Justified P/B multiple

Hi, on the justified P/B multiple, can someone please explain how E = B X ROE? Does B stand for book value? How does the justified P/B ratio = (ROE - g) / (r-g) ? Thanks!

B is earnings retention rate…

I should’ve known that. .it def. makes sense logically. . .I got confused b/c little b is used to represent retention rate elsewhere. . But how does justified P/B = (ROE - g) / (r-g)? Thanks planner!

sorry…my challenges with attention led me to only see the question regarding “b”… I am not the one to answer the rest of the question. I have just memorized to use the Gordon Growth Model with justified price multiples (r-g as the denominator)… Can anyone help?

Don’t have the answer in front of me, but if you look at the CFAI text in the footnotes it shows the transformation of the Gordon Growth to P/B.

B should be book value in that formular.

good catch dispatra… g=ROE x b where b = retention rate…

Yes. All of P/E, P/B, P/S formular can be derived from GGM. You need to plug in g = ROE * b, and E = B X ROE to GGM model. I think it is in the CFAI book as previous poster said.

Thanks everyone. I’ve been relying mostly on Schweser books, which have been helpful, but for a deeper understanding I should def. be looking at the CFA books.

I will put one here as a practice. Hope it is all good. P0 = (V1)/r-g; P0/B0 = V1/B0/r-g plug in B0 = E1/ROE, p0/B0 = (V1 / E1) *ROE/r-g = (1-b) * ROE/r-g = ROE-g/r-g

good explanation, disptra. another formula that is helpful is P/B = (ROE-g)/(r-g) = (ROE-r+r-g)/(r-g) = 1 + (ROE-r)/(r-g) P/B > 1 if ROE > r

maratikus Wrote: ------------------------------------------------------- > good explanation, disptra. > > another formula that is helpful is > > P/B = (ROE-g)/(r-g) = (ROE-r+r-g)/(r-g) = 1 + > (ROE-r)/(r-g) > > P/B > 1 if ROE > r Nice. This proves when there is dividend RI model and GGM model are same. It seems the key assumption to make these 2 equal is g = b * ROE, everything else is by definition.

yes, the key assumption is perpetual constant growth g = b*ROE

Heh Bro This will surely help Po = D1/r-g Since we are calculating BV which comes from E1 = Bo x ROE (remember B here is the BVPS not ret rate) If we divide both sides by Bo Po/Bo = (D1/Bo)/r-g from the above formula- = ((D1 x ROE)/E1)/r-g Notice that E1 is there, therefore we have not used ( x 1+g). If Eo had been in the formula, we would have added a term ( x 1+ g) like what we do in Po/So ratio Now, D1/E1 is the payout ratio or 1-b = ((1-b) x ROE )/ r-g = (ROE- (b x ROE))/ r-g = (ROE-g)/r-g Cheers !