You can't "build" a formula in this manner.

You can still do it with an added step.

Let's assume this formula in cell A2: =C5&C6&C7&C8

Returns the TEXT string: =countif(D20:E25,"JohnSmith")

With the cell selected do:

Right click>copy
Right click>Paste Special>Values

CTRL H (this opens the Find/Replace userform)
Find what: =
Replace with: =
Replace all

The cell should now contain the formula: =COUNTIF(D20:E25,"JohnSmith")

However, this is kind of going around in circles when you could have just typed in the COUNTIF formula.

What you need is a UDF (User Defned Function).

Put this code into a general module:

Function EVAL(Equation As String) As Variant
  Application.Volatile
  EVAL = Evaluate(Equation)
End Function
Then, this formula entered in some cell:

=EVAL(A2)