  The paper investigates the algebraic properties of Banach algebras of
complex-valued functions of bounded variation on a finite interval. It is
proved that such algebras have Bass stable rank one and are projective free if
they do not contain nontrivial idempotents. These properties are derived from a
new result on the vanishing of the second \v{C}ech cohomology group of the
polynomially convex hull of a continuum of a finite linear measure.
