The free, necessary, and costly gift of grace through the incarnation

There is so much more going on in the manger than we often recognize. The gift of the baby Jesus is the free, necessary, and costly gift of grace from God through the incarnation. Jesus, as the second Person of the Trinity, added the nature of humanity to the nature of divinity to give his life as a ransom for our sins. But how does a free gift cost both God and us so much?