  Finding the exact spanning ratio of a Delaunay graph has been one of the
longstanding open problems in Computational Geometry. Currently there are only
four convex shapes for which the exact spanning ratio of their Delaunay graph
is known: the equilateral triangle, the square, the regular hexagon and the
rectangle. In this paper, we show the exact spanning ratio of the parallelogram
Delaunay graph, making the parallelogram the fifth convex shape for which an
exact bound is known. The worst-case spanning ratio is exactly
$$\frac{\sqrt{2}\sqrt{1+A^2+2A\cos(\theta_0)+(A+\cos(\theta_0))\sqrt{1+A^2+2A\cos(\theta_0)}}}{\sin(\theta_0)}
.$$ where $A$ is the aspect ratio and $\theta_0$ is the non-obtuse angle of the
parallelogram. Moreover, we show how to construct a parallelogram Delaunay
graph whose spanning ratio matches the above mentioned spanning ratio.
