Capital

CF 5 ... (1 +k )5

Estimating Cost of Capital

WACC

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WACC = VD kd (1 Tm ) + VE ke D = Value of debt V = Enterprise value kd = Current borrowing rate (tax deductible) Tm = Corporate (marginal) tax rate (e.g. 26.3% in Sweden) E = Value of equity ke = Cost of equity I

Example 1 on the board

Cost of Capital

Estimating Cost of Capital

WACC

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Why do we need 2 full lectures to do the above calculations?

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kd and especially ke are unobservable

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We need theory (models) to estimate kd and ke

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In practice it may also be non-trivial to calculate (target) and VE

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We will put most e¤ort in estimating ke correctly since the uncertainty is largest in this number.

Cost of Capital

D V

Estimating Cost of Capital

Cost of debt

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Primary problem, non-‡at term structure of interest rates

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In principle 1 year CF should be matched with 1 year debt rate, 2 year CF with 2 year rate and so on

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In practice match with the duration on the company’s CFs

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Growth stocks, high duration, value stocks low duration

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The book recommends about 10 years for all companies

Cost of Capital

Estimating Cost of Capital

Duration I

Macaulay’s Duration: n

D= ∑

t

t =1

I

PV (CF t ) V

n

= ∑

t

t =1

CF t /(1 +r )t V

V = Enterprise Value

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Do loan example on the board

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What happens with the sum is in…nite (e.g. CF from a stock)?

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D= ∑

n

t

t =1

I

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Dcv =

PV (CF t ) V 1 r g

+ (n + Dcv ) PV (VCVn )

Duration of continuing value, derive on the board.

Do stock example on the board

Cost of Capital

Duration

Figure: Source: Own calculations

Term structure of interest rates

Estimating Cost of Capital

Estimate cost of debt

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Use Yield to maturity (YTM) on long term bond

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YTM > kd but small di¤erence for BBB companies and better

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P=

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Solve for YTM but this is an n:th order equation (numerical solution)

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Calculate YTM in Excel example

C 1 +ytm

+

C (1 +ytm )2

+

C ... C +P n (1 +ytm )3 (1 +ytm )

Cost of Capital

Cost of debt vs YTM YTM as a function of Recovery rate and defualt prob. cost of debt is 6%

0.45 0.4 0.35

YTM

0.3 0.25 0.2 0.15 0.1 0.05 0.25

0.13

0 .01 Default probability

0

0.05

0.10

0.15

0.20

0.25

Recovery rate

Figure: Source: Own calculations

0.30

0.35

0.40

0.45

0.50

Estimating Cost of Capital

Estimate cost of debt

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What to do with companies that only have untraded or short debt? I I

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Find credit rating Compare to traded long bonds with the same credit rating

What to do with companies with
Use BBB cost of debt and add 0.5% units (motivated by 0.1 higher CAPM beta)

Cost of Capital

Estimating Cost of Capital

Estimate cost of equity

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Estimating the cost of equity is the same thing as explaining the cross section of stock returns

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Why do companies have di¤erent expected returns? I I

Theory: Because of di¤erent exposure to systematic risk factor(s) CAPM, FF3, momentum, liquidity, risk aversion (APT)

Cost of Capital

Estimating Cost of Capital

The CAPM

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Security market line (SML) E [Ri ] = rf + βi (E [Rm ]

rf )

E [Ri ] = Expected return on asset i rf = risk free rate E [Rm ] = Expected return on the market portfolio cov (R i ,R m ) systematic risk in asset i βi = σ2 m

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Problem: E [Ri ], E [Rm ] and βi are all unobservable and rf varies with maturity

Cost of Capital

Estimating Cost of Capital

Estimating the risk free rate

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Same thing as with the cost of debt (Match each cash ‡ow)

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Make sure cash ‡ows and cost of capital uses the same currency

Cost of Capital

Estimating Cost of Capital

Estimating the market risk premium

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Interesting working paper at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1473225

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Compares the recommended market risk premium from 150 di¤erent textbooks

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CAPM actually gives the market risk premium as E (Rm ) rf = γσ2m assuming CRRA utility

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σ2m can, at least historically, be observed but not γ (the relative risk aversion)

Cost of Capital

Estimating the market risk premium

Figure: Source: Fernández (2009,WP)

Estimating Cost of Capital

Estimating the market risk premium

Figure: Source: Fernández (2009,WP)

Cost of Capital

Estimating Cost of Capital

Estimating Beta

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Lets look at the recommendations given by the book I I I

Use at least 60 data points Use monthly data Use SP500 or MSCI world index as market portfolio

Cost of Capital

Estimating Cost of Capital

At least 60 data points

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Number of data points is a trade o¤ between I I I

Precision and possible time variation If you think that beta is constant over time use all data you have 60 data points in not a magic number, happens to be 5 years of monthly data

Cost of Capital

Estimating Cost of Capital

Use monthly data I

Use monthly frequency - good idea if stock is very illiquid (traded infrequently)

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For e.g. the 30 stocks in Dow Jones you can use daily of even intra-daily (15-30 minute data)

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Andersen et al. (2006) (Dow Jones 30 between 15 minutes and 1 day),

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Lewellen and Nagel (2006, JFE) daily and weekly on all NYSE stocks

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You can also adjust (Dimson 1979, JFE) for infrequent trading

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Bid ask Bounce can be …xed by calculating returns using midquotes instead of transaction prices (bid price + ask price )/2

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Currently there is a shift towards use of higher frequency in beta estimation Cost of Capital

Estimating Cost of Capital

Use a broad market portfolio

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Use a broad value weighted stock index to calculate betas, otherwise their is no theoretical foundation.

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Never use a local market index, in e.g. Finland you would basically measure a stock’s sensitivity towards Nokia

Cost of Capital

Estimating Cost of Capital

Industry betas

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Idea: Improve precision in beta by using the mean beta of the industry (adjusted for leverage)

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Assumes that companies in the same industry has the same systematic operational risk

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Di¤erent betas within an industry is only due to di¤erent leverage

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Master thesis topic: How well does this assumption hold empirically?

Cost of Capital

Estimating Cost of Capital

How to calculate an industry beta

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First compute betas for all companies in the industry with regression analysis

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Unleverage beta with

Vu V u +V txa βu

+ VuV+txaVtxa βtxa = D D+E βd + D E+E βe ) βe = βu + DE ( βu βd ) + VEtxa ( βtxa βu ) assume βd = 0 and βu = βtxa ) βe = βu (1 + DE ) I

Do calculations on the board

Cost of Capital

Estimating Cost of Capital

How to calculate an industry beta

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Average βu over all companies

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Relever to each companies target

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Example on the board

D E

ratio

Cost of Capital

Estimating Cost of Capital

Other factor models I

Eugene Fama and Kenneth French 3 factor model FF3, Fama and French (1992, JoF)

E [Ri ] = rf + βi ,m (E [Rm ] rf ) + βi ,smb E [SMB ] + βi ,HML E [HML] SMB is the return on a small stock portfolio minus a big stock portfolio (small minus big) HML is the return on a high book to market minus a low book to market portfolio (high minus low) I

Is SMB and HML capturing risk exposure or misspricing?

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Still open research question, enough papers to be the topic for a separate course

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Momentum, Jegadeesh and Titman (1993,RFS) and Liquidity, Amihud (2002) are other prominent factors

Cost of Capital

Sample period is from March 1990 to April 2004 Panel A: 25 portfolios sorted on Book-to-market and size

λMKT CAPM

λSMB

λHML

λMOM

λMIM RA

-0.626

R2 0.27

[-0.87] CAPM+MIM RA FF3 FF3+MIM RA FF3+MOM+MIM RA

-0.935

-0.020

[-1.51]

[-2.07]

-1.602

0.141

0.353

[-2.92]

[0.46]

[1.24]

-0.988

0.174

0.289

[-1.41]

[0.57]

[1.03]

-0.666

0.178

0.325

1.895

-0.025

[-0.83]

[0.59]

[1.16]

[2.11]

[-2.80]

0.64 0.60

-0.023

0.66

[-2.61]

Source: Nyberg and Wilhelmsson (forthcoming, The …nancial review)

0.68

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 CAPM

λSMB

λHML

λMOM

λMIM RA

-0.031

R2 0.00

[-0.06] CAPM+MIM RA FF3 FF3+MIM RA FF3+MOM+MIM RA

-0.202

-0.012

[-0.41]

[-1.23]

-0.144

0.110

0.033

[-0.29]

[0.36]

[0.11]

0.019

0.154

-0.008

[0.04]

[0.50]

[-0.03]

0.176

0.141

0.013

1.211

-0.025

[0.31]

[0.46]

[0.04]

[1.34]

[-2.93]

0.15 0.03

-0.027

0.31

[-3.12]

Source: Nyberg and Wilhelmsson (forthcoming, The …nancial review)

0.33

Estimating Cost of Capital

In defence of beta I

Builds on solid theory I

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FF3 purely empirical evidence, no theory, size premium vanishing I

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Assumes multivariate normal distribution or investors with preferences for only mean and variance (both assumptions are wrong)

rejecting FF3 does not really support CAPM we have more than 2 competitors (evolution/creationism)

CAPM may hold conditionally (beta should be forward looking) I

E¤ect is too small to save CAPM according to Lewellen and Nagel (2006, JFE)

Cost of Capital

Estimating Cost of Capital

Importance of model selection

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How important is the selection of factor model? Lets try to …nd out!

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Calculate cost of equity for J&J using CAPM and FF3 in Excel.

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Is the J&J results typical or not? Possible master thesis topic.

Cost of Capital

Estimating Cost of Capital

Is the cost of equity time varying / are stock returns predictable ?

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E [ri ]

rf = βi [E (Rm )

rf ]

γσ2m

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E (Rm )

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Three possible sources of time variation

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Time varying betas

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Time varying risk aversion

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Time varying volatility

rf =

Cost of Capital

Estimating Cost of Capital

Time varying betas

Figure: Source: Andersen et al. (2004) AA is Alcoa, ALD is Allied capital corporation, DD is DuPont, and DIS is WaltDisney.The sample covers theperiod from 1962:3 through 1999:3. Cost of Capital

Estimating Cost of Capital

Time varying betas

Figure: Source: Andersen et al. (2004) Cost of Capital

Estimating Cost of Capital

Time varying betas

Figure: Source: Andersen et al. (2004) The sample covers the period from 1993:2 through 1999:3. We calculate the realized quarterly betas from daily returns. Cost of Capital

Estimating Cost of Capital

Time varying betas

Figure: Source: Andersen et al. (2004) The sample covers the period from 1993:2 through 1999:3. We calculate the realized quarterly betas from 15 minute returns. Cost of Capital

Estimating Cost of Capital

How important is the increased precision from 15 minute returns? I

Daily sampling gives uncertainty (95% CI) of about 1, 15 minute of about 0.2

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Simple illustration of e¤ect on valuation, say E (Rm ) rf = 3%, rf = 2% Company with constant growth in dividends of 2%, last dividend 1$. Point estimate of beta 1.5.

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Daily sampling gives beta between 1.0 and 2.0, 15 minute sampling gives beta between 1.4 and 1.6,

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How much will this e¤ect the equity value of a company with a constant growth of dividends of 2%, last dividend 1$. value = 1/(k g )

Cost of Capital

Estimating Cost of Capital

How important is the increased precision from 15 minute returns?

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Daily beta Capital cost between 5% and 8%. Value between 1/(k g ) = 1/(0.050 0.02) : 33. 33$ and 1/(0.080 0.02) = 16. 67$

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15 minute beta Capital cost between 6.2% and 6.8%. Value between 1/(k g ) = 1/(0.062 0.02) = 23. 81$ and 1/(0.068 0.02) = 20. 83$

Cost of Capital

Estimating Cost of Capital

Time varying risk aversion

Figure: Source: Bollerslev et al. (2009, JEc)

Cost of Capital

Estimating Cost of Capital

Time varying risk aversion

Figure: Source: Bollerslev et al. (2009, JEc)

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Conclusion - yes (not everyone agrees)

Cost of Capital

Estimating Cost of Capital

Time varying variance

Figure: Variance from 1960-2000

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Conclusion - Yes clear consensus Cost of Capital

Estimating Cost of Capital

Stock return predictability

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Emerging consensus that stock returns are predictable (a change since the book was written)

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Taken as evidence of time varying risk premium, not as evidence against EMH

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Remember EMH says risk adjusted returns are unpredictable, not regular returns

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Conclusion: The cost of equity is time-varying but it is extremely hard to estimate over short periods of time so we may be better of using a constant cost of equity

Cost of Capital

Estimating Cost of Capital

Hybrid …nancing

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Mix of debt and equity such as convertible bonds, options, CDS instruments etc.

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Can be broken down to basic parts using replicating portfolios

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E.g. Convertible bond = Corporate bond + Call option, Call option = Risk free bond + company stock

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More on this on the real option lectures

Cost of Capital