Let the present ages of the man and his daughter be x and y years respectively.
The average of their ages is (x + y)/2 = 34 years.
Four years from now, the ages of the man and his daughter will be (x + 4) and (y + 4) years respectively.
The ratio of their ages four years from now is (x + 4) : (y + 4) = 14:5.
Solving these equations for x and y, we get x = 52 and y = 16
Therefore, the daughter's present age is 16 years.