Answer
A realistic budget breaks the number into distinct pieces that each move independently. Power hardware pricing scales with the server tier and core count, IBM i licensing is tied to processor group and software tier rather than a flat per-machine fee, and most third-party ISV software licenses key off core count or named users, which means a partition sizing decision made for performance reasons can quietly change the software bill. On top of that sits software maintenance renewals, high-availability replication tools if the business needs one, and either internal staffing or a managed services contract to keep it all running.
Staffing deserves particular attention because it is often underestimated. RPG and COBOL expertise is scarcer and commands a premium compared to more common stacks, and that cost shows up whether the business hires directly, retains a contractor, or pays a managed services partner to cover the gap. When comparing quotes, ask each vendor to itemize hardware, IBM i licensing, third-party software, support, and staffing separately rather than accepting a single bundled number, since that is the only way to see which piece is actually driving the total cost of ownership.