  Detecting exoplanets around giant stars sheds light on the later-stage
evolution of planetary systems. We observed the M giant HD 18438 and the K
giant HD 158996 as part of a Search for Exoplanets around Northern circumpolar
Stars (SENS) and obtained 38 and 24 spectra from 2010 to 2017 using the
high-resolution Bohyunsan Observatory Echelle Spectrograph (BOES) at the 1.8m
telescope of Bohyunsan Optical Astronomy Observatory in Korea. We obtained
precise RV measurements from the spectra and found long-period radial velocity
(RV) variations with period 719.0 days for HD 18438 and 820.2 days for HD
158996. We checked the chromospheric activities using Ca ii H and H_alpha
lines, HIPPARCOS photometry and line bisectors to identify the origin of the
observed RV variations. In the case of HD 18438, we conclude that the observed
RV variations with period 719.0 days are likely to be caused by the pulsations
because the periods of HIPPARCOS photometric and H alpha EW variations for HD
18438 are similar to that of RV variations in Lomb-Scargle periodogram, and
there are no correlations between bisectors and RV measurements. In the case of
HD 158996, on the other hand, we did not find any similarity in the respective
periodograms nor any correlation between RV variations and line bisector
variations. In addition, the probability that the real rotational period can be
as longer than the RV period for HD 158996 is only about 4.3%. Thus we conclude
that observed RV variations with a period of 820.2 days of HD 158996 are caused
by a planetary companion, which has the minimum mass of 14.0 MJup, the
semi-major axis of 2.1 AU, and eccentricity of 0.13 assuming the stellar mass
of 1.8 M_sun. HD 158996 is so far one of the brightest and largest stars to
harbor an exoplanet candidate.
