This study investigates the internal information flow of large language models (LLMs) while performing chain-of-thought (CoT) style reasoning. Specifically, with a particular interest in the faithfulness of the CoT explanation to LLMs' final answer, we explore (i) when the LLMs' answer is (pre)determined, especially before the CoT begins or after, and (ii) how strongly the information from CoT specifically has a causal effect on the final answer. Our experiments with controlled arithmetic tasks reveal a systematic internal reasoning mechanism of LLMs. They have not derived an answer at the moment when input was fed into the model. Instead, they compute (sub-)answers while generating the reasoning chain on the fly. Therefore, the generated reasoning chains can be regarded as faithful reflections of the model's internal computation.