Here is a great article by Dian Hymer, a nationally syndicated real estate columnist and author
Sellers are inclined to go with the highest-priced offer when they receive more than one. But, price is only one factor to consider. An offer with a lower purchase price but a large down payment and a quicker close could be best. The terms of a purchase offer can make or break a deal, particularly given today's stringent mortgage qualification requirements. Buyers with large cash down payments usually have an easier time qualifying for a mortgage than do low-cash-down buyers. However, today even large-cash-down buyers need to qualify.
Unlike in 2006, lenders now require verification of employment, a great credit record, and one or two acceptable property appraisals. A large cash down payment can salvage a transaction that might otherwise fall apart if the property appraises for less than the purchase price. If the lender is willing to loan the buyer up to 80 percent of the appraised value, and the buyer needs a loan for only 60 percent of the price, the deal will probably stay together if the appraised value is 5 or 10 percent lower than the purchase price. But, if there is an appraisal contingency in the contract, the buyer could decide not to proceed with the transaction, or not at the purchase price, based on the fact that the property didn't appraise for the price he agreed to pay. The buyer might try to renegotiate the price to keep the deal together. If the seller doesn't agree, the buyer can usually withdraw without penalty, depending on the wording of the appraisal contingency.
When the appraised value comes in under the purchase price and the buyer is making a low down payment, you're sure to have a problem unless the buyer has more cash to put down or the seller agrees to lower the price, or a combination of the two. Let's say your home is listed for $775,000. You receive three offers from qualified buyers. One is for $850,000 from a buyer who has lost out in multiple-offer competition repeatedly. He will make a 10 percent down payment, and the contract includes an appraisal contingency. The second is for $825,000 with a 40 percent down payment and an appraisal contingency. The third offer is also for $825,000 with a 35 percent down payment and no appraisal contingency. You are told by the buyer's agent that the third buyer has more money to put down, if necessary. All offers include an inspection contingency.
HOUSE HUNTING TIP: One option would be to use a multiple counteroffer that includes a provision to alert the buyers that counteroffers are being issued to one or more other buyers. Acceptance of one of the counteroffers will occur when the seller re-signs the counteroffer after the buyer has signed it. The seller has only one house to sell so the multiple counters must be conditioned on the seller having the final say. The terms of multiple counteroffers don't need to be the same for each buyer. If the comparable sales don't support a price even close to $850,000 for your home, the offer from the "10 percent down" buyer is risky. You could counter this buyer and ask him to increase his deposit amount and waive the appraisal contingency. You could ask the second buyer to pay $850,000 and remove his appraisal contingency. And, you could increase the price to $850,000 on the third offer.
The risk of this approach is that you could lose one or all of the offers, particularly if the buyers think you're greedy. All offers are for significantly more than the list price.
Another option is to not use a multiple counteroffer, but accept or counter the third offer in primary position and counter the second offer for backup position.