A Question on SGR(sustained growth rate) formula

Am reading the FUNDAMENTAL OF CORPORATE FINANCE 7th Edition by Richard A Brealey, on the stock valuing chapter on how to get the SGR formula, the logic there is:

SGR for 2012 = increase in book equity per share in 2012 / book equity per share at the start of year.

As 

increase in book equity per share in 2012 = plowback ratio * earnings per share in 2011 = plowback ratio * [book equity per share at the start of year(1) * ROE]

SGR for 2012 = plowback ratio * [book equity per share at the start of year(1) * ROE] / book equity per share at the start of year(2)

                       = plowback ratio * ROE

While in my opinion,  book equity per share at the start of year(1) should be the beginning of 2011, and book equity per share at the start of year(2) should be the start of 2012, which are different from each other, how can they be eliminated....

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