 What’s the P/B if ROE = 10%, required rate of return on common equity (r_ce) = 9%, and earnings growth = 5%?

If you have memorized the formula, it’s quite easy, but you should be able to figure it out from GGM. With so many fomulas, it is quite possible you won’t always be able to recall a formula on command.

1.25

(ROE - r)/ (r - g)

.1 - .09/ (.09- .05) = .25

From the GGM i got d1// (r-g)

I forgot how to get to ROE, but I’ve got the justified P/B and P/S NPM (1-b)(1+g)/ r-g) memorized for some reason.

Miss Cleo, you’ve got yourself a wrong formula.

I remember it being something like

p/b = 1 + (roe-r)/(r-g) where Bookvalue of equity x (roe-r) gives the excess return?

P

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

No my formula is correct. You are probably thinking of residual income which would be Bo + (ROE - r) Bo / (r-g)

No you are not right Cleo. This is the right formula. Check your book.

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

That one throws a lot of people off, g is subtracted from the numerator and denom

Oops yeah sorry forgot about that… hehe… glad I did it now not on t day

lol! i like how you were so sure about it earlier, misscleo. made me think twice, but then i came to my senses and i was like no way she’s right.

My point exactly…we think a formula is easy and we try memorize it, only to find later that it looks like many other formulas, or you you forget whether it was r or g, etc.

Go back to basics:

P0 = D1/(r-g) is the grand daddy of many formulas.

Recall that D1 = E1(1-b)

Divide both sides by B, and you get P/B on the left side.

Then E1/B on the right side is ROE… a little algebra will get you P/B = (ROE-g) / (r-g)

To clarify Dreary since he didn’t “solve” the algebra. E1/B = ROE. E1/B * retention(b) = ROE*b = g.

Therefore Po/B = (ROE - g)/ (r-g). I think they show you how to get all the P/X ratio with algebra in either schweser readings or video?

Po/S = (E1 * (1-r))/(S * (r-g))

E1 = Eo * (1+g)

Eo / S = profit margin of current period.

Po/ S = (PMo * (1-b)*(1+g))/(r-g)

kys916, show that P/B = (ROE-g) / (r-g) = 1 + (ROE - r)/(r-g)…that’s your algebra quiz.

Note this last version is useful as it shows the relationship between ROE and r. You can see that:

P/B = 1 + (ROE - r)/(r-g) … multiply, both sides by B:

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

Here is an important concept: The value of the stock is current book value + the excess return above the required return that you get from the company, multiplied by the book value (using GGM in the last part).