We present the discovery of substellar-mass companions to three giant stars by the ongoing Penn State-Toruń Planet Search conducted with the 9.2 m Hobby-Eberly Telescope. The most massive of the three stars, K2-giant HD 240237, has a 5.3 MJ minimum mass companion orbiting the star at a 746 day period. The K0-giant BD +48 738 is orbited by a >=0.91 MJ planet which has a period of 393 days and shows a nonlinear, long-term radial velocity (RV) trend that indicates a presence of another, more distant companion, which may have a substellar mass or be a low-mass star. The K2-giant HD 96127 has a >=4.0 MJ mass companion in a 647 day orbit around the star. The two K2-giants exhibit a significant RV noise that complicates the detection of low-amplitude, periodic variations in the data. If the noise component of the observed RV variations is due to solar-type oscillations, we show, using all the published data for the substellar companions to giants, that its amplitude is anti-correlated with stellar metallicity.