Quick Answer: “It Depends — But Usually Less Than Buyers Think”
“At the closing table, the Seller will walk away with a check ” and whether the money comes from the Buyer or the lender doesn’t matter.”
–“Do Home Buyers Who Pay Cash Get a Discount?”; The Wall Street Journal (11/4/2010).
The answer to the question, “how much of a discount should a Seller give/Buyer expect for a cash deal?” depends mainly on two things, 
and varies a lot more than you might expect from one deal to another.
The two variables: 1) the home in question; and 2) the Seller’s patience (or lack thereof).
Homes in Disrepair
The big variable is usually the condition of the house.
At one end of the continuum, there are homes without working heat or plumbing that no lender will give a mortgage on, period.
In that situation, a cash offer is the difference between selling or not — and the discount is BIG.
Appraising Appraisal Risk
Assuming the home is in good repair, though, the question becomes, “how likely is the home to appraise?”
No appraisal, no loan — and no loan, no deal . . . at least not at the agreed-upon price.
The risk of non-appraisal increases the more the home’s sales price sticks out above the Comp’s — or there ARE no Comp’s.
So, when a home sells for way above list in multiple offers, the value of a cash offer is higher.
Similarly, when a home is sufficiently unique, or at a (high enough) price point where there are no recent deals to price off of, the Comp’s become trickier, and the risk of the home not appraising increases as well.
While there are ways for Sellers to reduce the risk in a financed deal — like requiring a higher down payment from the Buyer — a cash deal represents zero financing risk.
Advantage (again): cash buyer.
Time Value of Money
Of course, even where there is miniscule appraisal risk, getting a mortgage takes time.
Allowing for the appraisal, underwriting review, etc. is usually a 3-4 week process.
With interest rates essentially zero (at least on short-term money), it’s hard to argue that there’s much discount waiting 30 days to get your money (Mafia loans aside).
However, if the Seller is in dire financial straits and/or facing a looming deadline (Mafia loan??), I suppose getting the money instantly can be (very) attractive.
Bottom line: there are a couple, atypical situations where a cash deal is worth a 30% – 40% discount (I suppose infinite, if the deal can’t be financed).
But in the usual case, I’d estimate the discount for a cash deal is less than 5%.
Other Factors (like Credit Conditions)
While the Buyer’s creditworthiness is also a variable in a financed deal, the risk that a given Buyer won’t qualify for a mortgage can usually be gauged at the beginning of a deal.
See also, “Cash Deal = Quick Closing“; and “Vetting Home Buyers’ Finances.”
The above analysis also assumes normal credit conditions (although I don’t think anyone knows exactly what “normal” is anymore).
What I mean by that is that mortgages are available, on reasonable terms, to well-qualified borrowers.
In other words, the mirror image (sort of) to Walter Bagehot’s famous — and still correct — dictum regarding what central banks should do in a financial crisis.
Namely, they should lend freely, to solvent depository institutions, only against good collateral, and at interest rates that are high enough to dissuade those borrowers that are not genuinely in need (no wonder economics is called “the dismal science”).
Here that, Ms. Yellen??
Whetting Sellers’ Appetite; Role of Salesmanship
Finally, in addition to all the rational, logical arguments regarding cash and cash discounts, there’s the purely emotional angle associated with getting your hands on lots of cold, green cash.
And pre-Internet era agents, who were accustomed to presenting offers in person to the Seller (and their agent), knew it.
So, good Buyers’ agents would make a show of conspicuously flourishing a (big) earnest money check in front of the Seller, then leave it on the table in front of the Seller to salivate over during the rest of the presentation.
