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?
Correct Answer
C) $648,000
A multiplier applies to the level of income from which it was derived, and $54,000 is EGI, not PGI. The equivalent EGI multiplier is 10.8 ÷ (1 − 0.10) = 12.0, and $54,000 × 12.0 = $648,000, the same as restoring PGI of $60,000 and multiplying by 10.8. Applying 10.8 directly to EGI gives $583,200. Adding 10% to EGI instead of dividing by 0.90 gives $641,520, and grossing up twice gives $720,000.
Why This Is the Correct Answer
Option C is correct because $54,000 is EGI, so the PGI multiplier converts to 10.8 ÷ 0.90 = 12.0 on EGI, and $54,000 × 12.0 = $648,000. Restoring PGI gives the same result: $54,000 ÷ 0.90 = $60,000, and $60,000 × 10.8 = $648,000.
Why the Other Options Are Wrong
Option A: $583,200
Option A, $583,200, is $54,000 × 10.8. That applies a PGI multiplier to income already reduced by the loss, so the loss is counted against value twice; the correct result is $60,000 × 10.8 = $648,000.
Option B: $641,520
Option B, $641,520, adds 10% to EGI: $54,000 × 1.10 × 10.8. The loss is 10% of PGI, not of EGI, so PGI is $54,000 ÷ 0.90 = $60,000, which gives $648,000.
Option D: $720,000
Option D, $720,000, grosses up twice: $54,000 ÷ 0.90 ÷ 0.90 × 10.8. Only one conversion is needed, either on the income or on the multiplier, and it gives $648,000.
Same Level In, Same Level Out
Match the multiplier's income level before you multiply. A smaller income level takes a larger multiplier for the same price.
How to use: Use the level check whenever a multiplier and the subject's income come from different sources.
Exam Tip
Identify the level of each income figure before applying a multiplier; collected income is not potential income. A percentage of PGI is reversed by dividing, not by adding the same percentage.
Common Mistakes to Avoid
- -Applying a PGI multiplier directly to collected income
- -Adding the loss percentage to EGI instead of dividing by one minus the loss rate
- -Adjusting both the income and the multiplier for the same loss
Concept Deep Dive
Analysis
A multiplier and the income it is applied to must be on the same level. The survey reports a PGI multiplier, but the only subject figure is collected income, which is already net of the market loss. The candidate must bring the two to one level, either by restoring PGI or by converting the multiplier to an EGI basis.
Background Knowledge
Vacancy and collection loss is stated as a percentage of potential gross income, so EGI equals PGI times one minus the loss rate. For the same price, a multiplier on EGI is therefore higher than a multiplier on PGI. Dividing the PGI multiplier by one minus the loss rate gives the EGI multiplier when the loss rates match.
Real-World Application
A property manager gives an appraiser collected income for a small rental, but the market data service reports prices against potential income. The appraiser converts to one level so the multiplier is applied consistently.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
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?
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?
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?
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