The subject property's annual EGI is $450,000. The operating expense ratio, excluding debt service, is 32% of EGI. Using a 7.5% overall capitalization rate, what is the indicated value?
Correct Answer
C) $4,080,000
450000×(1−0.32)=306000; 306000÷0.075=4080000. Common errors: capitalizing EGI instead of NOI gives $6,000,000; capitalizing the expenses instead of NOI gives $1,920,000; misplacing the decimal in the 7.5% rate gives $408,000.
Why This Is the Correct Answer
Option C is correct because NOI = $450,000 × (1 − 0.32) = $306,000, and $306,000 ÷ 0.075 = $4,080,000. Direct capitalization divides NOI, not EGI or expenses, by the overall capitalization rate.
Why the Other Options Are Wrong
Option A: $408,000
Option A, $408,000, is wrong because it misplaces the decimal in the 7.5% rate, dividing $306,000 by 0.75 instead of 0.075. The correct value is $306,000 ÷ 0.075 = $4,080,000.
Option B: $1,920,000
Option B, $1,920,000, is wrong because it capitalizes the expenses instead of NOI ($450,000 × 0.32 = $144,000; $144,000 ÷ 0.075 = $1,920,000). Value comes from NOI: $306,000 ÷ 0.075 = $4,080,000.
Option D: $6,000,000
Option D, $6,000,000, is wrong because it capitalizes EGI without deducting expenses ($450,000 ÷ 0.075 = $6,000,000). The correct base is NOI of $306,000, giving $4,080,000.
IRV: Income over Rate
Value = Income ÷ Rate, where the income is NOI after operating expenses.
How to use: Use IRV whenever you are given an overall rate and must find value from net income.
Exam Tip
Convert percentage rates carefully (7.5% = 0.075) and confirm you are dividing NOI, not EGI or expenses.
Common Mistakes to Avoid
- -Capitalizing EGI instead of NOI
- -Capitalizing the expense amount
- -Writing 7.5% as 0.75 instead of 0.075
Concept Deep Dive
Analysis
This question tests the sequence of direct capitalization: deduct operating expenses from EGI to get NOI, then divide NOI by the overall rate. Expenses are 32% of EGI, so NOI is 68% of $450,000. Dividing that NOI by 0.075 gives the value.
Background Knowledge
Income processing moves from potential gross income, less vacancy and collection loss, to effective gross income, then less operating expenses to net operating income. Direct capitalization converts one year's NOI into value by dividing by an overall capitalization rate. Debt service is not an operating expense.
Real-World Application
An appraiser reviewing an apartment building finds that operating expenses typically run about a third of EGI in the market. After deducting those expenses to reach NOI, the appraiser divides by a market-derived overall rate to estimate value.
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A property has annual NOI of $82,800. Debt funds 70% of value at an annual mortgage constant of 8%, and the remaining equity has a current annual dividend rate of 12%. What value is indicated using an overall rate from the band of investment, rounded to the nearest dollar?