An appraiser is developing an overall rate for a stabilized office building and has researched four cash sales of similar buildings. Sale 1 sold for $1,280,000 with NOI of $96,000. Sale 2 sold for $2,000,000 with NOI of $156,000. Sale 3 sold for $1,000,000 with NOI of $72,000. Sale 4 was half vacant and in lease-up when it sold for $1,500,000, with in-place NOI of $61,500 and projected stabilized NOI of $136,500. Using the sales suited to this subject, what is the mean overall rate?
Correct Answer
B) 7.50%
Sale 4 is not stabilized, so it is excluded from a direct-capitalization rate for a stabilized subject. Sales 1 to 3 indicate 7.50%, 7.80% and 7.20%, with a simple mean of 7.50%. Including Sale 4 on in-place income at 4.10% gives 6.65%, and including it on projected income at 9.10% gives 7.90%. Pooling total NOI over total price gives 7.57%, which is a price-weighted figure and not the mean of the sale rates.
Why This Is the Correct Answer
Option B is correct because the stabilized sales indicate $96,000 ÷ $1,280,000 = 7.50%, $156,000 ÷ $2,000,000 = 7.80% and $72,000 ÷ $1,000,000 = 7.20%. Their simple mean is (7.50% + 7.80% + 7.20%) ÷ 3 = 7.50%. Sale 4 is excluded because a lease-up price and either of its income figures do not reflect stabilized operation.
Why the Other Options Are Wrong
Option A: 6.65%
Option A, 6.65%, includes Sale 4 on in-place income: $61,500 ÷ $1,500,000 = 4.10%, and (7.50% + 7.80% + 7.20% + 4.10%) ÷ 4 = 6.65%. Transitory in-place income does not fit a stabilized rate, so the correct mean of the three stabilized sales is 7.50%.
Option C: 7.57%
Option C, 7.57%, pools the three sales: $324,000 ÷ $4,280,000 = 7.57%. This correctly drops Sale 4 but produces a price-weighted figure rather than the mean of the three sale rates, which is 7.50%.
Option D: 7.90%
Option D, 7.90%, includes Sale 4 on projected income: $136,500 ÷ $1,500,000 = 9.10%, and (7.50% + 7.80% + 7.20% + 9.10%) ÷ 4 = 7.90%. The price reflects lease-up costs still ahead while the income assumes they are finished, so the two do not match. The correct mean of the stabilized sales is 7.50%.
Stabilized subject, stabilized sales
A rate carries the occupancy condition of the sales it came from. Screen the sales for that condition before you do any math.
How to use: Use this screen when a list of comparable sales includes one with unusual occupancy.
Exam Tip
When one sale in a list carries a descriptive note, consider whether that note makes the sale unsuitable. Check also whether a mean of the rates or a pooled result is called for.
Common Mistakes to Avoid
- -Including a lease-up sale in a stabilized rate analysis
- -Pairing projected stabilized income with a price that reflects lease-up
- -Pooling income and prices when a simple mean of rates is requested
Concept Deep Dive
Analysis
The skill tested is sale selection before any averaging. Direct capitalization assumes that the sales behind the rate are at stabilized occupancy, so a lease-up sale does not fit a stabilized subject on either income figure. Its in-place income understates the rate, while projected income set against a discounted price overstates it.
Background Knowledge
Direct capitalization assumes that the income being capitalized is at a stabilized level and does not reflect transitory conditions. It assumes the same of the sales from which rates are derived. A sale in lease-up has a price influenced by expected rent loss and leasing costs, so its rate is not directly comparable.
Real-World Application
While building a rate grid for a fully leased office building, an appraiser finds that one sale closed at half occupancy. Its in-place rate looks very low and its pro forma rate looks very high. The appraiser reports the sale but gives it no weight in the rate conclusion, and explains why.
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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