# ROE - g / r-g

ROE - g / r-g Very simple formula but in English, how does it equate to PBV?

CFAI V4 p.462

P/E = (1-b)/(r-g) P/B = E/B ( 1-b)/(r-g) = ROE(1-b)/(r-g) =(ROE-b.ROE)/(r-g) =(ROE-g)/(r-g)

P = Div / R-G and since Div = E*K P = (E*K) / (R-G) We know that ROE*(1-K) = G, rearrage it to K = (1 - G/ROE) Sub K in the price equation P = (E*(1- G/ROE)) / (R-G) Divide B on both side P/B = (E/B * (1 - G/ROE)) / (R-G) recall E/B = ROE, therefore P/B = (ROE (1- G/ROE) / (R-G) P/B = (ROE - G) / (R-G)

dont think any of the above counts as english… unfortunatly I dont have an answer for you bro.

You know that P/E = (1-b)/(r-g) You know that E = BV x ROE So substitute BV x ROE with E P/(BVxROE) = (1-b)/(r-g) Multiply both side by ROE: P/BV = (ROE)(1-b) / (r-g) = (ROE - ROE x b)/(r-g) Since b = retention ratio, and ROE x RR = g, you have: P/BV = (ROE -g)/(r-g) That should do it as far as the math goes.

If you compare the return you are generating for your equity holders in excess of the normal growth of the company, to the required return they are asking of you (also in excess of the normal growth of the company), you will see the same relation as that of the stock price to the book value per share. It’s an amazing formula because you can discover how large the stock price in comparison to book value by looking at the *excess* return generated for equity holders over what they are requiring from a company like yours.

So why then does P/BC use r = wacc? Am I wrong about that? (I got this wrong on the BSAS mock)

book value refers to equity ownership so you would be using return on equity

Was the question wrong in the BSAS mock?

P/B = (ROE-g)/(r-g) Now that I think about it, it is a weird formula! We know that price changes everyday, while ROE, r, and g don’t. So, how can they always be equal? hmmm.

As far as I know, they’re not supposed to be equal, as the equation is supposed to reprsent a ‘justified’ P/B ratio. This formula is supposed to calculate an intrinsic P/B based on fundamentals. Could you apply this in real life? Probably not - the damn g and r ratios are too bloody subjective.

TheAliMan Wrote: ------------------------------------------------------- > As far as I know, they’re not supposed to be > equal, as the equation is supposed to reprsent a > ‘justified’ P/B ratio. This formula is supposed to > calculate an intrinsic P/B based on fundamentals. > Could you apply this in real life? Probably not - > the damn g and r ratios are too bloody subjective. Exactly…r and g are totally subjective with no real solid means of estimating them. And to make matters worse, the formula blows up as g approaches r, and becomes totally useless if it surpasses it. Once again, I really don’t understand why things like this are even in the cirriculum.

so, mathematically, it is not correct to say P/B = (ROE-g)/(r-g) .

No, sorry I am not very clear. It is mathematically correct to say P/B = (ROE - g)/(r-g) based on the definition of book value, but in application, it doesn’t really have merit. The equation mathematically tells you what P/B “should be” but obviously in real life, your P/B calculated from the formula will deviate from the value taking market price divided by your book value. Remember, book value, in itself, has subjective adjustments, as well as r and g.