We present an analysis of the thermodynamic properties of chain molecules formed from Yukawa segments using the statistical associating fluid theory with interactions of variable range (SAFT-VR) and the high-temperature expansion of the mean-spherical solution (MSA-HTE) to the Ornstein-Zernike equation for a simple Yukawa fluid. The SAFT-VR expressions derived previously for this system allow the MSA-HTE equation of state to be reformulated in terms of first-order perturbation quantities, thus improving its accuracy. Furthermore, the MSA-HTE solution provides a full theoretical derivation of the perturbation theory used in SAFT-VR, together with a completely analytical equation of state for chain molecules composed of segments which interact via the Yukawa potential.