Hello fkopilak,
Hope you're all doing great! How exciting that your grandson is going to college and you are helping him out!! That's just awesome.
So if you are giving him stock that is appreciated in value and he then sells it, your cost basis and holding period will be transferred to him. If your grandson is in a lower tax bracket than you then he will owe less tax or maybe no tax (if it is long-term) as compared to if you sold it under your name and you are in a higher tax bracket.
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