I think the key here is this comment
We are hoping to raise a small amount of pre-seed capital (200K) and are trying to determine company valuation / equity.
What I really am hearing being asked is
We want to give away the smallest block of equity to get $200k that we can. How do we value ourselves to do this
The reality is that because you don't have the dollars, this is really more of a value sell more than anything
Here's why. Any seed investor that is going to put in $200k is going to expect a $2Million payout in 3 years. That means for you to retain any cash benefit, you have to be able to re-finance the company at $2million plus because regardless of whatever fraction of equity you give them, the contract will be written that
So that means that in 3 years, you really want to be able to refinance for about $4 million ($2 million to buy out the Seed investor, $300k to pay yourselves a salary boost, $1.7 mil to grow the company to $40 million in another 3 years).
Work backwards from that