Are you sure you have the proper year-end gift for your boss?
Years old of livelihood. This is each year of livelihood that you have, and at the end of each year you've reached the end of the year. This may also refer to a year end gift.
You've learned this reading, but it might not be the one you were expecting. It's せい, like the saber you use to cut down the old year before starting the new one.