I made some notes on a British study that showed the production of an "egg-strain domestic fowl moulted twice (at 60 weeks and 100 weeks of age)" from Principles of Poultry Science, by S.P. Rose.
These were commercial layers carried thru 3 laying periods. The study was done to determine the economics of keeping hens this long, not out of sympathy for battery hens. "Layer-fatigue" can be a problem for these birds but, obviously, not enuf of a problem to make too much difference in the research. 
During the first laying period, production thru the months was between about 95% and 80%.
The second laying period had production between about 85% and 70%.
The third was between about 80% and 55% production.
Commercial operations never let their birds get to that third laying period or have birds that are 140 weeks of age. Their profit margins are too small. You would have to decide if hens of that age would be valuable to you since, during their 3rd year, they are laying about one-third less eggs than young pullets. And remember, these were production layers and I bet the flock was culled carefully to eliminate, as best as could be determined, the birds that were not laying.
And I've gotta be honest with you: I've never kept a hen (except 1 pet) that long either but I may do so with the current little flock.
Steve