This paper studies the impact of load increase and a power system stabilizer (PSS) on the stability delaymargin of a single-machine-infinite-bus system including an automatic voltage regulator. An analytical method isproposed to determine the stability delay margin of the excitation control system. The proposed method first eliminatestranscendental terms in the characteristic equation of the excitation system without making any approximation and transforms the transcendental characteristic equation into a regular polynomial. The key result of the elimination process is that the real roots of the new polynomial correspond to the imaginary roots of the transcendental characteristic equation. With the help of the new polynomial, it is also possible to determine the delay dependency of system stability and the root tendency with respect to the time delay. Delay margins are computed for various loading conditions and PSS gains. It is observed that the delay margin generally decreases as the PSS gain and load demand increase, resulting in a less stable system.