  We present a systematic way for deriving a four-dimensional (4D) effective
action of the five-dimensional (5D) orbifold supergravity respecting the N=1
{\it off-shell} structure. As an illustrating example, we derive a 4D effective
theory of the 5D gauged supergravity with a universal hypermultiplet and {\it
generic} gaugings, which includes the 5D heterotic M-theory and the
supersymmetric Randall-Sundrum model as special limits of the gauging
parameters. We show the vacuum structure of such model, especially the nature
of moduli stabilization, introducing perturbative superpotential terms at the
orbifold fixed points.
