# Equities - market-based valuation

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! 1. EPS = Div/payout = 1.35/67% = 2.01493 2. Next year EPS = 2.01493 * (1 + g) = 2.01493 *1.076 = 2.16806 3. Next year dividend = 2.16806 * payout ratio = 2.16806 * 67% = 1.4526 4. Discounting perpetuity: Justified (fair current price) = 1.4526 / (r-g) = 1.4526 / (14% - 7.6%) = 22.69688 5. Now I have justified price, I need equity book value, given that ROE = 23% 6. ROE = NI/Equity BV… ROE = EPS (calculated in step 1) / Equity BV… 23% = 2.01493 / Equity BV…(solving equity BV = 8.76057) 7. 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!!! ROE = \frac{NI_1}{BV_0} 23\% = \frac{2.16806}{BV_0} BV_0 = \frac{2.16806}{0.23} = 9.426348 \frac{P_0}{BV_0} = \frac{22.69688}{9.426348} = 2.408 1 Like Thanks for your reply. The difference between my work and yours is that you used expected NI instead of current NI. I cannot relate what’s the rationale for that? Justified ratios are all based on Gordon growth: P_0=\frac{D_1}{r-g} The dividend at the end of the coming year is based on the coming year’s net income, not the previous year’s net income. Furthermore, ROE is calculated using the book value of equity at the beginning of the year, not at the end of the year, much as the rate of return on an investment is the amount of the return divided by the initial investment, not the terminal value. 1 Like Think of the 23% as you starting a business with an equity capital of$100 today (BV_0) and use it to generate a net income of \$23 at the end of the year (NI_1). That’s how much you have generated on your equity investment.

If we were to do 23/123 ( \frac{NI_1}{BV_1} ), it would not be meaningful as a measure of return.

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That’s not strictly true; bank discount yield is measured that way.

It would be unusual, to be sure, but still meaningful.

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