Cannot INSERT Into Newly Created Column
It's a binding issue. The code is bound to the metadata of the table at compile time and it is not late bound.
Try using EXEC and dynamic SQL to overcome this limitation:

BEGIN TRANSACTION;
    PRINT 'Adding column, ''SupplementalDividends'', to MyTable table.';

    ALTER TABLE MyTable
        ADD SupplementalDividends DECIMAL(18,6);

    PRINT 'Column added successfully....';

    PRINT 'Ready to INSERT into MyTable ...';
    EXEC('
    INSERT INTO MyTable (x, SupplementalDividends)
        VALUES (1, 3.2);
    ')

    PRINT '**** CHANGES COMPLETE -- COMMITTING.';
COMMIT TRANSACTION;


Another option is using a stored procedure to insert the data: late binding applies to stored procedure, but not to ad-hoc queries. Again, you would have to use dynamic SQL to create the procedure, but it could make it easier for you to pass parameters:

BEGIN TRANSACTION;
    PRINT 'Adding column, ''SupplementalDividends'', to MyTable table.';

    ALTER TABLE MyTable
        ADD SupplementalDividends DECIMAL(18,6);

    PRINT 'Column added successfully....';

    PRINT 'Ready to INSERT into MyTable ...';

    EXEC('
    CREATE PROCEDURE insData @p1 int, @p2 DECIMAL(18,6)
    AS
    BEGIN 
        INSERT INTO MyTable (x, SupplementalDividends)
        VALUES (@p1, @p2);
    END')

    EXEC InsData 1, 3.2;

    PRINT '**** CHANGES COMPLETE -- COMMITTING.';
COMMIT TRANSACTION;


A temporary stored procedure would work as well:

BEGIN TRANSACTION;
    PRINT 'Adding column, ''SupplementalDividends'', to MyTable table.';

    ALTER TABLE MyTable
        ADD SupplementalDividends DECIMAL(18,6);

    PRINT 'Column added successfully....';

    PRINT 'Ready to INSERT into MyTable ...';

    EXEC('
    CREATE PROCEDURE #insData @p1 int, @p2 DECIMAL(18,6)
    AS
    BEGIN 
        INSERT INTO MyTable (x, SupplementalDividends)
        VALUES (@p1, @p2);
    END')

    EXEC #InsData 1, 3.2;

    PRINT '**** CHANGES COMPLETE -- COMMITTING.';
COMMIT TRANSACTION;