The subject property is a fourplex with three one-bedroom units and one two-bedroom unit. Market rent is $1,100 per month for a one-bedroom unit and $1,400 per month for a two-bedroom unit. Stabilized vacancy and credit loss is 5% of PGI, annual operating expenses are $19,580, and the market overall rate is 8%. What is the indicated value by direct capitalization?
Correct Answer
A) $425,000
Weighting each rent by its own unit count gives monthly rent of $3,300 + $1,400 = $4,700, or PGI of $56,400. EGI is $56,400 × 0.95 = $53,580, NOI is $53,580 − $19,580 = $34,000, and $34,000 ÷ 0.08 = $425,000. $460,250 skips the vacancy and credit loss, $467,750 uses the simple average rent of $1,250 for all four units, and $705,000 capitalizes PGI without deducting the loss or expenses.
Why This Is the Correct Answer
Option A is correct because each rent is weighted by its own unit count: 3 × $1,100 + 1 × $1,400 = $4,700 per month, or $56,400 per year. Deducting the 5% loss gives EGI of $53,580, and deducting $19,580 of expenses gives NOI of $34,000. Dividing $34,000 by 0.08 indicates $425,000.
Why the Other Options Are Wrong
Option B: $460,250
Option B, $460,250, leaves out the vacancy and credit loss: $56,400 − $19,580 = $36,820, ÷ 0.08. Expenses come off effective gross income, so the $2,820 loss must be deducted first, which leads to $425,000.
Option C: $467,750
Option C, $467,750, uses the simple average rent of $1,250 for all four units: $1,250 × 4 × 12 = $60,000, × 0.95 = $57,000, − $19,580 = $37,420, ÷ 0.08. The average ignores that three of the four units are the cheaper type; the weighted calculation gives $425,000.
Option D: $705,000
Option D, $705,000, capitalizes potential gross income: $56,400 ÷ 0.08. Vacancy and credit loss and operating expenses must come off first, leaving NOI of $34,000 and a value of $425,000.
Count times rent, type by type
Write one line per unit type: count × monthly rent. Add the lines first, then multiply by 12.
How to use: Use this line-by-line layout whenever a property has more than one unit type or rent level.
Exam Tip
When units carry different rents, do not average the rents unless the counts are equal. Check which rent goes with which count before you multiply.
Common Mistakes to Avoid
- -Averaging two rents without weighting by unit count
- -Capitalizing PGI instead of NOI
- -Deducting expenses from PGI without first taking the vacancy and credit loss
Concept Deep Dive
Analysis
The skill here is building potential gross income from a rent schedule instead of receiving it as a given. Each unit type is multiplied by its own count and rent, then annualized, before the usual steps of loss, expenses and capitalization. Because there are more of the cheaper units, a simple average of the two rents overstates income.
Background Knowledge
Potential gross income is rent at full occupancy, and a rent schedule is the usual way to build it when a property has more than one unit type. Rent per unit is a unit of comparison, and each type is analyzed against rents for similar units. The income is then processed from PGI to EGI to NOI.
Real-World Application
An appraiser values a fourplex with a mix of one- and two-bedroom units. The rent survey indicates a separate market rent for each type, so the appraiser builds PGI by type and then applies a market loss and expenses to reach NOI.
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?
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?
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Previous Question
An appraiser is verifying the $340,000 cash sale of a triplex with a worn-out roof. Buyer and seller both knew the roof had to be replaced at once for $20,000, and the price reflected this. The buyer replaced it immediately and anticipates annual NOI of $28,800 with the new roof. The seller's marketing pro forma showed annual NOI of $32,300 at higher asking rents. What overall rate does this sale indicate for a similar triplex in good repair?
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