Might be worth considering placing a DEFAULT value of 0 on your column, otherwise you'll face the problem you know have.

Another approach might be to use COALESCE() like this

SET NOCOUNT ON

CREATE TABLE AveragingMultipleColumns

(year0 DECIMAL(8,5), year1 DECIMAL(8,5), year2 DECIMAL(8,5))

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(1,2,3)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(1,2,NULL)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(1,NULL,3)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(1,NULL,NULL)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(NULL,2,NULL)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(NULL,NULL,3)

INSERT INTO AveragingMultipleColumns (year0, year1,year2) VALUES(NULL,NULL,NULL)

SELECT year0, year1, year2,

CASE WHEN (year0 + year1 + year2) IS NOT NULL --most likely one first

     THEN (year0 + year1 + year2)/3.0

     WHEN (year0 + year1) IS NOT NULL

     THEN (year0 + year1)/2.0

     WHEN (year0 + year2) IS NOT NULL

     THEN (year0 + year2)/2.0

     WHEN (year1 + year2) IS NOT NULL

     THEN (year1 + year1)/2.0

     ELSE COALESCE (year0, year1, year2) END AS average --nulls and singletons

FROM AveragingMultipleColumns

DROP TABLE AveragingMultipleColumns

SET NOCOUNT OFF

year0      year1      year2      average         

---------- ---------- ---------- ----------------

1.00000    2.00000    3.00000    2.00000000

1.00000    2.00000    NULL       1.50000000

1.00000    NULL       3.00000    2.00000000

1.00000    NULL       NULL       1.00000000

NULL       2.00000    NULL       2.00000000

NULL       NULL       3.00000    3.00000000

NULL       NULL       NULL       NULL