Demystifying the Use of Beta in the Determination of the Cost of Capital and an Illustration of Its Use in Lazard’s Valuation of Conrail

Demystifying the Use of Beta in the Determination of the

Cost of Capital and an Illustration of Its Use in Lazard’s

Valuation of Conrail

Samuel C. Thompson, Jr.*

I. INTRODUCTION....................................................................................................................242

A. Net Present Value ........................................................................................................242

B. Cost of Capital.............................................................................................................243

C. Beta and the Capital Asset Pricing Model..............................................................244

D. Purpose of the Article.................................................................................................246

II. INTRODUCTION TO BETA...................................................................................................247

A. Systematic and Unsystematic Risk............................................................................247

B. Beta: A Measure of Systematic Risk.........................................................................249

C. Background Information on Return on the Market and on Four Securities .....249

III. DERIVATION OF BETA THROUGH THE USE OF COVARIANCE AND VARIANCE..........252

A. Introduction..................................................................................................................252

B. Expected Return ...........................................................................................................252

C. Variance........................................................................................................................254

D. Covariance...................................................................................................................258

1. Introduction ............................................................................................................258

2. Standard Deviation................................................................................................258

3. Correlation Coefficient.........................................................................................260

4. Computation of Covariance.................................................................................264

E. The Determination of Beta.........................................................................................264

IV. DERIVATION OF BETA THROUGH REGRESSION ANALYSIS ..........................................266

A. Introduction..................................................................................................................266

B. Scatter Diagrams .........................................................................................................266

C. The Method of Least Squares ....................................................................................268

D. Normal Equations for Least Squares Line..............................................................268

E. Shortcut Method for Computing Slope-Beta...........................................................275

F. Coefficient of Determination.....................................................................................277

V. DERIVATION OF BETA THROUGH THE USE OF EXCEL’S LINEAR REGRESSION

FUNCTON.............................................................................................................................282

* Professor and Director, Center for the Study of Mergers and Acquisitions, University of Miami School

of Law, and Tax Policy Advisor (on behalf of the United States Treasury Department), Ministry of Finance,

Republic of South Africa. The author would like to thank Tarek Sayed, a 1998 graduate of the University of

Miami School of Law and a student in the Graduate Program in Taxation at the University of Miami School of

Law, and Gheri Hicks, a third-year student at the University of Miami School of Law, for their assistance in the

preparation of this art icle.

300 The Journal of Corporation Law [Winter

Table VV (Part 2)

Computation of Conrail’s WACC

[5]

[Percentage

of Equity in

Capital

Structure

÷ø

ö

çè

æ

D + E

E

x

[6]

Cost of

Equity

(See column

[9][f])

=

[7]

Weighted

Average

Cost of

Equity

[8]

WACC

[Column [4] plus

column [7]]

(See Appendix A

column [11][g])

1. 100% x 11.8% = 11.80% 11.8%

2. 90% x 12.1% = 10.89% 11.5%

...