# A question for y'all

Here’s the info: Stock price: \$47.46 Trailing Annual EPS: \$3.22 Current Annual Dividend: \$1.03 Dividend Growth Rate: 7% Risk-free rate: 4.4% Equity Risk Premium: 6.39% Beta: .72 Calculate the justified trailing and leading P/E’s based on Gordon Growth Model.

re = 4.4 + 0.72 ( 6.39) = 9% g = 7% 1-b = Payout = 1.03 / 3.22 = .3198 Trailing = (1-b) * (1+g) / (r-g) = .3198 * 1.07 / .02 = 17.11 Leading P/E = Trailing P/E / (1+g) = 15.99

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EPScurrent = E0 = 3.22 EPSfuture = E1 = 3.22 * (1+0.07) = 3.45 P/E1 = (D1/E1) / (k - g) ke = 0.09 as CP calculated above D1/E1 = dividend payout ratio (stays constant since both earnings and dividends grow proportionately) = 1.03/3.22 = 0.3199 Therefore, P/E1 = 0.3199 / (0.09 - 0.07) = 15.99 (this should be leading P/E, since it’s forward looking with the denominator E1 being next year) CP, I haven’t got to this part of the curriculum yet, and I don’t recall “justified trailing P/E” from level 1, so I am wondering, is the rational behind the multiplication of 1+g due to earnings (in the denominator) being divided by next year’s growth rate?

Ali Trailing P/E = P0/E0 Leading P/E = P0/E1 and E1 = Eo * (1+g) So PO/E1 = P0/(E0*(1+g)) or Po/E1 = P0/E0 * 1/(1+g) Shortcut

Gotchya, thanks very much, as always