 Solution

Resource savings do not by themselves establish a financial saving. The one-recycle case avoids purchasing $34374.04$ kg U in natural feed and $1592.76$ kg-SWU per year. Those are the benefits to compare with the incremental costs, not the whole value of the recovered uranium or the gross avoided fresh-product separative work.

Let $p_U$ be the concentrate price per kilogram of uranium, $p_S$ the price per kg-SWU, and $C_{\mathrm{add}}$ the annual net extra cost of recovery, recycle-specific conversion and fabrication, waste management and financing, relative to the once-through alternative. Recycling is cheaper under this simplified boundary only ifEquivalently, if $p_S$ and $C_{\mathrm{add}}$ were supplied, the break-even uranium price would beAn avoided spent-fuel-disposal charge belongs as a credit in $C_{\mathrm{add}}$; a new radioactive waste conditioning or disposal liability belongs as a cost. They must not both be assigned the same sign simply because each concerns waste.

The natural-uranium saving is appreciable, but the fractional separative-work saving is small. Recovery losses and the uranium-236 compensation limit the value of recycling. Additional radiological handling, separate fabrication campaigns, secondary waste streams, capital tied up during storage and recovery, and uncertain future disposal costs can matter. Conversely, a higher natural-uranium price, a lower incremental recovery cost or an independently justified disposal credit can favour reuse. The calculation gives a conditional comparison, not a uniquely determined economic verdict or market-price threshold, because no costs are supplied. plutonium utilisation is a different option and has not been silently credited to this uranium-only recycle.