The dividend is 'cash' paid out to shareholders and 'cash' is an 'asset' so - yes it is deducted from BV. However - the last announced BV to which you refer is as of the end of the 3rd qtr and AGNC likely had 'earnings' during the 4th qtr, so the impact of the dividend payout on BV depends on how much AGNC earned (in interest income and possible capital sales) during the 4th qtr. Of course the other aspect of BV is the value of AGNC's assets other than cash - largely mbs and hedges less liabilities. The value of the mbs and hedges less liabilities could have gone up or down independent of AGNC's cash position. Realize that AGNC and other mreits are marked to mkt every day - since the value of their assets and liabilities are easily quantifiable - but the BV is only only reported out at what it was at the end of the qtr. However 4th qtr earnings will not be announced until early Feb - so when the 12-31-12 BV is reported it will already be more than a month old and any # of things could have happened in the interim.
It's like looking at your brokerage statement. You've got 10K shares and cash and your statement as of 12-31-12 tells you what your portfolio was worth as of 12-31-12, but that value could be up or down as of 1-15-12 if you've sold shares or even if you've done nothing and it won't reflect dividends that might not be payable until 1-28-13.