We divide all firms into 3 categories: FR includes all firms which acquire raw material (iron ore, farm products and so on), FH all those that produce semi-manufactured goods (steel, pulp and so on) and FF all firms producing finished goods (software, cars and so on). We use the symbol Y for GDP. All of Y will go to the firms in FF box. Though if we sum the value added from all firms, we would get exactly Y. This is why:

Figure

Goods in the circular flow

• If YR is total value of all goods going from FR to FH, then total value added from all firms in the FR box is equal to YR (they don't purchase any goods to which they add value).
• similarly if total value of all goods going from FH to FF is given by YH, then total value added from all firms in the FH box is YH - YR.
• Similarly total value added for all firms in FF box will be equal to Y - YH. If we sum all the value added from all firms then we get YR + (YH - YR) + (Y - YH) = Y.
• This result is independent of how many 'levels' or boxes we have in the production process. In place of three levels, we could have any number of levels and result would still hold.

Also a particular firm may be producing in many of the boxes. 

Because the value added in every firm is equal to the return to factors of production, total return to the factor market should be equal to the sum of value added from all firms that is equal to Y.