It's wise to shop around for funeral goods and services. But be extremely cautious about paying in advance for them. A mortuary may go out of business, leaving a prepaid customer without recourse. Or your parent may move unexpectedly -- and then find that the funds paid in advance are not refundable or that a refund entails a big penalty.

If your parent wants to set aside money for funeral expenses, a more prudent approach may be to set up a savings plan or trust, often called a Totten trust. These can usually be arranged for a small administrative fee through a bank -- and the funds can be readily withdrawn or transferred during life if needed.