P/B = ROE - r / r-g : how does r (cost of eq) comes in numerator instead of g ?

CFA Level II
#1

Hey Guys,

Schweser sometimes uses justified p/b as P/B = ROE-g / r-g which is correct according to derivations…but it sometimes also uses P/B = ROE - r / r-g while calculating growth rate. what does “r” means here and wat’s the derivtion behind this equation ?

#2

I think it should be 1 + (ROE-r)/(r-g)

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

= (ROE-r + r -g) / (r-g)

= (ROE-r) / (r-g) + (r-g)/(r-g)

= 1 + (ROE-r) / (r-g)

r = Cost of Equity

g = Growth Rate

ROE = Return on Equity

#3

+1

#4

is this equation (ROE-r + r -g) / (r-g) derived from this eqation (ROE-g) / (r-g) ? If yes, can u please elaborate it further in steps or this is justified P/B based on RI model ?

#5

what is -r + r (don’t forget your basic algebra, ever)

ROE - g = ROE -r + r -g

#6

I wrote an article on this that may help: http://financialexamhelp123.com/justified-ratios-price-multiples/

#7

oh ! I got it right now…thnks every1 :slight_smile:

#8

My pleasure.