Math Walkthrough
Seller's Net Problems: Working in Both Directions
Who customarily pays which closing item, how transfer taxes are levied, and how taxes are prorated differ by state and by contract. Exam items always supply the charges they want you to use, so take the item at its word and do not import local custom into it.
Net proceeds problems ask what a seller keeps once everything charged against the sale has been taken out. Exams run them in two directions, and only one of the two is straightforward.
Given a price, subtracting your way to the proceeds is arithmetic. Given a required proceeds figure, finding the price takes a division that candidates routinely skip, and the wrong shortcut produces an answer that looks close enough to appear among the choices.
Direction One: Price Is Known
With the price given, the work is a list of subtractions. Take the agreed price, remove the brokerage fee, remove the loan balance being paid off, remove the settlement charges assigned to the seller, and remove any credit the seller is giving the buyer. Whatever survives is the net.
Order matters for one reason only: the brokerage fee is quoted as a percentage of the price, so compute it from the price before anything else is deducted. Applying the rate to a balance you have already reduced is the most common way to get one of these wrong, and the resulting figure is always too small.
Keep the credits in the list. Repair allowances, closing-cost contributions and the buyer's share of prepaid taxes are all money the seller does not walk away with, and exam items include them precisely because candidates stop after the fee and the payoff. Prepayment penalties and the seller's share of prorated items belong in the same column.
Two quick sanity checks catch most errors. The net must be smaller than the equity implied by price minus payoff, and it must be positive unless the item is deliberately describing a shortfall. If either fails, the fee was almost certainly computed on the wrong base.
Direction Two: The Net Is Required and the Price Is Not
Here the seller states what must be left over and asks what the property has to sell for. The complication is that the brokerage fee is a share of the very number you are solving for, so you cannot add a known fee to the target and be done.
Set it up in two moves. First, add the fixed charges to the required net: the loan payoff, the seller's settlement costs, and any credits promised to the buyer. That sum is the money that must remain after the fee comes out. Second, recognize that the fee takes a fixed fraction of the price, so the remainder is the rest of the price expressed as a decimal. Dividing the sum by that decimal gives the price.
Put plainly: required price equals fixed charges plus required net, all divided by one minus the fee rate. A seven percent fee leaves ninety-three percent, so you divide by 0.93. A five percent fee leaves ninety-five, so you divide by 0.95.
If a settlement charge in the problem is itself stated as a percentage of the price, it belongs in the denominator rather than the numerator. A seven percent fee alongside a one percent transfer charge means dividing by 0.92, not adding a transfer charge you cannot yet compute.
Always verify by running the answer forward. Take the price you derived, subtract the fee computed on it, subtract the fixed charges, and confirm you land on the required net. Rounding to the cent at the end rather than midway keeps the check clean.
Where These Items Are Usually Lost
Errors on net proceeds problems fall into a handful of recognizable patterns. Every one of them is avoidable by reading the item twice.
Multiplying the fee rate by the net instead of the price. The fee is always a share of the sale price unless the problem explicitly says otherwise.
Solving a reverse problem by adding the fee to the target. Adding a percentage of the target rather than dividing by the complement always understates the price required.
Dropping a buyer credit. Repair allowances and contributions toward the buyer's costs reduce the seller's proceeds exactly as settlement charges do.
Mixing the parties' charges. Costs assigned to the buyer never come out of the seller's side. The item tells you which is which; assumptions about local custom do not.
Confusing equity with proceeds. Price minus payoff is equity. Proceeds are what remains after the fee, the settlement charges and the credits have gone too.
Rounding at each step. Carry the full figure through and round only the final answer, or the cents will disagree with every listed choice.
Answering the wrong question. Some items ask for the price, some for the proceeds, some for the fee alone. Underline the noun being requested before starting.
Three Problems, Worked Through
Original practice items. Work each one before reading the solution, and run the reverse problem forward as a check.
Question 1
A property sells for $288,000. The seller owes $196,400 on the existing loan, pays a brokerage fee of 5 percent, and is charged $3,750 in settlement costs. What are the seller's net proceeds?
Fee first, from the price: $288,000 x 0.05 = $14,400. Then subtract in a single pass: $288,000 - $196,400 - $14,400 - $3,750 = $73,450. Sanity check: equity before costs is $91,600, and $73,450 is below it, as it must be.
Question 2
A seller must clear $84,000 after the sale. The loan payoff is $212,500, settlement costs charged to the seller come to $6,300, and the brokerage fee is 7 percent of the sale price. What must the property sell for?
Add the fixed amounts to the required net: $84,000 + $212,500 + $6,300 = $302,800. A 7 percent fee leaves 93 percent of the price, so divide: $302,800 / 0.93 = $325,591.40 rounded to the cent. Check it forward: the fee is $325,591.40 x 0.07 = $22,791.40, and $325,591.40 - $22,791.40 - $212,500 - $6,300 = $84,000.
Question 3
A property closes at $415,000. The payoff is $260,000, the brokerage fee is 6 percent, seller settlement costs are $4,200, the seller agreed to a $2,500 repair credit, and the buyer is credited $1,150 for prorated taxes. What does the seller net?
Fee from the price: $415,000 x 0.06 = $24,900. Then remove everything charged against the seller, credits included: $415,000 - $260,000 - $24,900 - $4,200 - $2,500 - $1,150 = $122,250. The two credits are the whole point of this item; leaving them out returns $125,900, which will be sitting among the choices.
Questions on Net Proceeds Problems
Why does the reverse problem use division rather than addition?
Because the fee is defined against the unknown. If the rate is 7 percent, then 93 percent of whatever the price turns out to be is what remains for the payoff, the costs and the seller. You know that remainder in dollars, and you know it represents 0.93 of the price, so dividing recovers the whole. Adding 7 percent of the target instead computes the fee on a smaller base and leaves the seller short.
Do settlement charges come out of the proceeds?
Every charge assigned to the seller does: the brokerage fee, the seller's share of settlement services, transfer taxes where the seller pays them, prorated items owed to the buyer, and any prepayment penalty on the loan. Charges assigned to the buyer do not. Read the item for who is being charged rather than assuming.
How are credits to the buyer treated?
As deductions from the seller's side, identical in effect to a cash expense. A closing-cost contribution, a repair allowance and the buyer's portion of prepaid taxes all reduce proceeds dollar for dollar. Note that a credit for taxes can run either way depending on whether the seller has already paid them, so follow the direction the item states.
Should the fee be figured before or after the payoff comes out?
Before, and on the full price. The lender's balance has no bearing on the brokerage fee, which is earned on the sale price under the listing agreement. Computing it on price minus payoff is the single most frequent error on these items and produces a net that is far too high.
What if the problem gives a fee split between two firms?
It changes nothing about the seller's proceeds. The total fee leaves the seller's column in one piece; how the firms divide it afterward, and how each firm then splits with its affiliated licensee, is a separate calculation. If the item asks only for the net, compute the total fee and stop there.
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