Good Evening,
AmyC is correct. The basis of the mutual fund is the price your parents paid to purchase it, plus any transaction costs and adjustments to basis (dividend reinvestment, stock split, distributions, etc.). A custodial account is considered a gift, and gifted assets have a basis carryover feature.
If you can, the best thing to do in this situation would be to have your parents and the brokerage provide the account records from when your parents were the custodians for the account. You can also reach out to the mutual fund issuing company as well, they ought to have shareholder records somewhere. A tax accountant should be able to calculate your tax basis on the account given your parents' prior account data.
If for some reason you cannot get ahold of these records, you can always resort to taking an estimate by looking at the mutual fund closing price for the time period your parents bought each holding in the security. If there is only one position, then the tracking is less cumbersome. This will help substantiate your basis, but the IRS can still resort to giving you a '0' cost basis if there is no documentation confirming the purchase dates.
Once you've determined your total adjusted cost basis, you will need to refer to Publication 550, Chapter 4 to figure your cost basis for the portion of shares sold that are listed on Form 1099B section 1d, this is what gets entered on Form 1099B section 1e. The method you use (Cost Basis (FIFO, etc.) or Average Cost) to calculate this will depend on how much information you have and your tax needs.
It's normal for gross proceeds to be less than the cost basis, this just indicates that there was a capital loss. What matters is whether the cost basis is accurate given your information and circumstance. It's important to have your tax advisor walk you through how they arrived at that number since there are many methods and assumptions that are utilized to arrive at cost basis, especially if financial data is unclear or not available.
Hopefully this helps!
