January 2005

Regressions of Multiples on Fundamentals: Market Wide

The following regressions were run across four groupings. The first and most comprehensive set of regressions were run across all traded companies in the United States. The second set of regressions were run across all traded companies in Western Europe and the UK. The third set of regressions were run across companies in emerging markets in Asia, Eastern Europe and Latin America. The final set of regressions were run across just Japanese companies.

I have run the regressions with and without the intercept for most of the variables. Where the intercept is positive, I have reported on that regression. Where the intercept is negative, I have reported the regression without the intercept. The R squared reported are from the regressions with intercepts (since the R squared are artificially high when you remove the intercept).

All of the percentages are entered as absolute values (I am sorry but I have gone back and forth with this... In this iteration, all numbers are absolute values). Thus, a firm with an expected growth rate of 30%, a payout ratio of 10% and a beta of 1.25 can be expected to have a PE of:
PE = 2.9127 (30) + .3774 (10) - 21.62 (1.25) = 64.13

The variables used in the regressions are listed below.

• g = Expected growth in earnings over the next 5 years
• g(rev) = Expected growth rate in revenues over the next 5 years (If you do not have this, use the expected growth rate in EPS)
• PE = Price/ Current EPS
• PBV = Market value of equity/ Book value of equity
• PS = Market value of equity / Revenues in most recent financial year
• Enterprise Value = Market Value of Equity + Market Value of Debt - Cash and Marketable Securities
• Payout = DPS/EPS: from most recent year; if dividends are postive and earnings are negative, it is set to 100%.
• Debt/Capital = Book Value of Debt/ (Book value of Debt + Market value of equity)
• Beta = Betas based upon 3 years of data (You can use alternate periods or intervals)
• Net Margin = Net Income / Sales
• After-tax Operating Margin = EBIT (1-tax rate) /Sales
• Tax Rate = Effective tax rate in most recent year
• ROE = Net Income / BV of Equity
• ROC + EBIT (1-t)/ (BV of Debt + BV of Equity)
• Reinvestment Rate = (Cap ex - Depreciation + Chg in non-cash WC)/ EBIT (1 - tax rate)
• Std dev in Stock Prices = Standard deviation in stock prices over last 5 years. You can use alternate intervals.

### United States

Equity Multiples

PE = 14.781 + 0.914 g - 0.0489 Payout + 0.220 Beta (R2 = 23.6%) [Details]

PEG = 8.530 + 0.730 Beta -0.0008 Payout - 2.727 ln(g) (R2 = 31.0%) [Details]

Relative PE = 0.392 + 0.522 Relative Growth +0.0151 Beta (R2= 25.2%) [Details]

PBV= 0.202 ROE - 0.297 Beta + 0.0984 g - 0.0135 Payout (R2= 51.5%) [Details]

PS= 0.0516 g - 0.0069 Payout - 0.0705 Beta + 0.219 Net Margin (R2= 61.3%) [Details]

Firm Value Multiples

Enterprise Value/Book Capital= 1.851 + .149 g (rev) + .0406 (Return on Capital) - 0.0413 (Debt/Capital) - 0.0026 Reinvestment Rate(R2 = 49.9%) [Details]

Enterprise Value/Sales = 0.182 g(rev) + 0.0861 After-tax Operating Margin -.0256 (Debt/Capital) - 0.0013 Reinvestment Rate (R2 = 48.3%) [Details]

Enterprise Value /EBITDA= 8.554 + 1.016 g(rev) - .150 (Tax rate) -.0664 (Debt/Capital) -0.0188 Reinvestment Rate (R2=38.0 %) [Details]

To see the more detailed output from the regression, click on 'Details'.

### Europe

PE = 13.325+ .239 Payout Ratio -1.470 Beta + 0.271 g (R2 = 6.7%) [Details]

PBV = 2.149 + .0015 Payout Ratio -0.464 Beta + .111 ROE (R2 = 24.5%) [Details]

PS = 0.418 + .0064 Payout Ratio -0.176 Beta + .184 Net Margin (R2 = 38.8%) [Details]

EV/Book Capital= 1.179 +0.0897 Return on Capital + 0.0071 g - 0.00004 Reinvestment Rate (R2=40.9%) [Details]

EV/EBITDA = 16.80 + 0.518 (Debt/Capital) +0.0006 Reinvestment Rate- .356 Tax Rate (R2=30.3%) [Details]

EV/Sales = 0.163 + 0.0376 (Debt/Capital) -.00002 Reinvestment Rate +0.202 After-tax Operating Margin (R2=45.6%) [Details]

### Emerging Markets

PE = 7.189 + .0676 Payout Ratio + 3.057 Beta + 0.460 g (R2 = 20.2%) [Details]

PBV = 1.337 + 0.0228 g + .0005 Payout Ratio - 0.839Beta + 0.109 ROE (R2 = 27.2%) [Details]

PS =0.053 + .0007 Payout Ratio -0.307 Beta + .155 Net Margin + 0.0232 g (R2 = 50.6%) [Details]

EV/Book Capital = 2.38 +.05 Return on Capital -.034 (Debt/Capital) +.0009 Reinvestment Rate ( R2 = 23.7%) [Details]

EV/EBITDA = 15.619 - 0.135 (Debt/Capital) + 0.0116 Reinvestment Rate- .114 Tax Rate + 0.178 g (R2= 7.2%) [Details]

EV/Sales = -0.0345 - 0.0105 (Debt/Capital) +.0003 Reinvestment Rate +0.198 After-tax Operating Margin + 0.0316 g (R2=41.2%) [Details]

### Japan

PE = -8.110 + .528 Payout Ratio + 14.605 Beta + 0.799 g (R2 = 32.5%) [Details]

PBV = -0.06 - 0.649 Beta + .217 ROE +.0009 Payout Ratio + 0.0478 g (R2 = 54.9%) [Details]

PS = -0.760 + 0.0045 Payout Ratio - 0.670 Beta + .325 Net Margin + 0.0456 g (R2 = 60.0%) [Details]

EV/EBITDA = 24.24 + 0.072 (Debt/Capital) +.0108 Reinvestment Rate- 0.397 Tax Rate (R2=9.8 %) [Details]

EV/Book Capital= -0.246 + 0.0073 (Debt/Capital)+ 0.157 Return on Capital + 0.0003 Reinvestment Rate + 0.9272 g (R2= 66.3%) [Details]

EV/Sales = -3.557 + 0.0545 (Debt/Capital)+ 0.508 After-tax Operating Margin + 0.0019 Reinvestment Rate + 0.0346 g (R2= 69.8%) [Details]