An appraiser is extracting an overall rate from the $1,500,000 cash sale of an apartment building. The seller managed the property and reports income of $129,000 after all paid operating expenses. Market management for similar properties is $9,000 per year, buyers in this market deduct a $6,000 replacement reserve, and the seller's mortgage payments were $70,000. What overall rate does this sale indicate?
Correct Answer
A) 7.6%
Normalized NOI is $129,000 − $9,000 − $6,000 = $114,000, and $114,000 ÷ $1,500,000 = 7.6%. Mortgage payments are financing, not an operating expense, so they are not deducted. The 8.6% figure uses the seller's income as reported, while 8.0% deducts management alone and 8.2% deducts the reserve alone.
Why This Is the Correct Answer
Option A is correct because the seller's $129,000 must be reduced by $9,000 of market management and the $6,000 reserve, giving NOI of $114,000. Dividing by the $1,500,000 cash-equivalent price gives 7.6%. The mortgage payments are not deducted because NOI is measured before financing.
Why the Other Options Are Wrong
Option B: 8.0%
Option B, 8.0%, is $120,000 ÷ $1,500,000, which deducts management but leaves out the $6,000 reserve. Rates here are extracted after reserves, so NOI should be $114,000, giving 7.6%.
Option C: 8.2%
Option C, 8.2%, is $123,000 ÷ $1,500,000, which deducts the reserve but not the $9,000 of market management. A self-managing owner's unpaid effort is still a market cost, so the correct rate is 7.6%.
Option D: 8.6%
Option D, 8.6%, is $129,000 ÷ $1,500,000, which uses the seller's reported figure unchanged. That income omits both management and the reserve, so it does not match the market's basis. Normalized NOI gives 7.6%.
Normalize before you divide
Clean up the seller's income first by adding market costs and keeping financing out. Only then divide by the cash-equivalent price.
How to use: Use this whenever a sale's income comes from an owner's statement rather than a stabilized analysis.
Exam Tip
Sort each listed item into operating or financing before calculating. Mortgage payments stay out of NOI.
Common Mistakes to Avoid
- -Using an owner's reported income without normalizing it
- -Deducting mortgage payments in reaching NOI
- -Omitting management because the owner paid no cash fee
Concept Deep Dive
Analysis
Extracting a rate is simple division, but the income must first be on the market's basis. You have to judge which items belong in the normalized NOI. Market management and the reserve are deducted because the market's rates reflect them, while the mortgage payment stays out because it is financing.
Background Knowledge
An overall rate is income divided by the cash-equivalent price, but it is meaningful only when the income reflects the same convention used in the market. Operating expenses are estimated as a prudent buyer would expect them, even when an owner pays no cash for a service. A rate must later be applied to the same level of income from which it was derived.
Real-World Application
An appraiser verifies a sale of a small building run by its owner, whose statement shows no management cost. The appraiser adds a market fee and a reserve before extracting the rate, so it can be compared fairly with professionally managed sales.
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An owner's statement shows annual EGI of $96,000 and these property expenses: taxes $11,000, insurance $4,000, utilities $8,500, routine maintenance $7,000 and management $4,800. The appraiser measures NOI after an additional $2,700 reserve. The owner's mortgage payments of $31,000 are excluded. What is the NOI after the reserve?
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