An appraiser is extracting an overall capitalization rate from the sale of a 16-unit apartment building. The recorded price was $1,500,000, including favorable seller financing, and the cash equivalent price is $1,400,000. The broker reports NOI of $124,000. The owner managed the property, and the statement shows no management charge; management of similar properties costs $12,000 per year. The appraiser's income estimate for the subject includes a market management expense. What overall capitalization rate is indicated?
Correct Answer
B) 8.00%
Both figures need correcting first: NOI becomes $124,000 − $12,000 = $112,000 to match the subject's model, and price becomes the $1,400,000 cash equivalent, so $112,000 ÷ $1,400,000 = 8.00%. Adjusting NOI but keeping the recorded price gives 7.47%. Taking the broker's figures as reported gives 8.27%, and adjusting the price alone gives 8.86%.
Why This Is the Correct Answer
Option B is correct because the rate pairs the $1,400,000 cash-equivalent price with NOI restated to include market management: $124,000 − $12,000 = $112,000. Dividing gives $112,000 ÷ $1,400,000 = 8.00%. Since the subject's income estimate also deducts market management, this rate and the subject's NOI are on the same basis.
Why the Other Options Are Wrong
Option A: 7.47%
Option A, 7.47%, corrects the NOI but keeps the recorded price: $112,000 ÷ $1,500,000 = 7.47%. The recorded price includes the value of the financing, so the denominator should be the cash-equivalent $1,400,000, giving 8.00%.
Option C: 8.27%
Option C, 8.27%, accepts the broker's figures as reported: $124,000 ÷ $1,500,000 = 8.27%. Neither figure is on the required basis, so the correct calculation is $112,000 ÷ $1,400,000 = 8.00%.
Option D: 8.86%
Option D, 8.86%, corrects the price but not the NOI: $124,000 ÷ $1,400,000 = 8.86%. Applying a rate from NOI without a management charge to a subject NOI with that charge would understate value, so NOI should be $112,000, giving 8.00%.
Clean the top, clean the bottom
The rate is a fraction with two parts to check. Put NOI on the subject's basis on top and the cash-equivalent price on the bottom before dividing.
How to use: Use this whenever a sale reported for rate extraction mentions financing terms or an unusual expense treatment.
Exam Tip
Watch for details about seller financing or owner-performed work when extracting a rate. They usually signal an adjustment to the price or the NOI before you divide.
Common Mistakes to Avoid
- -Using the recorded price when it includes the value of favorable financing
- -Extracting a rate from NOI with no management charge and applying it to NOI with one
- -Correcting one side of the ratio and leaving the other as reported
Concept Deep Dive
Analysis
The division is one step, but both inputs must be fixed before it. The price has to be cash equivalent, and the NOI has to be stated on the same basis as the income the rate will capitalize. Each of the four possible pairings produces a believable rate, so careful reading decides the answer.
Background Knowledge
A market-derived overall rate is net income divided by the sale price adjusted for cash equivalency. For the rate to be usable, the comparable's income must be stated on the same basis as the subject's income, including how items such as management are treated. Differences between the two can distort the value indication.
Real-World Application
A broker's sale summary shows a price and an NOI for an apartment building bought with seller financing, and the owner handled management personally. Before including the rate in a rate analysis, the appraiser verifies a cash equivalent price and adds a market management charge so that the rate matches the subject's income estimate.
More Income Approach Questions
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An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
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Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
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Previous Question
A supported price-to-income multiplier of 18 is explicitly defined on the same period and income basis as the subject’s $96,000 annual income. With no further adjustments, what value is indicated by multiplying the two?
Next Question
The subject property is a triplex. Its operating statement shows PGI of $52,000, EGI of $48,000 and operating expenses of $19,200, including a $2,400 replacement reserve. The appraiser's survey of similar triplexes shows operating expense ratios of 33% to 37% of EGI, all reported with no replacement reserve in expenses. On the same basis as the survey, what is the subject's operating expense ratio, and how does it compare with the survey?