I'm currently on a trial run contract (hourly) for a division of a company I'm interested in working with in the future. They've asked me to do some work, for which if I were just a contractor would usually charge at least in the $35-55/hour range, depending on the work. However, due to previous relationships with other parts of the company I am already on payroll, officially being paid hourly at $15/hour.
I've been asked to quote an hourly rate for this contract work for them. It's pretty small - probably 8 hours max of work - and at the end of the day I'm willing to do it at the 15/hour rate I'm currently getting, because the opportunity for future full-time work is far more valuable than the extra few hundred dollars right now. Even if it doesn't pan out, the risk-reward analysis in my mind still is okay with doing this work for 15/hour. The full-time position is not definite yet by any means, but there does appear to be significant interest on all parts. Finally, one of my mentors works in this division so I do have a personal relationship already - I wouldn't be doing this with strangers.
That said, I'm not quite sure how to proceed. I am willing to be underpaid for this because I'm here to prove my competence, but at the same time I don't want to be undervalued or seem low-value/unprofessional - things that would be relevant during the negotiation phase if a full offer is extended.
How should I proceed? Should I ask for a higher rate, say that my current hourly is fine, maybe go the other direction and offer to do it for free?
To add some more clarification, the complex part of this is that the full-time position is not yet formalized, nor offered. This contract is something they happen to need right now anyway, and if I were to work for them is part of the work I might do, and so it's partially one-shot contract and partially trial run.
They know they will hire someone and are strongly considering me -- to the point that they joked about writing the job listing so I would be the only qualified applicant. On a more serious note, I've essentially already had a first interview with them before they've even posted. I've also been given a probable pay range for if this does go through, which is pretty good.
Finally, I currently hold a full-time job, but they're trying to recruit me away so I feel like trying to undervalue me during negotiations later on will not be a productive strategy for them - I can turn them down without fear.