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?
Correct Answer
A) 8.00%
The buyer's effective cost of a triplex in good repair is $340,000 + $20,000 = $360,000, and the income that goes with that condition is $28,800, so the rate is 8.00%. Dividing by the recorded price alone gives 8.47%, which matches good-repair income with a price for a worn-out roof. Subtracting the roof from the price gives 9.00%, and using the seller's pro forma gives 9.50%.
Why This Is the Correct Answer
Option A is correct because the buyer's total cost to own the triplex in good repair is $340,000 + $20,000 = $360,000. The $28,800 NOI is the income with the new roof, so the rate is $28,800 ÷ $360,000 = 8.00%. Income and price then describe the same condition as the property the rate will be applied to.
Why the Other Options Are Wrong
Option B: 8.47%
Option B, 8.47%, is $28,800 ÷ $340,000. It pairs income with a new roof against a price for a worn-out roof, which overstates the rate a buyer accepted. The correct base is $360,000, giving 8.00%.
Option C: 9.00%
Option C, 9.00%, is $28,800 ÷ $320,000, which subtracts the $20,000 from the price. The roof is money the buyer spends on top of the price, so it is added, giving $360,000 and 8.00%.
Option D: 9.50%
Option D, 9.50%, is $32,300 ÷ $340,000. It uses the seller's pro forma at asking rents, while rate derivation depends on the investor's anticipated income of $28,800, and it omits the roof. The correct rate is 8.00%.
Match condition to condition
New-roof income goes with a new-roof cost. Add the known repair to the price before dividing.
How to use: Use this when verifying a sale in which a buyer planned an immediate repair priced into the deal.
Exam Tip
During sale verification, ask whether the buyer had to spend money right away. Then check that the income and the price you divide describe the same condition.
Common Mistakes to Avoid
- -Dividing post-repair income by the recorded price
- -Subtracting a required repair from the price
- -Using a seller's pro forma income in rate extraction
Concept Deep Dive
Analysis
Income and price must describe the same condition. The $28,800 NOI assumes a new roof, but the $340,000 price bought a worn-out one. The buyer paid $360,000 in total to own what produces that income, so that is the proper denominator when the rate will be applied to a property in good repair. The seller's pro forma is not the investor's anticipated income.
Background Knowledge
An overall rate is extracted by relating anticipated net income to a cash-equivalent sale price. The income used must be the investor's anticipated income. When a buyer must spend a known sum at once and the price reflects it, the income after the work should be compared with the total outlay.
Real-World Application
An appraiser calls the buyer of a small rental property and learns that the price was negotiated down because the roof needed immediate replacement. The appraiser adds the verified repair cost to the price before extracting the rate used for a subject in good repair.
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
The subject property's annual NOI is $96,000, and its land value is known to be $400,000. Capitalization rates are 5% for land and 8% for the building. What total property value does the building residual technique indicate?
Next Question
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?