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Completed Contract Method may only be used by small contractors and any home construction contracts. The fact that you are an LLC does not factor into the choice.
The disadvantages of the completed contract method are:
If your annual gross receipts for the last 3 years were $10 million or less then you are a small contractor. Large contractors are required to account for long-term contracts using the percentage-of-completion method (PCM) for their general construction contracts.
I hope this information is helpful,