Heads-Up10: P/B and RI

CFA Level II
#1

Krackd, Inc., has a book value per share as of FYE 2006 of $4.50. The required return on equity is 10%. Earnings per share in 2007 are forecast to be $0.45. Assume Krackd can be valued using a single-stage residual income model. The justified price-to-book ratio and the present value of expected residual income are closest to:

Justified price-to-book ratio … PV of expected RI

A. 1.0 … $0.00

B. 1.45 … $0.41

C. 1.45 … $4.05

#2

A) since 4.5x .1 - .45 = 0?

#3

I should have put in more tricky answers…now how do you find the justified price-to-book ratio?

#4

ROE - g / r - g = justified price to book

ROE = .45 / 4.5 = .1

r = .1

ROE = r

ROE - g / r - g

ROE = r = X

X - g / X - g = 1

#5

Only you if you assume ROE = r, but that may not be the case.

#6

Answer is A right?

#7

Answer is A, but you should be able to know that without assuimg r=ROE.

#8

Right, but in the absence of other information how do you derive P/B

#9

Not sure, but I found that assumption not valid (that r=ROE), since they didn’t say it. Also, it gets a little confusing for me with these different names:

Required rate of return on equity

Required return on equity

Required rate of return on common equity

ROE

?

#10

ROE = return on equity, nothing to do with Required return.

all the other 3 are the same for me which is r

#11

Well, theres a lot of assumptions you have to make for the justified P/B given the lack of information in that problem.

Either way, you can solve the problem just figuring out RI (so the answer has to be A). I don’t see how you can solve for justified P/B in the absence of assumptions around ROE and b (as g = b*ROE).

#12

You can ROE = EPS/BV = .45/4.50 = .1

P/B = ROE-g/r-g = .1-g/.1-g = 1

#13

Same logic as njcfa11.

ROE = NI/BVE = .45/45 = .1

r giving = .1

ROE - g = r - g = if they divide each other it’s one.

For those who like to memorize and it’s stated in the book, if ROE < r, P/B <1 if ROE = r, P/B = 0. ROE> r, P/B >1.

#14

Agreed, and that was already derived a few days ago. The question was whether the ROE was expected to be consistent over time, since that assumption is necessary for the one period model. But, given that they say you CAN use the one period model, now it only makes sense that the ROE is assumed to stay constant.

#15

There is no G given and another way to get justified P/B:

1- [(ROE-r)/(r-g)]

Once numerator was 0 was obvious. ROE is EPS/BV

Also you can get the second part of the question first as RI = .45 - .1(4.50)

#16

Or without calculating ROE…

RI = EPS(t) - rB(t-1)

=0.45 - .1(4.5)

=0

V = B0 + Sum(RI)

=4.5 + 0

V/P or P/B = 4.5/4.5 = 1

#17

Second that.

Theres no assumption to be made. ROE can be calculated.

And there is no need to find g since ultimately g/g = 1.