Starting with (8) we have
Partial integration of the left-hand side yields
because the derivative of v(t) is as is seen from (2). (The economic interpretation of
is naturally that the change in
capital stock (= book value) is cash outflows less depreciation.)
By substituting (5) into the right-hand side of (I1), we have
Equating (I2) and (I3) gives (9).