This question is mainly for those who cull your hens at a certain age and bring in a new flock of layers. What age do you cull and bring in your new layers? What time of year do you normally do it?
My grandfather would cull around 1 1/2 and bring in 8 or even 16 week old girls around that time so they would be laying full time in the spring.
In Maryland, with spring and fall colder, most of the chickens for sale seem to be April and September.
I think part of the answer for you depends on your goals, why do you have chickens and what do you hope to get out of them. My goals are different than yours. The main reason I raise chickens is for the meat, the eggs are a nice side benefit, but I don't try to sell them. I give my excess away. I also play with genetics, which means I have to hatch chicks. For me it is more of a hobby, I've never tried to figure costs but I know the store chicken meat is less expensive. I expect the people that break even or even make a bit of money on eggs get a lot more per dozen than regular store eggs. Often you can.
I don't keep individual chickens as pets. To me the entity is the flock and I make my decisions on what is best for the flock and my specific goals, not a specific individual chicken.
My system is that I hatch as many chickens as I will eat in a year. I select my replacements for my laying/breeding flock from them and eat the rest, male and female. Usually by fall I am down to four pullets already laying that I'll keep. Most of these tend to lay through the winter with no lights so I have eggs to eat.
I'll keep three or four of the previous year's pullets that have laid for a full season, about a year and half old. These go through a molt and come back laying like gangbusters the following laying season. I've bred mine so they often go broody which i like. At the end of the laying season I put the 2-1/2 year old hens in the freezer and only overwinter the pullets and 1-1/2 year olds.
My year is really uneven with egg laying. During the winter I typically have 3 or 4 pullets laying which is plenty of eggs for us to eat. In the spring and summer I typically have 7 or 8 hens laying when they are not broody so plenty of excess eggs. Then when that year's hatch of pullets start laying and I'm evaluating which to keep and which to eat I'm swamped with eggs. Not a very good business model if you are trying to keep customers happy.
One reason I replace my 2-1/2 year olds is that they tend to lay fewer eggs after their next molt. For some hens it is not much of a drop-off, for some it is really significant. I don't want to feed them through another molt when I'm unsure how many eggs they will lay. But that 's not the main reason. I spoke with a chicken disease expert. He said that if I kept them more than three years they tend to have more problems with disease or physical problems. Not all are going to have medical problems as they age, but there is a tendency. That's not the main reason.
I have the will-power to limit how many chickens I keep and only hatch what I need. By replacing these older birds with pullets I usually get eggs throughout the winter. It doesn't always work but usually does. I went two months with practically no eggs a few years back as the 1-1/2 year olds were molting and those darn pullets did not start laying until December.
This is a bit if a reason but the main reason is that I play with genetics. Some people that play with genetics won't breed a hen or rooster until they are a couple of years old, it takes that long to see if those chickens have the genetics they want. My goals are more short-sighted. Once I achieve something and see how it turns out I often change direction and go on to something else. So I need new blood.
I process my 2-1/2 year olds when they molt and stop laying, occasionally a bit before if I have a lot of pullets laying. I skin mine instead of pluck so the pin feathers they have during molt is not an issue. The eggs aren't that important to me but it's the principle of the thing. I paid to feed them during the previous year's molt so I want those eggs, even if I give them away. Not really logical.
That's how I go about it and I've tried to give reasons why. A lot of that won't apply to you because I'm sure your goals are different.