APPENDIX A
Mathematical Review of Growth Rates for Earnings, Dividends, and Book Value per Share
The growth rates of earnings and dividends per share are tethered to the growth of book value per share. As shown, the growth of book value per share will, in turn, be determined by the return on equity (ROE) that is earned, the rate at which new shares are issued or retired, and whether such issuance or retirement is dilutive. In addition, the payment of dividends reduces book value per share.
The relationship among these variables is relatively straightforward, in addition to being of significant intuitive and practical use. The relationships can be developed from the fundamental accounting and cash flow identities set forth in this appendix.
First we define:
BVPSt = book value per share at the end of period t
EPSt = earnings per share paid out during period t
DPSt = dividends per share paid out during period t
rt = return on equity, ROE, based on beginning of period book value in period t
Nt = number of shares; shares outstanding at period end
st = growth rate of shares
dt = dividend payout ratio, that is, DPSt ÷ EPSt
MVPSt = market value per share at the end of period t
λt = market-to-book ratio, that is, MVPSt ÷ BVPSt
Then we turn to the fundamental accounting and cash flow equation of conservation:
Beginning Period Book Value
plus Earnings
less Dividends Paid
plus Stock Issuance
less Stock Repurchases/Retirements
equals Ending Period Book Value
We will find it easier to manipulate ...
