What an interesting question. Program evaluation has been in existence for, literally, thousands of years, and the way your question is worded makes it really easy to answer (as long as you know some specifics about this type of evaluation). Let's begin with the definition and continue with the rest of the things you ask.
First, the purpose of program evaluation can be found within its definition. Basically, it is a method that uses specific steps to collect and analyze information about different projects (within a company, organization, or simple group). A secondary purpose is to show any interested parties if the project is producing its intended effect.
Second, the process of program evaluation involves different stages and involves answering a number of questions. Is the project needed? Is the project designed logically? Is the project coming about according to the intended plan? Does the project have an impact and, if so, what is the impact? Is the project cost efficient? The answer to each one of these questions has its own detailed process, but the compilation of all of them together constitutes the actual "process" of the general program evaluation.
To satisfy the learners, we have to go no further than their title to figure out the answer. Are the learners truly learning what is intended to be learned? In order to find this out, the learners can be tested or assessed to find this out. The facilitators and/or the agency can also simply ask the learners if they are satisfied through a questionnaire or the like.
To satisfy the facilitators, we must look back at the learners. Most likely the facilitators are the "teachers" of the learners, so the questionnaire mentioned above would be instrumental for the facilitators to find out if they are helping the learners achieve the intended consequences of the project. Further, are the facilitators being compensated (in whatever way) for their participation? Without this important segment, the facilitators wouldn't be satisfied. Sometimes the simple knowledge of learners learning is enough. In other cases, monetary compensation might be provided. In still other cases, verbal recognition is sufficient.
To satisfy the agency/company responsible we need to look at the final questions in the third paragraph (the ones dealing with the process). To satisfy the company, the company leaders will be looking at the bottom line. They want the project to achieve its overall intended purpose. They want both the learners and the facilitators to be actively involved. They want the project to have a positive (instead of a negative) impact on the agency as a whole. Perhaps most of all, the company wants the outcome to be cost effective. It is this last segment, in my opinion, that will constitute the greatest happiness for the company or the agency involved.
In conclusion, it is obvious that the last part section of your question shows that you must be referring to some kind of educational program (hence the terms "learners" and "facilitators"), but without more specifics, all of the answers to your questions had to be fairly general.