January 2006

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 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
• 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)
• 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 = 6.747 + 1.131 g + 0.073 Payout -0.919 Beta (R2 = 30.7%) [Details]

PEG = 4.273 -0.417 Beta + 0.008 Payout - 0.830 ln(g) (R2 = 21.5%) [Details]

Relative PE =1.381 Relative Growth + 1.065 Relative Payout-1.062 Beta (R2= 67.8%) [Details]

PBV= 0.170 ROE - 0.841 Beta + 0.117 g +0.001 Payout (R2= 55.6%) [Details]

PS= 0.0839 g - 0.0069 Payout - 0.832 Beta + 0.218 Net Margin (R2= 58.4%) [Details]

Firm Value Multiples

Enterprise Value/Book Capital= 0.211 g (rev) + .102 (Return on Capital) - 0.003 (Debt/Equity) - 0.008 Reinvestment Rate (R2 = 57.3%) [Details]

Enterprise Value/Sales = 0.177 g(rev) + 0.067 Pre-tax Operating Margin - 0.0065 Reinvestment Rate (R2 = 52.6%) [Details]

Enterprise Value /EBITDA= 0.03 + 1.296 g(rev) - .051 (Tax rate) + 0.012 Return on Capital -0.0168 Reinvestment Rate (R2=50.9 %) [Details]

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

### Europe

PE = 29.628 - 0.204 Payout Ratio + 0.547 Beta + 0.237 g (R2 = 4.3%) [Details]

PBV = 1.471 - .009 Payout Ratio +0.372 Beta + .113 ROE (R2 = 31.3%) [Details]

PS = 2.049 -0.010 Payout Ratio -0.478 Beta + .139 Net Margin (R2 = 30.3%) [Details]

EV/Book Capital= 1.737 +0.138 Return on Capital - 0.002 Reinvestment Rate - 0.016 Debt/Capital (R2=52.2%) [Details]

EV/EBITDA = 22.96 + 0.407 (Debt/Capital) - 0.023 Reinvestment Rate- .419 Tax Rate (R2=25.4%) [Details]

EV/Sales = 0.102 (Debt/Capital) -.007 Reinvestment Rate +0.189 After-tax Operating Margin (R2=59.0%) [Details]

### Emerging Markets

PE = 5.579 + .0524 Payout Ratio -0.705 Beta + 0.816 g (R2 = 34.5%) [Details]

PBV = 2.446 + .0101 Payout Ratio - 0.349 Beta + 0.124 ROE (R2 = 12.0%) [Details]

PS = 1.453+ .0122 Payout Ratio -0.514 Beta + .185 Net Margin + 0.0232 g (R2 = 36.8%) [Details]

EV/Book Capital = 3.45 +.097 Return on Capital -.067 (Debt/Capital) ( R2 = 35.3%) [Details]

EV/EBITDA = 32.534 - 0.441 (Debt/Capital) + 0.0264 Reinvestment Rate- .292 Tax Rate (R2= 8.4%) [Details]

EV/Sales = 1.613 - 0.059 (Debt/Capital) +.006 Reinvestment Rate +0.214 After-tax Operating Margin (R2=42.5%) [Details]

### Japan

PE = 0.457 Payout Ratio + 12.839 Beta + 0.441 g (R2 = 46.9%) [Details]

PBV = 0.983 Beta + .166 ROE +.0026 Payout Ratio (R2 = 36.1%) [Details]

PS = 0.0014 Payout Ratio + 0.220 Beta + 0.291 Net Margin (R2 = 49.6%) [Details]

EV/EBITDA = 17.60 + 0.320 (Debt/Capital) +0.311 Return on Capital - 0.250 Tax Rate (R2=10.3 %) [Details]

EV/Book Capital= 1.360 - 0.0208 (Debt/Capital)+ 0.0021 Reinvestment Rate + 0.179 Return on Capital (R2= 45.3%) [Details]

EV/Sales = 0.0397 (Debt/Capital)+ 0.349 After-tax Operating Margin + 0.0040 Reinvestment Rate (R2= 51.9%) [Details]