An appraiser verifying the sale of a fourplex with owner-paid utilities finds a cash equivalent price of $432,000, and the buyer confirms pricing the property at a 7.5% overall rate. Annual PGI at the time of sale was $80,000, and stabilized vacancy and credit loss was 10% of PGI. There is no other income. What operating expense ratio, based on EGI, do these figures indicate?
Correct Answer
C) 55.0%
NOI is $432,000 × 0.075 = $32,400 and EGI is $80,000 × 0.90 = $72,000, so expenses are $72,000 − $32,400 = $39,600 and the ratio is $39,600 ÷ $72,000 = 55.0%. Reporting NOI ÷ EGI gives the 45.0% net income ratio, not the expense ratio. Dividing the $39,600 by PGI gives 49.5%, which uses the wrong base. Skipping the vacancy step and comparing PGI with NOI gives 59.5%.
Why This Is the Correct Answer
Option C is correct because price times rate gives NOI of $432,000 × 0.075 = $32,400, and PGI less the 10% loss gives EGI of $72,000. Expenses are the difference, $39,600, and $39,600 ÷ $72,000 = 55.0%.
Why the Other Options Are Wrong
Option A: 45.0%
Option A, 45.0%, is NOI divided by EGI: $32,400 ÷ $72,000 = 45.0%. That is the net income ratio, the complement of the expense ratio, whereas expenses of $39,600 on EGI of $72,000 give 55.0%.
Option B: 49.5%
Option B, 49.5%, divides expenses by PGI: $39,600 ÷ $80,000 = 49.5%. The ratio is based on EGI, so the correct division is $39,600 ÷ $72,000 = 55.0%.
Option D: 59.5%
Option D, 59.5%, skips the vacancy step: ($80,000 − $32,400) ÷ $80,000 = 59.5%. That treats the $8,000 loss as an expense; the correct result is $39,600 ÷ $72,000 = 55.0%.
Price to NOI to expenses
Multiply price by rate to reach NOI, then subtract NOI from EGI to reach expenses. Divide by EGI last.
How to use: Use this three-step chain when a sale gives price and rate but not the expenses.
Exam Tip
Write the denominator named in the question next to your work before dividing. Ratios on PGI and EGI differ whenever there is a vacancy loss.
Common Mistakes to Avoid
- -Reporting the net income ratio as the expense ratio
- -Dividing expenses by PGI when EGI is the stated base
- -Treating the vacancy loss as part of operating expenses
Concept Deep Dive
Analysis
This item reverses the usual direct-capitalization path. You start with price and rate to find NOI, build EGI separately from PGI, and take the gap between EGI and NOI as expenses. The final care point is the denominator, because the ratio is requested on EGI rather than PGI.
Background Knowledge
Income, rate and value are linked by V = I ÷ R, so any two of them give the third. Expense ratios are normally stated on EGI, and the expense ratio and net income ratio add to 100% on that base.
Real-World Application
An appraiser verifying a sale learns the price and the rate the buyer underwrote but not the buyer's expense budget. Backing into the implied ratio shows whether the buyer's expense assumption is in line with competing buildings.
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
The subject property has annual PGI of $105,000, with combined vacancy and collection loss of 4% of PGI. Other property expenses total $15,000, plus an annualized leasing-cost allowance of $8,000 that is not included in that total. Market sales indicate a 10% overall rate on income calculated after these same deductions. What is the indicated value?
Next Question
An appraiser is valuing the fee simple interest in a triplex at market rents. A similar triplex sold for $450,000 cash with all units on leases that have four years remaining at rents well below market. Its NOI on those contract rents is $27,000, or 6.0% of the price; at market rents its NOI would be $36,000. Two other sales of similar triplexes leased at market rents indicate overall rates near 7.5%. How should the appraiser treat the 6.0% rate in valuing the subject?