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# Berkshire Hathaway Inc. Message Board

• trysail1952 trysail1952 Oct 20, 2004 10:55 PM Flag

## Charts for quants

Appropriate P/E Ratios for various Risk Premiums:

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Effect of a change in the Risk Premium on the P/E Ratio:

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More charts for those with a quantitative bent. It appears to me that ye olde market is already discounting a 5-5� % 10-year Treasury if 2005 S&P earnings come in at the forecast area of \$72. Thirty-nine year growth of operating earnings (i.e., from 1966) to that level would be roughly 6.7%, roughly in line with the S&P. While stocks may not be demonstrably "cheap," one can make the case that they are valued to return 6-8%.
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• Hi trysail1952:

Thanks for posting the charts.

With regard to the first chart:
� Appropriate P/E Ratios for various Risk Premiums:�

I wonder what the equation is behind the curve?

I would have used:

Equation # 1 ("E" based on trailing earnings)

P/E = D/E * ( 1 + g ) / ( rfr + erp - g )

or

Equation # 1 ("E" based on forward earnings)

P/E = D/E / ( rfr + erp - g )

Where:
P/E = the justifiable price to earnings ratio, the dependent variable, to be determined.
D/E = the payout ratio = 43% = 0.43
g = the long-term sustainable growth rate = 6.7% = 0.067
rfr = the risk-free rate = 3.99% = 0.0399
erp = the equity risk premium, the independent variable = [ 3.5% = 0.035, ..., 5.5% = 0.055 ]

I get different P/E using either of those equations.

erp ................................ 3.5% ... 4.5% ... 5.5%
P/E from chart ............... ~30 .... ~20 ..... ~15
P/E using equation # 1 ... ~58 .... ~26 ..... ~16
P/E using equation # 2 ... ~54 .... ~24 ..... ~15

Oh, well, got to get ready for work, I'll give it some more thought.

Thanks again,