The people that generally resolve their debts for pennies on the dollar either have a very large debt and a modest income, or have a small fixed income and a limited amount of assets. An offer in compromise is based on a taxpayer's ability to pay. This means the IRS takes a person's income, assets, retirement accounts, past earnings, and future earning potential.
To give you an idea, here is a very simplfied description of the OIC determination. The amount of the offer is based on a formula in the IRS OIC booklet, Form 656. The formula asks about income, equity in assets, retirement and bank accounts and then provides an amount that is considered your ability to pay. This is the amount the IRS considers the minimum they will accept for an offer. If the amount is in excess of the amount you owe an offer will not be accepted. If it is less than the amount you owe, this is the amount by which you may be able to reduce your tax debt.
The truth is the IRS accepts about 25% of all OICs submitted. However, I think this number is artificially inflated by people making an OIC that doesn't meet the requirements to submit an OIC. If you meet the requirements to make an Offer in most cases the OIC will be accepted. In my experience, most OICs are initially rejected, even if they otherwise appear to meet all of the requirements. To have one approved, there is usually some back and forth with the reviewing agent, and if that is not succesful, IRS appeals is the next step. For a correctly submitted OIC, these first two steps are all that is necessary and the majority are accepted by this point. They last resort is Tax Court and the outcome there really does depend on what has occured prior to the court date.
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As with everything related to the IRS, it is difficult to provide comprehensive information related to taxes and tax law on the web. Please do not rely on this article without consulting your tax professional.