January 2008

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 for regressions without intercepts cannot be directly compared to the regressions with intercepts - they will be higher.

All of the percentages are entered in decimals (I am sorry but I have gone back and forth with this... In this iteration, all numbers are decimals). 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 = 2.74 + 142.63 (.30) + 5.67 (.10) + 0.55 (1.25) = 46.78

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 = 2.74 + 142.63 g + 5.67 Payout +0.55 Beta (R2 = 41.8%) [Details]

PEG = 0.133 Beta + 0.541 Payout - 0.78 ln(g) (R2 = 82.5%) [Details]

PBV= 18.02 g - 2.344 Payout - 0.110 Beta + 17.3 ROE (R2= 64.0%) [Details]

PS= 14.93 g - 1.892 Payout - 0.632 Beta + 21.83 Net Margin (R2= 74.3%) [Details]

Firm Value Multiples

Enterprise Value/Book Capital= 41.33 g (rev) + 11.34 (Return on Capital) - 8.67 (Debt/Capital) (R2 = 70.0%) [Details]

Enterprise Value/Sales = 26.49 g(rev) + 7.56 Pre-tax Operating Margin - 4.67 (Debt/Capital) (R2 = 74.7%) [Details]

Enterprise Value /EBITDA= 4.490 + 96.97 g(rev) - 9.28 (Tax rate) + 1.745 Return on Capital - 1.837 Reinvestment Rate (R2=44.8 %) [Details]

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

### Europe

PE = 14.15 + 7.488 Payout Ratio -2.62 Beta + 29.06 g (R2 = 17.9%) [Details]

PBV = 1.475 + 2.37 g + 0.05 Payout Ratio - 0.88 Beta + 12.58 ROE (R2 = 38.6%) [Details]

PS = 1.085 -0.03 Payout Ratio + 1.68 g - 0.605 Beta + 12.34 Net Margin (R2 = 32.8%) [Details]

EV/Book Capital= 2.446 + 4.702 Return on Capital - 2.29 Debt/Capital (R2= 27.7%) [Details]

EV/EBITDA = 6.54+ 43.75 (Debt/Capital) + 2.91 g- 12.45 Tax Rate (R2=31.5%) [Details]

EV/Sales =0.955 + 6.785 (Debt/Capital) +6.064 After-tax Operating Margin (R2=25.6%) [Details]

### Emerging Markets

PE = 5.63 + 2.707 Payout Ratio + 11.354 Beta + 92.72 g (R2 = 13.9%) [Details]

PBV = 10.02 g + .205 Payout Ratio + 1.362 Beta + 14.27 ROE (R2 = 72.1%) [Details]

PS = 0.071 Payout Ratio + 8.37 g + 1.03 Beta + .16.03 Net Margin (R2 = 69.3%) [Details]

EV/Book Capital= 5.262 +6.189 Return on Capital - 13.268 Debt/Capital + 5.97 g (R2=33.3%) [Details]

EV/EBITDA = 41.85+ 63.79 (Debt/Capital) + 52.72 g- 46.65 Tax Rate (R2=12.7%) [Details]

EV/Sales = 4.412 +7.086 g -10.58 (Debt/Capital) +16.10 After-tax Operating Margin (R2=27.5%) [Details]

### Japan

PE = 13.55 + 26.05 Payout Ratio + 1.25 Beta + 11.87 g (R2 = 18.4%) [Details]

PBV = 0.407 - 0.503 Beta + 19.26 ROE +.175 Payout Ratio (R2 = 33.9%) [Details]

PS = 0.85 - 0.019 Payout Ratio - 0.406 Beta + 13.51 Net Margin + 0.405 g (R2 = 36.6%) [Details]

EV/EBITDA = 5.30 + 20.98 (Debt/Capital) +16.38 Return on Capital - 3.15 Tax Rate (R2=14.6 %) [Details]

EV/Book Capital= 1.25+ 0.665 (Debt/Capital)+ 6.735 Return on Capital (R2= 53.4%) [Details]

EV/Sales = 3.954 (Debt/Capital)+ 18.183 After-tax Operating Margin (R2= 59.1%) [Details]