Hi lazarus,
While there are many different “definitions” of quality (see post #4 here) … in most of the information on this site “quality” is synonymous with durability.
There is more about the 3 most important parts of “value” of a mattress purchase in post #13 here which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists based on suitability, durability, and all the other parts of your personal value equation that are most important to you).
Unfortunately there is no way to quantify how long any mattress will last for a specific person or predict exactly when you will decide to replace it because it is no longer suitable or comfortable for you (because this is the only real measure of durability or the useful life of a mattress that really matters) because there are too many unknowns and variables involved that are unique to each person but if a mattress is well inside a suitable comfort/support range and isn’t close to the edge of being too soft when it is new (see post #2 here) and meets the minimum quality/durability specs that are suggested in the guidelines here then it would be reasonable to expect a useful lifetime in the range of 7 - 10 years (although in your case it may be less than that if your mattress only meets the minimum specs in the guidelines) and with materials that are higher quality and more durable than the minimum guidelines (in the top comfort layers especially) it would likely be in the higher end of the range or even longer.
The relationship between the quality/durability of the materials in a mattress isn’t linear so it very unlikely that a mattress that is half the cost of another mattress would have half the useful lifetime. If a mattress uses much lower quality materials that will soften or break down more rapidly then in some cases you may be looking at a useful lifetime that can sometimes be measured in only months or a very few years even though the mattress is in a higher budget range. In some cases a mattress that is twice the cost of another mattress may contain less durable materials and may last for a significantly shorter period of time than the lower cost mattress.
There is more about the many variables that can affect the durability and useful life of a mattress relative to different people in post #4 here and the posts it links to.
While you can assess the durability and useful life of a mattress relative to another mattress by comparing the type and quality of the materials inside them that would tell you “this mattress” would likely be more durable than “that mattress” … there really isn’t a way to predict the number of years that you will sleep well on any specific mattress (and how well you sleep is the most important part of the “value” of a mattress purchase) which also means that there really isn’t a way to predict the “cost per year” of ownership because you can only know this after you decide to replace it.
The most reliable way to assess the durability and useful life of a mattress relative to another one would be based on the quality and durability of the materials inside it rather than trying to use the cost of the mattress as a way to calculate a “cost per year” of ownership ahead of time.
In most cases in “real life” the strategy of buying twice as many mattresses that each cost half as much (or similar mathematical strategies) will be much less effective than most people believe it will partly because they aren’t including how well they sleep on the mattress as a significant part of value and partly because the relationship between price and durability isn’t linear.
I would also keep in mind that there are many mattresses that use the same type and quality/density of materials as the Tempurpedic mattresses that would be just as “comfortable” and just as durable (or sometimes more comfortable and durable) but are in significantly lower budget ranges than Tempurpedic which is one of the reasons that I would avoid Tempurpedic mattresses along with all the other major brands (see the guidelines here) because they generally either use much lower quality and less durable materials (in the case of Simmons, Sealy, Serta etc) or they are generally poor value (in the case of Tempurpedic).
This article about mattress budgets may also be helpful.
Phoenix