For the effect of “A Rival Appears!”, refer to the levels of the monster on the field and the monster in the hand at the time “A Rival Appears!” resolves (for purposes of “Cost Down”, “Level Conversion Lab”, “Mystical Space Typhoon” in a chain destroying “Demotion”, etc.)
If the opponent’s monster is face-down or not on the field when “A Rival Appears!” resolves, then its effect disappears.
If you do not have a monster of the same level as the target, you cannot activate “A Rival Appears!”