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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!

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 !

TOP

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

TOP

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.

TOP

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

TOP

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

TOP

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.

TOP

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.

TOP

good catch dispatra...

g=ROE x b where b = retention rate...

TOP

B should be book value in that formular.

TOP

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