To evaluate the cost-efficiency of your boiler, you can calculate its annual fuel utilization efficiency (AFUE) rating. AFUE is a measure of a boiler's energy efficiency, expressed as a percentage. It represents the amount of fuel that is actually used to heat your home, compared to the amount of fuel that is consumed by the boiler. A boiler with an AFUE of 90% is considered to be highly efficient, while one with an AFUE of 70% is considered to be less efficient.

To calculate your boiler's AFUE, you'll need to know the amount of fuel that it consumes in a year and the amount of heat that it produces over the same period. The formula is:

AFUE = (Heating output) / (Fuel consumption)

If you don't have this information, you can contact a heating contractor to have them perform an evaluation of your system.

When evaluating different heating systems, you can use the AFUE rating as a starting point. In addition, you can also look at other factors such as the type of fuel that the system uses (natural gas, oil, propane, etc.), the initial cost of the system, and any ongoing maintenance costs. It may also be helpful to compare the energy costs of different systems over time to get a sense of their long-term cost-effectiveness. The size of your home and your local climate will also play a role in determining the most energy-efficient heating system for your needs.
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