10.1 Percentage, Flat, Mixed & Per-Head Commissions

Percentage, Flat, Mixed & Per-Head Commissions

Math is 10 of the 50 scored items on the Illinois auctioneer PSI exam — 20 percent of the test. The passing score is at least 70 percent of those 50 items, so a candidate who is merely adequate on Articles 5, 10, 15, 20, and 30 can still fail by missing most of the arithmetic. This chapter is the first math chapter. Section 10.1 is the commission engine: percentage of hammer, flat fee, mixed percentage-plus-add-on, and the handbook's per-head livestock sample.

Read the written auction contract before you touch the calculator. 225 ILCS 407/15-10 requires a written seller contract entered into before the auction date, and the fee the seller pays the auctioneer or firm is a mandatory term. The number on the sale bill is not a substitute for that clause. PSI will hand you a rate and a dollar figure and wait to see whether you multiplied the right base.

Hammer is not the invoice

Hammer price is the amount accepted at the fall of the hammer, before buyer premium and before tax. Commission is usually a percentage of hammer. Confirm the contract. A clause that says "8 percent of the hammer price" is not the same as "8 percent of the amount the buyer pays" or "8 percent of the invoice including premium."

Build the stacks separately:

• Buyer invoice (before tax): hammer plus buyer premium. Section 5-10 defines buyer premium as a fee paid by the successful purchaser other than the purchase price. Tax, if the item is taxable, is a later add-on (Section 10.3).
• Seller-side firm compensation: the commission or flat fee the contract measures, plus any listed seller-paid add-ons (catalog, advertising, clerking).
• Seller net: hammer minus seller commission minus authorized expenses. The premium often stays with the firm unless the contract says otherwise. Section 15-10(1)(D) requires the contract to state the buyer premium and the party to the transaction that receives it. Do not assume the seller shares it.

Percentage of hammer — work every sample

The percentage formula is:

Commission = Hammer × Rate

Rate as a decimal is the percent divided by 100. Work these three PSI-style lots in full. Do not round until the contract tells you to; these land on whole dollars.

Check the middle row another way: 10 percent of $28,000 is $2,800; 7 percent is seven-tenths of that, and 0.7 × $2,800 = $1,960. Check the 12 percent row as 10 percent plus 2 percent: $6,200 + $1,240 = $7,440. If your screen shows $744 or $74,400, the decimal is in the wrong place.

Those three hammers reappear in later sections as livestock, farm equipment, and estate settlements. The commission number does not change just because the lot is an animal, a combine, or a sideboard. What changes is which expenses you are then allowed to subtract, and whether Illinois Retailers' Occupation Tax is even in the problem.

Flat fee — hammer does not move the number

A flat fee is a stated dollar amount regardless of hammer. If the 15-10 contract says the firm is paid $2,500 to conduct the auction, a $40,000 hammer and a $400,000 hammer both produce $2,500 of seller-side compensation under that clause. PSI writes the trap as a high hammer next to a familiar percentage. A candidate who automatically takes 8 percent of $180,000 ($14,400) has answered a different contract.

Flat fees are lawful compensation. They are not a substitute for writing the fee in the contract, and they are not a buyer premium. The buyer premium is what the successful purchaser pays on top of hammer. The flat fee in this paragraph is what the seller pays the firm for the sale.

Mixed: percentage of hammer plus a listed add-on

Mixed compensation is a percentage plus a stated dollar charge. Compute the percentage first, then add the flat item. Do not apply the percentage to the add-on unless the contract says the rate is on a broader base.

Worked mixed example. The contract is 6 percent of hammer plus an $800 catalog fee, seller-paid. Hammer is $85,000.

1. Percentage piece: $85,000 × 0.06 = $5,100.
2. Catalog fee: $800 (a flat add-on, not 6 percent of $800).
3. Total firm compensation from the seller side: $5,100 + $800 = $5,900.

If the item asks only for the commission percentage, the answer is $5,100. If it asks for total firm compensation from the seller side, the answer is $5,900. Forgetting the $800 is the most common miss. Applying 6 percent to $85,800 (hammer plus catalog) is the second.

Per-head livestock — PSI handbook sample

The Candidate Handbook's livestock sample is not a percentage-of-hammer problem. It is a cost-of-livestock plus per-head commission problem. Memorize the path; the numbers are the ones the handbook uses.

Facts. The order buyer purchases 10 head of 200-pound sheep at $0.60 per pound and is charged $5 per head commission.

1. Cost of livestock = head × weight × price per pound = 10 × 200 × $0.60. First, 10 × 200 = 2,000 pounds. Then 2,000 × $0.60 = $1,200.
2. Commission = head × $ per head = 10 × $5 = $50.
3. Total cost = $1,200 + $50 = $1,250.
4. Cost per head = $1,250 ÷ 10 = $125.00. That is the handbook sample Q2 answer.

Do not take 5 percent of $1,200. The $5 is a dollar per head, not a percent. Do not stop at $1,200 and call that the per-head figure; $1,200 ÷ 10 = $120.00, which is the livestock cost per head without the commission. The tested number includes the $50.

The same $28,000 livestock hammer from the percentage table is a different problem: that is 7 percent of a $28,000 fall-of-the-hammer total ($1,960), used when the contract is a percentage of livestock proceeds rather than $5 a head. Read which fee the item actually gives you.

"Of hammer" versus "of invoice including premium"

Two clauses look alike and are not.

• "8 percent of hammer." Multiply the fall-of-the-hammer amount. Buyer premium is ignored for this multiplication.
• "8 percent of the invoice including premium." Multiply hammer plus premium. Tax still stays out unless the clause says tax is inside the base — and Illinois tax items are Section 10.3.

Worked trap. Hammer $8,500. Buyer premium 10 percent. Seller commission 8 percent of hammer.

• Buyer invoice before tax = $8,500 + ($8,500 × 0.10) = $8,500 + $850 = $9,350.
• Correct seller commission = $8,500 × 0.08 = $680.
• Wrong commission, using the invoice as the base = $9,350 × 0.08 = $748.

The $68 difference is the 8 percent of the $850 premium. PSI will park $748 in the options. The contract said of hammer, so $680 is the commission.

Same trap at a larger scale: $45,000 hammer, 15 percent buyer premium, 10 percent seller commission of hammer. Invoice before tax is $45,000 + $6,750 = $51,750. Commission of hammer is $4,500. Commission wrongly taken of $51,750 is $5,175. Use $4,500 unless the clause includes premium.

Traps to mark before you multiply

Walk this list on every commission item:

1. Wrong base. Applying the seller rate to hammer plus premium, or to hammer plus tax, when the contract says of hammer.
2. Forgotten add-on. Computing 6 percent of $85,000 as $5,100 and stopping, when the question asked for total seller-side compensation including the $800 catalog fee.
3. Percent versus dollars per head. Treating $5 per head as 5 percent of livestock cost.
4. Total versus per head. Reporting $1,250 as the per-head answer, or $120.00 as the all-in per-head answer.
5. Flat fee overwritten by a habit percentage. Replacing a $2,500 flat clause with 8 percent or 10 percent of a large hammer.
6. Mixing buyer and seller stacks. Subtracting buyer premium from the seller, or adding seller commission to the buyer's invoice, without a contract that says to do that.

Percentage, flat, mixed, and per-head are four different machines. Identify which machine the 15-10 clause describes, write the hammer (or the head-count arithmetic) first, then multiply. Section 10.2 puts a sliding scale on the same hammer and then builds the buyer invoice with premium.