An appraiser is verifying the sale of an apartment building. The stated price of $1,600,000 consisted of $600,000 in cash and a $1,000,000 seller note at a below-market interest rate. The market value of the note is 96.25% of its face amount. The seller paid a $50,000 brokerage commission. Stabilized annual NOI is $125,000. What overall rate does this sale indicate?
Correct Answer
B) 8.00%
The cash-equivalent price is $600,000 + ($1,000,000 × 0.9625) = $1,562,500, so the rate is $125,000 ÷ $1,562,500 = 8.00%. Using the stated price gives 7.81%. Applying the 3.75% note discount to the whole price gives 8.12%. Also subtracting the commission gives 8.26%, but a commission pays for services and is not a cash-equivalence adjustment.
Why This Is the Correct Answer
Option B is correct because the note is worth $1,000,000 × 0.9625 = $962,500, and adding the $600,000 down payment gives a cash-equivalent price of $1,562,500. The rate is $125,000 ÷ $1,562,500 = 8.00%. The commission stays out of the calculation because it pays for services rather than for the real property.
Why the Other Options Are Wrong
Option A: 7.81%
Option A, 7.81%, uses the stated price: $125,000 ÷ $1,600,000 = 7.81%. Favorable seller financing can inflate a stated price, so the denominator needs the cash-equivalent figure of $1,562,500, which gives 8.00%.
Option C: 8.12%
Option C, 8.12%, applies the discount to the entire price: $1,600,000 × 0.9625 = $1,540,000, and $125,000 ÷ $1,540,000 = 8.12%. The $600,000 down payment was cash and needs no discount, so the correct denominator is $1,562,500, which gives 8.00%.
Option D: 8.26%
Option D, 8.26%, also subtracts the commission: $1,562,500 − $50,000 = $1,512,500, and $125,000 ÷ $1,512,500 = 8.26%. A commission is a payment for services rather than a reduction in the cash equivalence of the price, so the correct rate is $125,000 ÷ $1,562,500 = 8.00%.
Discount the note, not the cash
Split the price into what the seller got in cash and what the seller got in paper. Only the paper needs a market discount.
How to use: Use this split when a comparable's price includes seller financing.
Exam Tip
Check the sale terms before you divide NOI by price. Then ask whether each adjustment affects what the seller received in cash-equivalent terms or merely what the seller paid for services.
Common Mistakes to Avoid
- -Extracting a rate from the stated price despite non-market financing
- -Applying a note discount to the cash down payment as well
- -Deducting the seller's commission as a cash-equivalence adjustment
Concept Deep Dive
Analysis
The skill tested is the denominator of an extracted rate. The stated price includes a below-market note, so the price must first be restated to cash equivalence, with the discount applied only to the note. The commission is a distractor, because it does not change the cash equivalence of what the seller received.
Background Knowledge
A market-derived overall rate relates income to a sale price adjusted for cash equivalency. A note with a below-market rate is worth less than its face amount, and the seller is presumed to have made up for the low rate through a higher stated price. Ordinary selling costs such as commissions are treated differently because they pay for services.
Real-World Application
An appraiser confirms a comparable sale and learns the seller carried a large note at a low rate to help the buyer close. The appraiser estimates the note's market value and restates the price before extracting a rate. The commission noted on the closing statement is not treated as a cash-equivalence adjustment.
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