# P/BV

Not a horrible question, but I have an add on question after everybody takes a stab at this question… An analyst has gathered the following data about the Garber Company: Payout Ratio = 60%. Expected Return on Equity = 16.75%. Required rate of return = 12.5%. What will be the appropriate price-to-book value (PBV) ratio for the Garber Company based on return differential? A) 0.58. B) 1.73. C) 1.38. D) 1.85.

g = (1-.6)(.1675) = .067 P/B = (.1675-.067)/(.125-.067) = 1.73

gotta be B for this … 1.73

B. justified p/b = roe - g/r-g

What is the follow up question?

Agreed. B.

yeah thats right… B… anyway… I initially looked at this problem as trying to first solve for g (as you did) g=0.67 Then use the P/E Leading multiple [(1-b)/(r-g)] to find a price/\$1(earning) = 6.897 I then took the \$1 and divided by .1675 (expected ROE) to find what the BV should be (5.97) Finally I took the P/E (6.897) and divided by BV (5.97) for what I thought should be a useable P/BV number … = 1.16 The question is why does this approach not yeild the same ans? Is the math wrong or does this just plain not work as you would think it should? Thanks for any input…

i’m probably not following correctly. but how do you get book value by dividing 1 into ROE? Sorry. i think the \$1 in earnings confused me.

Well P/E is price per \$1 in earnings If your ROE was 16.75% and you earned \$1 then the Equity Value should be \$5.97 5.97(16.75%) = 1

My guess is that in your method, you do: P/B = P/E * 1/B while it should be P/B = P/E * E/B and as E = ROE * B, equation becomes P/B = P/E * ROE

I got it chad. think you just plugged in the wrong numbers on your leading P/E. plugging in numbers i get 10.34483 as the p/e divide that by your book value of 5.97 (you’re right on this) and you get 1.73

Yeah you used ROE instead of r in the P/E calc.

leading p/e = (1-.40)/(.125-.067) = 10.3448

Works now.

ahhh… thanks guys! Makes sense…

ROE-r/ r-g

justified p/b is (roe-g)/(r-g) i don’t have my books with me, but i’m certain.

i derived the formula and i initially got 1.16 like another poster. and couldn’t figure out why (and remember i am trying to derive from scratch, not memory of formula) and i found my error. i was taking ROE*.4 on top, but it should be ROE*(1-.4) or ROE*0.6… be very careful on that b if you are deriving formulae. my derivation was Po = Bo x ROE x b DIVIDED by r-g… then divide both sides by Bo… not something i’ve studied for awhile or memorized. couldn’t remember was b was payout ratio or retention ratio. doesn’t matter if you model it properly, but of course i goofed. i’m hoping to do both memory and derivation on the exam.