In January of Year $1,$ Ford Co$.$ purchased a patent from a research institution for $$350,000.$ The patent was estimated to have a useful life of $15$ years. In December of Year $2,$ Ford Co$.$ unsuccessfully defended the patent in legal proceedings. The fair value of the patent on December $31$ of Year $2,$ is now estimated to be $$70,000$ with a $2-$year useful life.

a$.$ Record the entry for the legal fees of $$28,000,$ paid in cash.

b$.$ Record any adjusting entry required on December $31$ of Year $2.$

c$.$ Determine the carrying value of the patent on December $31$ of Year $2.$