Kaplan question 1 page 157 (reading 29) states the following data:

Recently paid div = $ 1.35 per share

Payout ratio = 0.67

ROE = 0.23

Expected growth rate in earnings and dividends for foreseeable future = 7.6%

{if you calculate SGR = ROE * RR = 0.23 * (1-.0.67) = 7.59%}

Required rate of return 14%

Calculate justified price to book value multiple??

The answer in the book is given this way: P0/B0 = (ROE - g) / (r-g) = (23%-7.6%)/(14%-7.6%) = 2.41

My question is: I tried to solve using the following logical steps (DDM) but I end up with different answer!

- EPS = Div/payout = 1.35/67% = 2.01493
- Next year EPS = 2.01493 * (1 + g) = 2.01493 *1.076 = 2.16806
- Next year dividend = 2.16806 * payout ratio = 2.16806 * 67% = 1.4526
- Discounting perpetuity: Justified (fair current price) = 1.4526 / (r-g) = 1.4526 / (14% - 7.6%) = 22.69688
- Now I have justified price, I need equity book value, given that ROE = 23%
- ROE = NI/Equity BV… ROE = EPS (calculated in step 1) / Equity BV… 23% = 2.01493 / Equity BV…(solving equity BV = 8.76057)
- Now I have P0 from step 4 and equity BV from step 6… justified P/BV = 22.69688 / 8.76057 = 2.59080 !!! what makes this answer differs from the answer given in the book!!!