A rental property generates $120,000 in gross annual income. Operating expenses are $45,000. If the overall capitalization rate is 8%, what is the indicated value using direct capitalization?
Correct Answer
A) $937,500
Net Operating Income (NOI) = $120,000 - $45,000 = $75,000. Using the formula Value = NOI ÷ Cap Rate: $75,000 ÷ 0.08 = $937,500.
Why This Is the Correct Answer
Option A is correct because it follows the proper direct capitalization formula: Value = NOI ÷ Cap Rate. First, we calculate NOI by subtracting operating expenses ($45,000) from gross annual income ($120,000), yielding $75,000. Then we divide this NOI of $75,000 by the capitalization rate of 8% (0.08) to get $937,500. This represents the market value that would generate the given NOI at the specified rate of return.
Why the Other Options Are Wrong
Option B: $1,500,000
Option B ($1,500,000) incorrectly uses the gross annual income instead of NOI in the calculation ($120,000 ÷ 0.08 = $1,500,000), failing to account for operating expenses which is a fundamental error in income approach methodology.
Option C: $1,062,500
Option C ($1,062,500) appears to use an incorrect cap rate of approximately 7.06% ($75,000 ÷ 0.0706 ≈ $1,062,500) rather than the given 8%, or involves some other calculation error in the direct capitalization process.
Option D: $843,750
Option D ($843,750) seems to result from using gross income minus a portion of expenses or applying an incorrect cap rate, possibly confusing the relationship between income, expenses, and the capitalization rate in the valuation formula.
NOI-CAP Value Recipe
Remember 'NOI over CAP gives you the MAP (Market value)' - NOI ÷ CAP = Market Value. Think of it like a recipe: take your NET ingredients (NOI), divide by your CAPacity rate, and you get the MAP to value.
How to use: When you see a direct capitalization problem, immediately identify: 1) Calculate NOI (Gross Income - Operating Expenses), 2) Identify the CAP rate, 3) Apply the MAP formula (NOI ÷ CAP = Market Value). Always ensure you're using NOI, not gross income.
Exam Tip
Double-check that you've calculated NOI correctly by subtracting ALL operating expenses from gross income before applying the cap rate - this is the most common error on direct capitalization questions.
Common Mistakes to Avoid
- -Using gross income instead of net operating income in the calculation
- -Forgetting to subtract operating expenses before applying the cap rate
- -Confusing the cap rate percentage with decimal form (8% vs 0.08)
Concept Deep Dive
Analysis
This question tests the fundamental income approach concept of direct capitalization, which is one of the three primary methods used in real estate valuation. Direct capitalization converts a single year's net operating income into an estimate of market value by dividing NOI by an appropriate capitalization rate. The process requires understanding the relationship between gross income, operating expenses, net operating income, and how market-derived cap rates are applied. This method assumes that the property's income and expenses are stabilized and representative of typical market performance.
Background Knowledge
Direct capitalization is a valuation method that converts net operating income into market value using a single capitalization rate derived from comparable sales. The cap rate represents the relationship between a property's NOI and its market value, expressed as NOI ÷ Value = Cap Rate, which can be rearranged to solve for value.
Real-World Application
Appraisers use direct capitalization when valuing income-producing properties like apartment buildings, office buildings, and retail centers by analyzing comparable sales to extract market cap rates, then applying these rates to the subject property's stabilized NOI to estimate market value.
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