I don't agree with most of those commenting on this topic. My advice: dump the contractor immediately and have a talk with the CEO about trading equity for services.
I'm a Silicon Valley based founder of multiple start-ups, had a few successful exits, and I'm an active angel investor.
First, the contractor doesn't know what he's talking about. If he did, he'd be asking for a cap table instead of balance sheets, P&Ls or historic financials.
The fact you've been asked to mediate an agreement at this early stage is a bad sign and evidence the contractor will be a problem in the future.
Tell the CEO to find someone who understands risk. There are contractors large and small out there who can do the job, understand equity exchanges, and will work with the company.
Second, don't equivocate the contractor's risk with that of an investor. Investors put their money up and bet on the team scoring a win. They don't have the ability to change the outcome of their investment (this applies even to VCs). Conversely, a contractor has work product and input. He can help shape the success or failure of the company - he should be part of the team, not an "investor".
Finally, the reason any of us take risk with a start-up is because of excitement. We get excited about a team committed to making the venture succeed against all odds. We get excited about growth, the market potential, the user base. I've yet to find a VC or investor get excited about historic financials.
Closing point: Slack just raised $180 Million at a $1.1 Billion valuation. Started in February, the tech press says they have about 125,000 users and a phenomenal growth rate. I doubt any of those involved talk about Slack's P&L or balance sheet - obviously Slack is too new to have historic financials.
Slack isn't successful because of the valuation, the valuation is because many believe the company will succeed. This applies to all start-ups.
If a contractor doesn't have this kind of faith, find someone who does.