January 2007

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
• Relative Growth = Expected growth in earnings/ Average growth rate for market
• 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
• Relative PE = Current PE for company/ Average for the market
• 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%.
• Relative Payout = Payout/ Average payout ratio for market
• Debt/Equity = Book Value of Debt/ Market value of Equity
• Debt/Capital = Book Value of Debt / (Book value of Debt + Market value of Equity)
• Beta = Betas based upon 5 years of data (You can use alternate periods, intervals or betas from an estimation service)
• Net Margin = Net Income / Sales
• After-tax Operating Margin = EBIT (1-tax rate) /Sales
• Pre-tax Operating Margin = EBIT/ 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- Cash )
• 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 = 10.645 + 1.178 g + 0.074 Payout - 2.621 Beta (R2 = 41.4%) [Details]

PE = 11.298 + 1.169 g - 2.834 Beta (R2 = 40.0%) [Details]

PEG = 6.480 + 1.060 Beta - 0.007 Payout - 2.140 ln(g) (R2 = 21.4%) [Details]

Relative PE =0.239+ 0.470 Relative g + 0.012 Relative Payout - 0.060 Beta (R2= 40.8%) [Details]

PBV= 0.161 ROE - 0.970 Beta + 0.155 g (R2= 59.8%) [Details]

PS= 0.100 g - 0.0031 Payout - 0.966 Beta + 0.212 Net Margin (R2= 63.4%) [Details]

Firm Value Multiples

Enterprise Value/Book Capital= 0.171 g (rev) + .120 (Return on Capital) - 0.002 (Debt/Equity) (R2 = 57.1%) [Details]

Enterprise Value/Sales = 0.149 g(rev) + 0.080 Pre-tax Operating Margin - 0.012 (Debt/Equity) (R2 = 47.1%) [Details]

Enterprise Value /EBITDA= 6.081 + 0.926 g(rev) - .126 (Tax rate) - 0.068 (Debt/Equity)-0.0153 Reinvestment Rate (R2=36.5 %) [Details]

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

### Europe

PE = 18.364 + 0.036 Payout Ratio - 4.074 Beta + 0.578 g (R2 = 8.6%) [Details]

PBV = 0.512 + 0.093 g + .017 Payout Ratio -0.415 Beta + .135 ROE (R2 = 20.3%) [Details]

PS = 4.497 -0.017 Payout Ratio -1.368 Beta + .0.075 Net Margin (R2 = 15.4%) [Details]

EV/Book Capital= 1.874 +0.136 Return on Capital - 0.019 Debt/Capital (R2=23.8%) [Details]

EV/EBITDA = 19.069+ 0.412 (Debt/Capital) - 0.229 Return on Capital- .242 Tax Rate (R2=34.4%) [Details]

EV/Sales = 0.636 + 0.086 (Debt/Capital) +0.096 After-tax Operating Margin (R2=30.4%) [Details]

### Emerging Markets

PE = 11.603 + .080 Payout Ratio -0.115 Beta + 0.856 g (R2 = 26.4%) [Details]

PBV = 0.093 g+ .006 Payout Ratio - 0.414 Beta + 0.188 ROE (R2 = 48.4%) [Details]

PS = 0.564 + .002 Payout Ratio - 1.689 Beta + .281 Net Margin + 0.078 g (R2 = 30.3%) [Details]

EV/Book Capital = 1.737 +.138 Return on Capital -.016 (Debt/Capital) -0.002 Reinvestment Rate (R2 = 52.2%) [Details]

EV/EBITDA = 36.421 - 0.385 (Debt/Capital) -0.336 Return on Capital- .265 Tax Rate + 0.282 g (R2= 14.4%) [Details]

EV/Sales = 5.062 - 0.065 (Debt/Capital) +0.107 After-tax Operating Margin (R2=25.3%) [Details]

### Japan

PE = 0.702 Payout Ratio + 6.237 Beta + 0.263 g (R2 = 37.3%) [Details]

PBV = 0.246 Beta + .181 ROE +.010 Payout Ratio (R2 = 34.6%) [Details]

PS = 0.012 Payout Ratio - 0.017 Beta + 0.203 Net Margin (R2 = 54.3%) [Details]

EV/EBITDA = 10.104 + 0.196 (Debt/Capital) +0.124 Return on Capital - 0.065 Tax Rate (R2=11.5 %) [Details]

EV/Book Capital= 0.0009 (Debt/Capital)+ 0.268 Return on Capital (R2= 54.6%) [Details]

EV/Sales = 0.0497 (Debt/Capital)+ 0.276 After-tax Operating Margin - 0.0121 Tax Rate (R2= 51.8%) [Details]