This paper studies the joint design of user scheduling and precoding for the maximization of spectral efficiency (SE) for a multigroup multicast scenario in multiuser MISO downlink channels. Noticing that the existing definition of SE fails to account for group sizes, a new metric called multicast spectral efficiency (MC-SE) is proposed. In this context, the joint design is considered for the maximization of MC-SE. Firstly, with the help of binary scheduling variables, the joint design problem is formulated as a mixed-integer non-linear programming problem such that it facilitates the joint update of scheduling and precoding variables. Further, useful reformulations are proposed to reveal the hidden difference-of-convex/concave structure of the problem. Thereafter, we propose a convex-concave procedure based iterative algorithm with convergence guarantees to a stationary point. Finally, we compare different aspects namely MC-SE, SE and number of scheduled users through Monte-Carlo simulations.