CFA Vol 3 page 256, Question 8C. Essentially the same question, and they (CFAI) clearly use the most recent earnings (which, they point out to be the same in the next period as they state the formula uses E1)
In order to get to 3.90 from 3.25, there has to be growth in the firm within the year. If you’re assuming no growth, the EPS must stay the same (because they’ve paid out the 3.25 as dividends and so b * ROE = 0)
And in either case, the market wouldnt have priced it at 6.95 - it’s the analyst that is assuming EPS of 3.9. The question makes no statement about the market assumption of earnings. All you know is that given recent earnings, the market price is 45. If you assume no growth, E1 = E0 and E1 / r = 3.25 / .1025