The most useful arithmetic in a short-sale study file is transparent subtraction. Start with the proposed sale price, identify each assumed deduction and calculate the amount available to the relevant creditors. Then distinguish this estimate from the servicer's approved settlement terms and the closing professional's final figures.
Worked example one
Assume a fictional sale price of $300,000. Combined selling and settlement costs are estimated at $21,000. A separate $6,000 allocation to a junior lienholder is proposed. For this exercise only, there are no other deductions and the first-mortgage payoff is $310,000.
Net before the junior allocation is $300,000 minus $21,000, or $279,000. Net proposed to the first mortgage is $279,000 minus $6,000, or $273,000. The difference between the assumed first payoff and its proposed receipt is $37,000.
That $37,000 is an arithmetic difference, not a legal finding of collectible deficiency and not a tax calculation. The payoff amount, permitted expenses, lien treatment, written approvals and applicable law still matter. Never label a spreadsheet difference “taxable income” or “debt forgiven” without the relevant professional analysis.
Compare the right figures
The first mortgage's proposed receipt should be compared with the first mortgage's payoff, not with the total of every obligation unless the calculation explicitly calls for that. Mixing total debt with a payment to only one creditor produces a misleading gap. Similarly, a statement balance may omit interest, fees or other amounts reflected in a dated payoff.
Track the date through which an estimate or payoff applies. If closing moves, ask the responsible party to refresh the figures. Do not add a generic daily interest amount unless it is actually supplied and applicable. An estimate that was accurate last week can become wrong without any change in the sale price.
Worked example two the stronger offer
Offer A is $310,000 with $22,000 in assumed selling costs and a $5,000 proposed junior allocation. Offer B is $315,000 with $24,000 in assumed costs, an $8,000 buyer credit and the same $5,000 junior allocation. All deductions are separate in this exercise.
A produces $283,000 for the first mortgage: $310,000 - $22,000 - $5,000. B produces $278,000: $315,000 - $24,000 - $8,000 - $5,000. The higher headline offer produces $5,000 less on these assumptions.
This does not establish which offer should be accepted. Financing, contingencies, timing, authorization and applicable duties also matter. The lesson is that price and net are different measures. Present both with their assumptions, and let the proper decision-makers evaluate the complete terms.
Sensitivity exercise
Return to example one. If costs increase by $2,500 and all other assumptions stay fixed, what is the proposed first-mortgage receipt? What additional question must be asked before treating the revised figure as acceptable?
Debrief
The receipt falls to $270,500 and the arithmetic gap rises to $39,500. The responsible team must confirm whether the changed costs and resulting net are permitted by the written approval or require a revised decision. The formula can tell you the difference; it cannot approve it.
Adapted from the independent CDPE Study Companion by Rowan Ellery Voss. Fictional examples are educational; no legal or professional review is claimed.