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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:

    http://www.geocities.com/trysail1952/RiskPremium.htm
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    Effect of a change in the Risk Premium on the P/E Ratio:

    http://www.geocities.com/trysail1952/Delta-RiskPremium.htm
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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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    Home:
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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,
      jad1148

      • 1 Reply to jad1148
      • jad1148-

        Rather than utilizing one equation, the methodology behind the charts employs a dividend discount model. A perpetual future dividend stream (based on a constant payout ratio at the stated earnings growth rate) is discounted back to present value at various discount rates. The present value is then compared to the current (or projected) earnings to produce the Price Earnings Ratio. As you appreciate, since the current risk-free rate is known, the difference between the discount rate that approximates the current price and the observable risk-free rate lets a card shark know what Mr. Market is using for his risk premium today. The curves give one an idea of how Mr. Market might price things were he to have one of his periodic mood swings.

        Glad you enjoyed the charts.

 
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