# Conflicting formula for justified P/B

1. Justified P/B = (ROE-r)/(r-g) 2. By using the residual income model, V(0) = B(0) + {(ROE - r) * B(0)}/ ( r-g) ==> V/B = 1 + (ROE - r)/ (r-g) Related Question: Century Scales has a required return on equity of 12% and is expected to grow indefinitely at a rate of 5%. The ROE that would justify a P/B of 2.14 is closest to?

Your formula for the RI model is incorrect, I’m pretty sure.

V (0) = B(0) + … + (RI(n)+ [RI(n+1)/(r-g)])/(1+r)^(n) The r-g in the denominator is only the last part of the “to infinity and beyond” part of the numerator. For just the simplest 1-stage RI, the formula would be: V(0) = RI(1)/(r-g)

No I think it is right. I’ve asked myself this before DonYuan, but then I quickly concluded “Who cares. It is in the material. Just memorize the formula and plug and chug”

Justified P/B is (ROE-g)/(r-g). Stalla uses a subscript of 1 for ROE, not sure if we’re supposed to grow it or not. Can anyone confirm?

Justified P/B is (ROE-r)/(r-g), not (ROE-g)/(r-g). There isn’t a dividend or cash flow to grow. What did you want to grow, ROE? No need to grow anything.

no, P/B = (ROE-g)/(r-g)

you can solve this from the RI model: P = B + [(ROE-r)B] / (r-g) or P/B = 1 + (ROE-r) / (r-g) P/B = (ROE-r) / (r-g) + (r-g) / (r-g) P/B = (ROE-r + r-g) / (r-g) P/B = (ROE-g) / (r-g)

oh ok. My bad, got mixed up. ^^ thanks.

oh, yes, thanks FinNinja… the first post got me mixed up. Thanks for the correct formula and the algebra.

Answer is 20% by the way.