On January $1,2014,$ Cardinal Corporation issued $5\%25-$year bonds at par and used the $$12,000,000$ proceeds to finance the construction of a new plant. On January $1$

$2024,$ the company acquired the bonds on the open market for $$11,500,000.$ Assuming that Cardinal is neither bankrupt nor insolvent, the acquisition and retirement of

bonds results in which of the following?

a$.$ The company can amortize the $$500,000$ gain, recognizing income over the remaining life of the bonds.

b$.$ The company can make an election to recognize a $$500,000$ gain or reduce the company's basis in the plant by $$500,000.$

c$.$ The company must recognize a $$500,000$ gain and increase its basis in the plant by $$500,000.$

d$.$ The company must recognize a $$500,000$ gain.