An appraiser is verifying the sale of a 12-unit apartment building. The broker will not release dollar income figures but reports that the price was 6.0 times EGI and 5.4 times PGI, and that the buyer's anticipated operating expenses were 55% of EGI. What overall capitalization rate does the sale indicate?
Correct Answer
A) 7.50%
The net income ratio is 1 − 0.55 = 0.45 of EGI, and the matching multiplier is the EGI multiplier, so the rate is 0.45 ÷ 6.0 = 7.50%. Dividing by the PGI multiplier mismatches the income levels and gives 8.33%. Dividing the expense ratio instead of the net income ratio gives 9.17% with the EGI multiplier and 10.19% with the PGI multiplier.
Why This Is the Correct Answer
Option A is correct because expenses of 55% of EGI leave a net income ratio of 0.45, and price is 6.0 times the same EGI. The rate is therefore 0.45 ÷ 6.0 = 7.50%. A proof with any EGI works: at EGI of $100,000, NOI is $45,000, price is $600,000, and $45,000 ÷ $600,000 = 7.50%.
Why the Other Options Are Wrong
Option B: 8.33%
Option B, 8.33%, divides by the PGI multiplier: 0.45 ÷ 5.4 = 8.33%. The 0.45 is a share of EGI, so it must be paired with the EGI multiplier: 0.45 ÷ 6.0 = 7.50%.
Option C: 9.17%
Option C, 9.17%, uses the expense ratio as the numerator: 0.55 ÷ 6.0 = 9.17%. Expenses are the part of EGI that does not reach the investor; the numerator should be the remaining 0.45, giving 7.50%.
Option D: 10.19%
Option D, 10.19%, makes both errors: 0.55 ÷ 5.4 = 10.19%. It uses the expense share rather than the net income share and the PGI multiplier rather than the EGI multiplier; the correct calculation is 0.45 ÷ 6.0 = 7.50%.
Net ratio over matching multiplier
Write the rate as NOI over price, then express each per dollar of EGI. What remains is the net income ratio over the EGI multiplier.
How to use: Use this when a sale is reported with a multiplier and an expense or net income ratio but no NOI.
Exam Tip
When unsure of a ratio formula, pick a round income such as $100,000 and calculate NOI and price. The dollar proof shows at once whether the rate is right.
Common Mistakes to Avoid
- -Taking the reciprocal of the multiplier as the overall rate without reflecting expenses
- -Pairing an EGI-based net income ratio with a PGI multiplier
- -Dividing the expense ratio rather than the net income ratio by the multiplier
Concept Deep Dive
Analysis
An overall rate is NOI divided by price, and both can be expressed per dollar of EGI. NOI is 0.45 of EGI and price is 6.0 times EGI, so EGI cancels and the rate is 0.45 ÷ 6.0. The key judgment is matching income levels: the 45% ratio is based on EGI, so the PGI multiplier does not belong in the calculation.
Background Knowledge
An overall rate can be derived from an effective gross income multiplier and a net income ratio, because the rate equals the net income ratio divided by the multiplier. The expense figure used matters: when deriving a rate, the buyer's anticipated expenses are the relevant ones, and standardized expenses may be less reliable. The multiplier and the ratio have to rest on the same level of income.
Real-World Application
An appraiser hears from a broker that an apartment building traded at six times effective gross income and that the buyer underwrote expenses at 55% of income. Without a full operating statement, the appraiser can estimate the implied overall rate from those ratios, then look for more evidence before relying on it.
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?
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 lender asks an appraiser to review a 16-unit apartment building with annual PGI of $180,000, a stabilized vacancy and credit loss of 10%, and operating expenses of $54,000. The current mortgage payments of $60,000 per year will end when the existing loan is paid off at closing. The new loan requires a debt coverage ratio of 1.25 at an annual mortgage constant of 8%. What is the maximum loan amount?
Next Question
When applying single-period direct capitalization, what is important about the income and overall rate?