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I think reprocessing is actually cheaper than creating a new rod because you don't have to do as much enrichment of the uranium material.It's not cheaper, at least not with current uranium prices:
* https://fred.stlouisfed.org/series/PURANUSDM
* https://tradingeconomics.com/commodity/uranium
* https://world-nuclear.org/information-library/nuclear-fuel-c...
Prices would need to about double before break-even AFAICT:
> Under the range of fuel cycle unit costs evaluated in this report, unit costs for uranium ore concentrates and PUREX reprocessing have the greatest impact on the overall fuel cycle costs for both fuel cycles. Assuming that other fuel cycle cost components are at the nominal values, the fuel cycle costs for a once-through fuel cycle will be lower than those for a plutonium recycle when the unit costs of uranium are $312/kgU ($120/lb U3O8) or lower, and PUREX reprocessing costs are $750/kgHM (kilogram heavy metal) or higher.
* https://www.epri.com/research/products/1018575
For another perspective, the French do it and claim it is economical enough:
* https://www.orano.group/en/unpacking-nuclear/recycled-uraniu...