How did you come to the $10K number? Based on revenue? Each of your contributions? Tough to answer this without understanding if the app is on the upswing or on decline etc.

So...

Does he want 5% equity of the app or 5% residual royalties? My guess is that he wants to participate in the revenue. If that is the case, I would structure an X-year sliding deal that eventually worked him out of the app. It could be something like Year 1: 5% of PROFIT share. Year 2 3% of PROFIT share. Year 3 1% of PROFIT. Year 4? Nothing. It has to be based on PROFIT not REVENUE.

Structuring a company and then issuing "shares" in an app is insane to me given the likely lifespan of an app. Too much hassle.

I will leave the valuation and counterquestions about how you arrived at $10k out of this response since others have handled it. My advice would be to setup a formal entity asap (LLC or C Corp) using the resources here (FREE and thorough entity setups) http://www.foundersworkbench.com/

If you never plan on raising money for this and it is a lifestyle business then you can use an LLC and issue yourself 95% of the member units and your former partner 5% of the member units.

If you want to be more strategic and think you may have something that will grow into something or potential take on new investors in the future go with a Delaware C Corp and

Authorize 10m shares
Issue yourself 5m shares at par value .001 (will cost you $500 to establish the basis and you put this money into the corporate account in exchange for the shares you receive)

You then have another 5million shares for any potential option pools or future investors you need, but until issued your 5m shares represent 100% of the company undiluted.

You can either issue your former partner a warrant to purchase up to 250,000 shares of common stock at par value for a period of the next 2-3 years (you decide the runway) which would be 5% of what you have issued and outstanding.

Or you could put a 4 year vesting schedule in place whereby he has to provide certain ongoing advisory services etc and can buy the common stock today at par value like you ($25 to purchase the 250,000 shares) which would go into the corp acct in exchange for the stock certificates.
The 4 year vesting schedule means that each year he fully vests 50,000 of his purchased shares and that if he underperforms his agreed advisory role or you guys go a different direction the company has the right to buy those remaining unvested shares back from him at par value.)

In both cases you (and he) will have 30 days to file your 83B election with the IRS so talk to your accountant asap to make sure your 5m shares are registered for long term capital gains and that you won't pay ordinary income tax on the value of the shares in the future. (see http://www.orrick.com/Events-and-Publications/Documents/1955.pdf)

Hope some of those tips and links help you. :)

If you're offering him the 5%, you need to legalize it by forming a company and having it put into the documents. Your CPA or lawyers will guide you through the process.