This study analyzes the impact of changes in central bank digital currency (CBDC) issuance and interest rates on commercial bank profitability, considering the interaction of individuals (savers and borrowers), commercial banks, and the government (central bank). We show that the profitability of commercial banks in the deposit sector decreases when interest rates higher than deposit rates are imposed on CBDC or liquidity constraint policies are enforced. On the other hand, if the interest rate on CBDC is lower than the deposit rate, the effect on the profitability of commercial banks is minimal, and the profitability of the loan sector is not affected by the CBDC issuance. We also suggest implications for the method of operating CBDC. If the CBDC is not operated directly by a central bank, but indirectly by commercial banks, the government's costs may decrease and the profits of the commercial banks may increase due to the business connectivity and effects of the economy of scale.