Peel the carrots so that the thick ends are roughly the same width as the thinner ends; cut each carrot in thirds crosswise. Put the carrots in a medium skillet with the carrot juice and beer and bring to a boil. Cover and simmer over moderate heat until the liquid is reduced by half, about 10 minutes. Add the sugar, cover and cook until tender, about 10 minutes. Transfer the carrots to a plate.
Whisk the butter into the sauce and simmer until thickened, 1 minute. Return the carrots to the skillet, season with salt and toss to coat. Transfer to plates and serve.