Cost of Capital

Dr. Laura Grassi laura.grassi@polimi.it

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Components of WACC

Es#ma#ons of Beta

Agenda

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WACC is the Weighted Average Cost of Capital of the firm

Weighted Average Cost of Capital - WACC

WACC =Ke ED+E

!

"#

$

%&+Kd(1 tc)

DD+E

!

"#

$

%&

Kd is the cost of debt for a firm

i.e. the interest that the firm has to pay on financial debts to remunerate the debtholders for the risk they take by providing debt capital to the firm

on the other hand, Kd is a return for debtholders

Kd can be computed as:

The credit default spread is associated with the the company credit ra#ng

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Cost of debt Kd

Kd= rf+CreditDefaultSpread

Lets assume

Two companies are iden#cal (same business, same size etc.) but they have a different capital structure. Company A has D/E=5 while company B has D/E=1

All the rest being equal, which company has has the riskier profile? Two companies are iden#cal (same business, same size, same capital structure

etc.) but company C has a liquidity shortage while company D has stable cash flows.

All the rest being equal, which company has the riskier profile?

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Cost of Equity Ke

Ke is the cost of equity capital of a firm

i.e. the interest that the firm pays to its shareholders to remunerate them for the risk they take by providing equity capital to the firm

on the other hand, Ke is the minimum expected return for shareholders We can es1mate Ke using the CAPM (Capital Asset Pricing Model) method rf= risk-free rate BL= Beta levered (equity beta) rm= market return (rm-rf)= market premium

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Ke= rf+L rmrf( )

Risk free rate rf

rf is the theore1cal return on an investment with no risk

Does a risk free investment exist?

Can we use a proxy? We use the return on government bonds since they are (generally) less

risky than corporate bonds

In Eurozone the 10Y German Bund is used as a proxy of the risk free rate

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Risk free rate rf

List of some European 10Y government bonds (update Sept.2014, Sole24Ore)

Market Return

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Risk free rate rf

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http://www.bloomberg.com/markets/rates-bonds/ as of 16 October 2014

Market Return rm

rm is the return on theore1cal market porZolio which contains all the stocks in

the market

We can use a proxy?

We use market indexes which are representa9ve of the market in which the company operates

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Lets assume

You want to evaluate the Ke of a company opera#ng only in Italy

Which rf and market index would you use?

You want to evaluate the Ke of a company opera#ng only in the US

Which rf and market index would you use?

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Market index

Index Country Description

FTSE MIB Italy 40 most liquid and capitalised Italian shares traded on Borsa Italiana

DAX Germany 30 largest and most liquid German companies traded on the Frankfurt Exchange

CAC 40 France 40 largest and most liquid French companies traded on the Paris Bourse

FTSE 100 UK 100 largest and most liquid Bri#sh companies traded on the London Stock Exchange

EUROSTOXX 50 Eurozone 50 largest and most liquid European companies traded on the Eurozone

S&P 500 US 500 largest and most liquid US companies traded on NYSE or NASDAQ

DOW JONES US 500 largest and most liquid US companies traded on NYSE or NASDAQ

NASDAQ composite

US 3000 largest and most liquid US companies traded on NASDAQ

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Beta

L measures how vola#le is the firm stock if compared to the overall market

movements

BL>1 means that the stock is more vola#le than the market (i.e. aggressive)

BL=1 means that the stock is as vola#le as the market BL

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Components of WACC

Es9ma9ons of Beta

Agenda

L and U

L measures how vola#le is a stock if compared to the overall market movements

It depends on the capital structure of the firm Also known as equity beta

U measures how vola#le is the underlying business, irrespec#ve of the firms capital

structure It depends on the industry/business of a firm but not on the capital structure of

the firm! Also known as asset beta

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L

HOW TO ESTIMATE IT? In case of a listed company: it can be computed through a regression of the stock returns against

the market returns In case of an unlisted company: we cannot use the regression since basically the company does not

have listed stocks. In this case, we have to infer the unlevered beta. We can follow two

methods:

Comparable companies Beta industry

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L estimation (comparable companies)

U L

Capital Structure

U L

Capital Structure

U L

Capital Structure

U, avg L

Capital Structure

L comparables L target?

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L estimation (comparable companies)

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1. We take comparable companies for which we have L 2. We compute the U of each comparable company (i.e. by stripping out the

capital structure characteris#cs from L)

3. We compute the average beta U,avg of the comparable companies 4. We re-lever U,avg with the capital structure characteris#cs of the target

company

U,comp =L ,comp

(1+(1 tc,comp)(DcompEcomp

))

L ,target =U,avg(1+(1 tc,target )(DtargetEtarget

))

L estimation (Industry beta)

Industry Number of firms Avg. Levered

Beta Market D/E

ra9o Tax rate Unlevered

Beta Oil-Gas Distribu#on 12 1,02 53,4% 18,1% 0,71 Restaurant 65 1,16 13,2% 19,2% 1,05 Drug 223 1,08 14,8% 5,1% 0,94 Biotechnology 214 1,23 15,9% 3,0% 1,07 Internet 194 1,17 2,3% 8,4% 1,15 Entertainment 76 1,60 33,9% 12,6% 1,24 Bank 416 0,77 128,2% 16,4% 0,37 Steel 33 1,65 56,2% 24,2% 1,16 Automo#ve 12 1,73 103,4% 16,2% 0,93 Natural gas u#lity 27 0,46 66,2% 28,8% 0,31 Water u#lity 11 0,49 73,2% 31,5% 0,33

As second best as beta unlevered it could be used the one of the industry in which the company operates

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L ,target =U,Industry (1+(1 tc,target )(DtargetEtarget

))