Should you assign a valuation to price your startup's investment round?
Whether or not you price your round will depend very much on your stage. Early-stage founders will probably need a valuation, if only because friends-and-family investors won't be able to determine a price. Later stage investors, however, know better.

One question we're asked, from time to time is: should founders price their round?
The answer we give is that is depends entirely on your stage.
How should early-stage founders value their startup?
If you're an early-stage startup founder, raising a friends-and-family round, or perhaps your pre-seed, it's likely that you'll be raising from unsophisticated investors. In this case, almost always, you'll need to price the round. Your investors will probably not know what a fair valuation is, so the onus will be on the founder.
In this case, not only should you aim to come up with a fair valuation, but also you'll need to be able to defend it. You should also have investment documents at the ready. You'll want to move from verbal commitment to formal signature relatively swiftly, so don't wait until someone says yes before putting your docs together. Creating shareholder and subscription agreements will take time - definitely long enough for your investor to have a change of heart.

What is a fair valuation for a new startup?
Valuations for your first raise are more art than science. A good rule of thumb for a startup that has the potential for a $100m exit is $2-5m. Where in that bracket you sit will depend on several factors, like IP, founder experience, traction, and any unfair advantage you may have.
In any case, the valuation needs to be high enough to allow you to raise without getting too diluted, and low enough that your first investors have a chance of a 50-100x return, to offset the inordinate amount of risk these super-early investors take on.
That's true whether the friends-and-family investors want it or not, because the next round of investors are going to want it too, and they know better!
In the early stages, it's in everyone's interest that the founder retains (at least a sense of) control and majority ownership. So you need to be able to raise enough to hit your next milestones without running out of fuel, and without the core team losing interest. (The latter is the silent killer of a very large percentage of startups!)
Don't get fancy with classes of shares either, or think about getting fancy with non-dilutive shares. These are red flags to experienced investors. Just issue everyone with ordinary shares. Your earliest investors deserve to be on the same deal as you, if not better.

What percentage should your first investors expect?
If your investors accept your business idea is worth $2m, and they decide to invest $100K, what percentage of shares will they get? 5%?
No.
To industry insiders, the difference between pre-money and post-money valuation is clear, but most first-time investors will not understand it. Sadly, many early-stage founders don't either.
I learned this the hard way. I was a board observer in a startup with a very impressive board - excellent, smart founders, and accomplished investors. I was a newbie. We were discussing the merits of a funding round, and I got all tangled up by pre- and post-money. Embarrassing. For anyone who hasn't come across this, here's the difference...
If your company is worth $2m pre-money, and you raise $500,000. The startup instantly becomes worth $2.5m (post-money). It's the same $2m company, but now with an extra $500K in the bank. The investor doesn't just own a percentage of the company they invested in. Their shares also entitle them, theoretically, to the appropriate share of the money that is now in the bank, which wasn't there when the valuation was agreed. So they own 20% of the $2m company (worth $400K) and 20% of the $500K in the bank ($100K). Of course, now the startup and its assets are all considered one unit, so the investor owns 20% of the startup and all its assets, represented by their equity in the company.
If this seems obvious, take it from me, a lot of smart, experienced people get this wrong, and expect to own 25%! If you're a founder, make sure your investors understand this.
Should later-stage startups price their seed or series A rounds?
At the later stage it pays to be more circumspect. Don't scare off investors by aiming too high, and equally you shouldn't do yourself a disservice by pricing too low.
The best advice I've seen on this came from entrepreneur-turned-VC, Mark Suster. He offered this suggestion:
"We’re hoping to raise $5–7 million in this round. We know roughly how VCs price rounds and we think we’ll likely be within the normal range of expectations. But obviously we’re going to let the market tell us what the right valuation is. We only raise every 2 years so the market will have a better feel for it than we will.”
If you're speaking to funds, or more experienced investors, I agree that this is the best approach, at least when you're starting out. Of course, once you have a lead investor locked in, you'll have your price, and other investors can either take it or leave it.
Image credits
– Shocked lady by Andrea Piacquadio.
– Grumpy cat investor by Niranjan.
– Confused dog by Dex Ezekiel.