A property valued at $550,000 has annual PGI of $95,000. Combined vacancy and collection loss is 7% of PGI, and all annual property expenses, excluding debt service, total $28,000. What overall capitalization rate is indicated, rounded to two decimals?
Correct Answer
A) 10.97%
(95000×0.93−28000)÷550000×100 = 10.97. Common errors: not deducting the operating expenses gives 16.06%; not deducting the 7% loss gives 12.18%; applying the 7% loss after deducting expenses gives 11.33%.
Why This Is the Correct Answer
Option A is correct because $95,000 x 0.93 = $88,350 EGI, $88,350 - $28,000 = $60,350 NOI, and $60,350 / $550,000 x 100 = 10.97%. The loss is applied to PGI before expenses are deducted. Debt service is excluded, as the question states.
Why the Other Options Are Wrong
Option B: 11.33%
Option B, 11.33%, comes from applying the 7% loss after deducting expenses: ($95,000 - $28,000) x 0.93 / $550,000 x 100 = 11.33%. The loss applies to PGI first, giving ($88,350 - $28,000) / $550,000 = 10.97%.
Option C: 12.18%
Option C, 12.18%, comes from not deducting the 7% loss: ($95,000 - $28,000) / $550,000 x 100 = 12.18%. After the loss, NOI is $60,350 and the rate is 10.97%.
Option D: 16.06%
Option D, 16.06%, comes from not deducting the operating expenses: $95,000 x 0.93 / $550,000 x 100 = 16.06%. That divides EGI by value; subtracting the $28,000 in expenses gives NOI of $60,350 and a rate of 10.97%.
PGI, EGI, NOI, then rate
Walk down the income ladder in order: potential, effective, net, then divide by value.
How to use: Use this to order the steps in any multi-step income calculation.
Exam Tip
Write each step's subtotal; most wrong answers come from skipping or reordering one step.
Common Mistakes to Avoid
- -Dividing EGI by value as if it were NOI
- -Skipping the vacancy and collection loss
- -Applying the vacancy percentage after expenses
Concept Deep Dive
Analysis
This question tests building NOI from PGI and then extracting an overall rate. The correct order is PGI minus vacancy and collection loss, then minus expenses, then NOI divided by value. The distractors come from skipping a deduction or applying the loss at the wrong step.
Background Knowledge
Potential gross income minus vacancy and collection losses equals effective gross income, and effective gross income minus operating expenses equals NOI. An overall rate is NOI divided by value or price.
Real-World Application
Analyzing a comparable sale at $550,000, an appraiser reconstructs its income: $95,000 PGI, a 7% loss and $28,000 in expenses. The resulting 10.97% overall rate becomes one data point for selecting the subject's rate.
More Income Approach Questions
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The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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