An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Correct Answer
A) EGI 3.2%; value 5.5%
The added loss is 3% × $60,000 = $1,800, which takes EGI from $57,000 to $55,200, a 3.2% decrease. Expenses stay at $24,000, so NOI falls from $33,000 to $31,200, or 5.5%. At an unchanged 7.5% rate, value falls from $440,000 to $416,000, the same 5.5%. Assuming value tracks EGI gives 3.2% for both, and carrying over the three points gives 3.0% for both.
Why This Is the Correct Answer
Option A is correct because the extra $1,800 of loss is 3.2% of the original $57,000 EGI but 5.5% of the original $33,000 NOI. With the rate fixed at 7.5%, value moves with NOI, from $440,000 to $416,000, a 5.5% decrease.
Why the Other Options Are Wrong
Option B: EGI 3.2%; value 3.2%
Option B, EGI 3.2% and value 3.2%, assumes value falls in step with EGI. That would hold only if expenses fell in the same proportion, but these $24,000 of expenses stay fixed, so NOI falls $1,800 ÷ $33,000 = 5.5% and value does too.
Option C: EGI 3.0%; value 3.0%
Option C, 3.0% for both, carries the three-point change in the loss rate straight through. Three percent of PGI is $1,800, but that is $1,800 ÷ $57,000 = 3.2% of EGI and $24,000 ÷ $440,000 = 5.5% of value.
Option D: EGI 5.5%; value 3.2%
Option D, EGI 5.5% and value 3.2%, swaps the results. The $1,800 is 5.5% of the $33,000 NOI, not of the $57,000 EGI, and value follows NOI, so EGI falls 3.2% and value falls 5.5%.
Same Dollars, Smaller Base
The same dollar loss looks bigger against a smaller base. NOI is smaller than EGI, so its percentage drop is larger.
How to use: Use the smaller-base idea to check that NOI and value fall by more than EGI when expenses are fixed.
Exam Tip
Note whether expenses are fixed or vary with occupancy before judging the size of a value change. At a constant rate, the percentage change in NOI is also the percentage change in value.
Common Mistakes to Avoid
- -Treating a change in the vacancy rate as the same percentage change in value
- -Measuring the income loss against EGI when value follows NOI
- -Reducing fixed expenses when occupancy falls
Concept Deep Dive
Analysis
A change in the vacancy allowance lands in EGI, but its effect on value runs through NOI. Because these expenses do not fall with occupancy, the whole dollar loss comes out of a smaller NOI base. With the rate unchanged, value falls by the same percentage as NOI, which is larger than the percentage fall in EGI.
Background Knowledge
Vacancy and collection loss is stated as a percentage of potential gross income and is deducted to reach effective gross income. Fixed expenses do not change with occupancy, so they magnify the percentage effect of income changes on NOI. In direct capitalization at a constant rate, value changes by the same percentage as NOI.
Real-World Application
A lender questions why a three-point rise in market vacancy cuts a small rental property's value by more than three percent. The appraiser walks through the same dollar loss against EGI and NOI and shows that the fixed costs do not shrink with occupancy.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
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?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
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?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
A lender will fund 70% of value at an annual mortgage constant of 8%. The remaining equity requires an annual equity dividend rate of 12%. Annual NOI is $92,000. Using the band of investment to develop the overall rate, what value is indicated, rounded to the nearest dollar?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
A client owns a duplex and asks an appraiser about two costs. A new city rental license fee of $1,200 a year, paid by the owner and not passed on to tenants, is expected to continue indefinitely. A sewer line needs a one-time repair costing $8,000, with no further cost expected. Buyers of similar duplexes deduct the full cost of a needed repair from the price. The overall rate is 8%, and neither item changes the rents or the rate. Which item has the larger effect on indicated value, and how much larger is that effect?
Next Question
Using an occupancy-based fixed/variable classification for property operating expenses, which pair is properly classified?