We do get asked occasionally which measure of 'number of shares' we use in the denominator to calculate 'per share' measures like EPS, DPS, BVPS etc.
Firstly, there are multiple measures of the number of 'shares' in a company. There is the 'basic' shares outstanding - which is the amount of common shares outstanding published in the accounts. But often staff have unexercised options on shares, while other securities (like convertible bonds) can be converted into common shares. If all these shares were converted into common shares the total number could be much higher. As a result it's often wise to create a more prudent number called "fully diluted shares outstanding" for calculating per share items.
Another issue is that companies often issue new shares through the year... sometimes as secondary placings to raise capital, at other times to reward staff. It's therefore wise to create a 'weighted' number of shares outstanding to take this into account. The combination of fully diluting and weighting shares outstanding creates a measure called 'diluted weighted average shares' for the year.
For all income statement per-share metrics we use 'diluted weighted average shares'... as income / sales etc accrue over the accounting time period, the weighted average shares is most appropriate.
For all balance sheet per-share metrics (like Book Value per share) we use the Total Common Shares Outstanding at the end of period. Balance Sheet statements are point in time snapshots, so it's more appropriate to use the shares outstanding as of that date. While there is an argument to use diluted total shares outstanding, it's not a data point that we currently have access to. Incidentally - it's the same process that Thomson Reuters use in their institutional terminals, even though they are calculating independently.