A potentially large client that would like some Mobile App development done, has asked us to do a mockup of our concept of the app. Should I charge?

Completely agreed with Evan. The only time I would ask a shop to do work without money being exchanged is when they're taking equity in a project. A blended rate of $79 per hour is at the mid point of reasonableness and $120-$150 per hour would be the high point.

If you're asking about rates, it sounds like you don't have a lot of experience building mobile apps so if that's the case, I'd suggest you charge the low end of the range because it has the potential to act as a big reference account for you. If on the other hand, I'm reading the situation incorrectly, then charge whatever your normal rate is.

I refer a lot of work to a couple of mobile app shops I trust and like and have previously worked at an interactive agency. Happy to talk to you in a call to give you more perspective and clarity.

Best of luck!

My shop produces hundreds of software project estimates for everyone from high-impact entrepreneurs to multi-billion dollars companies each year (and probably half or more of those are mobile specific.) It's not uncommon to have clients request these sorts of deliverables upfront to help in their evaluation and selection process.
Generally speaking I would agree with the previous posters on it being fairly standard to charge something for producing mockups (in particular using the example of discounting what you would charge towards the bid price of the eventual full project; only being collected if they decided to move in another direction.)
However, I will play the devil's advocate here just to offer a contrarian opinion:
When done properly, producing a mockup for any project (particularly a mobile application) takes into account things like researching the target end-user, studying competitors and UX patterns, the integration of market/industry best practices and even mapping out your entire user flow (information architecture, API integrations etc.) However, purely as a UI exercise, just creating a mockup of a few screens should in and of itself being a straight forward process. While this does not mean you should put a limitless amount of research/design time into the project before being “on the clock”, it does mean that you should be ready to accept a certain amount of sunk-time for each project you onboard. What I would recommend, in order to not let this get out of hand, it to come up with a formula to track/monitor if you are allocating an appropriate amount of time to the business development opportunity. Let’s say, for example, you are willing to spend 1 free hour of work for every $2,000.00 of opportunity the project represents: if the total bid/budget from a client is somewhere in the $40,000.00 range you should be ready to spend no more than 20 total hours on business development and related tasks (in this case, creating mockups is part of that total.) This should at least give you a sense of how to scale your Biz Dev efforts beyond just this one opportunity moving forward.
The bottom line is if the opportunity is something that is game-changing for your venture (i.e. larger clients are far less common for you currently), now is the not the time to quibble over a few hundred dollars. The focus you should be spending is on making a high-quality mockups and value-added exchanges to help land that new business. I’m available for a call to discuss estimating, bidding and business development tactics with you further. Good Luck!

I absolutely agree with Laura.

All good answers but I'd come at this from a different perspective, i.e. the perspective of a product manager or product marketer.

Here's what I mean. If the prospective large customer is in a segment with multiple competitors--and the workflows and UX mockups you do can be repurposed and rebranded with the name of one of their competitors---then I'd do it on spec, i.e. for free, if it's only 20 hours.

I'd then say to the prospective client, "Hey, this is a core competency of ours and we've built these workflows for an industry segment. We'll rev share with you on the customized 'app' we spin up with no upfront cost to you."

If (or when) they freak out at that concept of you having so much "lock in" market power in relationship to your project and future iterations of the app, they'll be glad to pay you for it upfront---especially now that they think you are a domain expert in their space.

Good luck.

We're working on a mobile project for a client right now and, in order to scope the project properly, we created very basic wireframes with no functionality. I think it's imperative that this be accomplished to set and meet expectations on the delivery for the agreed upon price.

Defintely! This is your beta version . A proof of concept for the idea. This is what will make them see how the project flow goes.

Analysis and design is the core of any successful project. Why do you want to do it for free ?

Execution of the plan is not the issue.