it could just be a seasonal change of colour. In the spring tip it out of its pot and see if the roots look healthy, if they are then pot it up in a slightly bigger pot and put outside after all frosts are past - or plant it somewhere in the garden. (sun or part shade) Keep an eye on the areas right at the base of the leaves in the centre. They can be prone to a white, fluffy pest called mealybug, if you have it, it can weaken or even kill the plant. There are chemical sprays that can help - but while the plant is small it is possible to jet water/soap into it and try and get rid of them that way. a long job but worth it if you have a lovely form! I remember my husband clearing every particle of soil from a beloved fig of mine that had been infested by the dreaded vine weevil - it took him hours - but now we have a good crop of figs each year off the healthy plant to make it worthwhile!!!

Depends on what variety you have ... and the bugs suggestion from Hoya. Copied off wikipedia ... "A favourite is Cordyline ‘Rubra’. Rubra means red, and boy, it’s red all right ... Brown tips on the leaves indicates that last winter was a bit tough on it – and if you live in a cold climate, the plants might develop more of these." They don't like cold winds, so maybe, if Hoya's suggestion is ruled out, you need to keep it indoors or in a more protected spot, even during the summer if you have cold breezes where you are.

Brown leaves may mean that you waited a little too long to bring it in, and it either froze before you got it in, or there was too sudden a change between the outdoor and indoor environments. Also note that it will need blazingly bright light indoors--better in a conservatory or greenhouse.