An investor is considering the purchase of Microscopics, which has a price to book value (P/B) ratio of 4.00. Return on equity (ROE) is expected to be 12 percent, current book value per share is \$12.00, and the cost of equity is 10 percent. What growth rate is implied by the current P/B rate? A) 0.67%. B) 10.00%. C) 9.33%. D) 12.00%.

I had this question before. I forget the formula because I remember looking at the answer and thought “F-this, I’ll come back later.”

my thoughts exactly.f this. i just had a bad schweser session and i thought i’d share the cheer… i’m done for the night on that note.

C??

Here’s what I did to get none of the above answers in case this helps someone get to the right answer by spot-checking my logic. I mutiplied the BV of 12 x 4 (P/BV) to arrive at P of 48. I then multiplied ROE by BV to get 1.44 for the forecasted earnings. That left me with a DDM of P = Earnings/(Cost of Equity- growth) or 48 = 1.44 / (.1 - g) which rearranged to g = -(1.44/48) + .1 g = .7 which of course happens to be none of the options.

I had to derive the formula starting from GGM … and that took me 5 mins. Vo = D1/ (r - g) Vo/Bo = D1/[Bo * (r-g)] E1 = B0 * ROE Bo = E1/ROE Justified PB Rotio = [D1 * ROE]/ [E1 * (r-g)] D1/E1 = DPR DPR = 1 - b D1/E1 = 1-b Justified PB Rotio = ROE*(1-b)/(r-g) = (ROE - ROE*b)/(r-g) Justified PB Rotio = (ROE - g)/(r-g) 12 = (0.12 - g)/(0.10 - g) g= 0.09333 = 9.333% = C??

P/E = ROE - g / (r-g) 4 = .12-g / .1-g .4 - 4g = .12 - g .4 - 3g = .12 -3g = -.28 g = .0933 I say C.

Black Swan Wrote: ------------------------------------------------------- > That left me with a DDM of P = Earnings/(Cost of > Equity- growth) P = Dividends/(Cost of Equity - Growth)

P0/B0 =1 + ROE -r/r-g 3 = 0.02/r-g and so, g = 10 -0.667 =9.33. why is this tricky?. i thought both schweser and the texts had this formula presented directly.

wanderingcfa Wrote: ------------------------------------------------------- > P/E = ROE - g / (r-g) > 4 = .12-g / .1-g > .4 - 4g = .12 - g > .4 - 3g = .12 > -3g = -.28 > g = .0933 > > I say C. Correct - except that its P/B = ROE - g / (r-g) and not P/E = ROE - g / (r-g) Anyway, it’s correct from the next line

Good job, folks. the bit about the curriculum not providing the expression is from schweser, not me. either way, i should have gotten it. The correct answer was C) 9.33%. The P/B ratio of 4.00 and the current book value per share of \$12.00 imply a current market price of \$48.00. This implies a growth rate of: g = r – [{B0(ROE – r)}/{V0 – B0}] = 0.10 – [{12.00(0.12 – 0.10)}/{48.00 – 12.00}] = 0.0933 = 9.33%. Note that the reading in the curriculum does not provide this expression directly.

Thank you Kabhii, I was wondering where I messed up. I’m beginning to realize that for every day I spend on derivatives / port mgt. I lose a little more basic background. kabhii Wrote: ------------------------------------------------------- > Black Swan Wrote: > -------------------------------------------------- > ----- > > > That left me with a DDM of P = Earnings/(Cost > of > > Equity- growth) > > P = Dividends/(Cost of Equity - Growth)

Bacaladitos Wrote: ------------------------------------------------------- > Correct - except that its P/B = ROE - g / (r-g) > and not P/E = ROE - g / (r-g) > > Anyway, it’s correct from the next line Oh yea…oops, mental lapse with typing my equation.

i can’t get to any “calculated answer” to this… but growth rate must be less than required return… so B/D don’t work. company has very high price to book. so must be very profitable (i.e. above required return, and that’s not the case). or must be high growth. as its roe isn’t much higher than required return, then the r-g term must be very small… hence c… i didn’t some ad-hoc equity calcs and came up with 6.66% and 9.95%, so they’re alot more consistent with C as well… basically B/D ruled out, and A doesn’t make that much sense (of course, A could be correct. but doubtful)…

i also got C -> solved equation for RetentionRatio -> growth = RR*ROE

C: P/B=ROE-g/r-g