Let $ABCD$ be a parallelogram with an area of 160. The diagonals $AC$ and $BD$ intersect at point $E$. Point $P$ is on the line segment $\overline{AE}$ such that $EC = 4EP$. If the line $DP$ intersects $AB$ at point $F$, find the area of quadrilateral $BFPC$.

Let's think step by step and output the final answer within \boxed{}.
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