R32 - Justified P/B value

How Justified P/Book value ratio is derived :

P/B = (ROE - g) / (r - g)


So here goes:

V0 = D1/(r-g)

D1 = EPS1 (payout ratio)

Payout ratio = (1- retention ratio). Retention ratio is known as b, hence (1-b)

Rephrase the entire equation,

V0 = EPS1 (1-b)/(r-g)

Since we need the price to book, divide both sides by BV, we get

V0/BV = EPS1/BV (1-b)/(r-g)

EPS/BV = ROE and ROE*b = growth, so we finally have:

P/BV = (ROE - g)/(r - g)

Hope this helps.

ok Thanks. Got It