This paper addresses the power penalty in an illumination LED caused by visible light communication (VLC). This study models the extra power consumption of the LED by taking into account the convex relation between the dissipated electrical power versus the LED current on one hand and the concave relation between the output luminous flux versus the current on the other hand. The ratio of the output luminous flux to input electrical power, which is known the LED luminous efficacy, is analyzed considering various recombination mechanisms and their dependency on current and temperature. As examples, the rapid light fluctuations induced by Pulse Amplitude Modulation (PAM) and orthogonal frequency division multiplexing (OFDM) are analyzed for joint illumination and communication (JIC) systems. Due to the signal modulation, there is a decrease in the output light of LED. Nevertheless, the total power offered to LED is larger than without modulation and thus extra heating occurs. Moreover, particularly when burst transmission is used in communication networks, visible flicker may occur.