My Doubt is In the calculation of payout ratio i.e. (1-b) For leading PE we need to divide D1/E1 but in the book in the solutions it has used the E0 value i.e. $1.81 Arent we supposed to use E0 in trailing and E1 in Leading for calculation of Payout Ratio

Given Are The Data Current Stock Price = $23.84 Trailing Annual Earnings = $1.81 Current Level of Annual Dividends= $0.58 Dividend Growth Rate= 3.5% Risk Free Rate= 2.8% Equity Risk Premium = 4% Beta= 0.80

Let me explain the derivation of Justified Leading P/E & Justified Trailing P/E:

_ Justified Leading P/E _

P0 = D1/r-g

Because D1= D0*(1+g)

=>P0 = D0*(1+g)/r-g

Now divide both sides by E1 (Next Year’s earnings)

P0/E1 = (D0/E1)*(1+g)/r-g]

We know that E1 = E0*(1+g)

=> P0/E1 = [D0 / E0* (1+g)] * [(1+g) / (r - g)]

(1+g) will cancel out each other in the Numerator and the Denominator

So P0/ E1 = (D0/E0) * [1/ (r - g)]

D0/E0 = 1 - Retention Rate Now Let’s say the Retention Rate = b

So the Justified Leading P/E is P0 / E1 = (1-b) / (r - g)

_ Justified Trailing P/E _

P0 = D1/r-g

Because D1= D0*(1+g)

=>P0 = D0*(1+g)/r-g

Now divide both sides by E0

P0/E0 = (D0/E0)*(1+g)/r-g]

We know that D0/E0 = 1 - Retention Rate Now Let’s say the Retention Rate = b

So the Justified Trailing P/E is P0 / E0 = (1-b)*(1+g) / (r - g)

r & g is already given in the question.

(1-b) = D0/E0

As D0 and E0 both are given, we can replace 1-b with the calculated value as D0/E0 in both formulas above (In Justified Leading P/E and Justified Trailing P/E)