Taxpayer is on the cash method. On December $1,$ Taxpayer receives a signed agreement with Customer in which Customer agrees to Taxpayer $$5,000$ for restoring Customer's vehicle. Taxpayer completes the restoration on December $28.$ Not entirely pleased with the work, Customer pays Taxpayer $$4,500$ on January $5,$ Year $2.$ Taxpayer decides not to pursue the $$500$ difference. What are the results to Taxpayer?

Taxpayer has no gross income in year $1$ and $$4,500$ gross income in year $2.$

Taxpayer has gross income in year $1$ of $$5,000$ because the agreement is a cash equivalent. Taxpayer is entitled to a deduction of $$500$ in year $2.$

Taxpayer has gross income of $$4,500$ in Year $1$ because Taxpayers finds out before filing the Year $1$ tax return that only $$4,500$ would be received.

Taxpayer has $$5,000$ gross income in Year $2$ because Taxpayer voluntarily relinquished the claim to the remaining $$500.$