The impulse of the Fourth Industrial Revolution is triggering the demand for few specific metals. These include copper, silver, gold, and platinum group metals (PGMs), with important applications in renewable energies, green hydrogen, and electronic products. However, the continuous extraction of these metals is leading to a rapid decline in their ore grades and, consequently, increasing the environmental impact of extraction. Hence, obtaining metals from secondary sources, such as waste electrical and electronic equipment (WEEE), becomes imperative for both environmental sustainability and ensuring availability. This recovery entails few problems such as allocation due to the simultaneous production of several metals, the use of non-renewable resources, and the exergy destruction during the life cycle of the metals. Therefore, this work analyses the waste printed circuit boards (PCBs) recycling process by proposing different exergy-based cost allocations for the mentioned metals, disaggregating the exergy cost into non-renewable and renewable, and considering the complete life cycle of metals with the Circular Thermoeconomics methodology. The results show a significant saving of non-renewable energy by using renewable energies in primary extraction (67-87%), recycling (97.6-98.5%), and renewable energies in recycling (98.7%, 99.0%), compared to conventional primary extraction. However, when considering the entire life cycle, between 47% and 53% of the non-renewable exergy is destroyed during recycling. Therefore, delaying recycling as much as possible would be the most desirable option for maximizing the use of non-renewable resources, which nature cannot replace in a short time.