First of all, in the U.S., no Federal gift tax has to be paid by the recipient of
the gift; it is the donor who has to pay gift tax, if any is due. Nor does the
recipient have to pay Federal income tax on the gift; it is not considered
taxable income. I do not believe that any states view matters differently for
the purposes of state gift and income taxes, but I am always ready to be
disabused of any such fondly-held notions.
If your parents were required to pay any gift tax, that would have been at the
time the gift was originally given and only if they gifted more than the maximum
allowable exemption per person for that year. Currently the exemption is $14K
from each donor per recipient per year. Additional gifts were made by your
parents to you during your minority when your parents paid any income tax
due on the distributions in your account, but these amounts would unlikely to have been larger than the exemption for that year. In any case, gift tax is
none of your concern.
If you have been declaring the income from distributions from the mutual
funds all these years, then the only tax due on the distributions
from the funds in 2013 is the Federal income
tax for the 2013 tax year (plus a special assessment of Medicare tax
on investment income if your income is large; unlikely based on your
question and follow-up comment). If you sold all or part
of your shares in the funds in 2013,
then you would need to calculate the basis of your investments in the
fund in order to figure out if you have capital gains or losses. Ditto
if you are thinking of cashing out in 2014 and wish to estimate how much
income tax is due. But if you want to just hang on to the funds, then
there is no immediate need to figure out the basis right away, though
taking care of the matter and keeping in top of things for the future
will be helpful.
As a final note, there is no tax due on the appreciation of the fund's
shares. The increased value of your account because the fund's share
price rose is not a taxable event (nor are decreases in the account
These are called unrealized capital gains (or losses) and you do not pay tax
on them (or deduct them as losses) until you realize the gains by
disposing of the property.