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P/E and justified P/E (Trailing)

From CFAI book:

Harry Trice wants to use the Gordon growth model to find a justified P/E for the French company Carrefour SA, a global food retailer specializing in hypermarkets and supermarkets. Trice has assembled the following information:

  • Current stock price = €23.84.

  • Trailing annual earnings per share = €1.81

  • Current level of annual dividends = €0.58.

  • Dividend growth rate = 3.5 percent.

  • Risk-free rate = 2.8 percent.

  • Equity risk premium = 4.00 percent.

  • Beta versus the CAC index = 0.80.

Now if I calculate : P0/E= 23.84/1.81 = 13.17

and if I calculate the trailing P0/E= (1+g)*(1-d)/(r-g) = 13.248 

Why are these two number different wouldn’t the direct calculation of  P0 / E0  be the same as (1+g)*(1-d)/(r-g)

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Ignore the question :  I figured out  trailing and leading P/E help in valuing the actual P/E

They’re different because the market price of the stock is lower than what the Gordon growth model says that it should be.

There’s no reason for them to be the same, which is the point of the justified multiple.

Simplify the complicated side; don't complify the simplicated side.

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