A client is comparing two four-unit apartment properties. Property A has PGI of $72,000, vacancy and credit loss of 8%, an operating expense ratio of 45% of EGI, and a market overall rate of 8%. Property B has PGI of $63,000, vacancy and credit loss of 4%, an operating expense ratio of 40% of EGI, and a market overall rate of 7.5%. Which property has the higher indicated value, and by how much?
Correct Answer
C) Property B, by $28,440
Property A's EGI is $66,240 and its NOI is $36,432, so its value is $36,432 ÷ 0.08 = $455,400. Property B's EGI is $60,480 and its NOI is $36,288, so its value is $36,288 ÷ 0.075 = $483,840, which is $28,440 more. Applying 8% to both makes A look $1,800 higher, skipping the losses gives $9,000, and applying the expense ratios to PGI gives $47,400.
Why This Is the Correct Answer
Option C is correct because Property B's lower overall rate outweighs its slightly lower NOI. Property A indicates $36,432 ÷ 0.08 = $455,400 and Property B indicates $36,288 ÷ 0.075 = $483,840. The difference is $28,440 in favor of Property B.
Why the Other Options Are Wrong
Option A: Property A, by $1,800
Option A, Property A by $1,800, capitalizes both properties at 8%: $36,432 ÷ 0.08 = $455,400 and $36,288 ÷ 0.08 = $453,600. Property B has its own 7.5% rate, so its value is $483,840 and it exceeds Property A by $28,440.
Option B: Property B, by $9,000
Option B, Property B by $9,000, skips the vacancy and credit losses: $72,000 × 0.55 ÷ 0.08 = $495,000 and $63,000 × 0.60 ÷ 0.075 = $504,000. Each ratio works on EGI after its own loss, so the true difference is $28,440.
Option D: Property B, by $47,400
Option D, Property B by $47,400, applies the expense ratios to PGI: A is ($66,240 − $32,400) ÷ 0.08 = $423,000 and B is ($60,480 − $25,200) ÷ 0.075 = $470,400. The ratios are stated on EGI, which makes the difference $28,440.
Same NOI, lower rate wins
Value equals income over rate. When the incomes are about equal, the smaller denominator gives the bigger value.
How to use: Use this as a quick check on the direction of your answer when comparing two properties.
Exam Tip
Do not rank properties by gross income. Take each to NOI on its own terms, then divide by its own rate.
Common Mistakes to Avoid
- -Assuming the property with the higher gross income has the higher value
- -Capitalizing both properties at one rate when each has its own
- -Applying an EGI-based expense ratio to PGI
Concept Deep Dive
Analysis
The properties have almost the same NOI, $36,432 and $36,288, even though Property A has more gross income. The ranking therefore turns on the capitalization rate, and each property must be capitalized at its own rate. Working each one through in full is safer than judging by gross income.
Background Knowledge
Direct capitalization divides NOI by an overall rate, so value depends on both figures. A lower rate indicates a higher value for the same income, and market evidence on risk and income expectations can justify different rates for different properties. Gross income alone does not rank properties.
Real-World Application
An investor is choosing between a larger, older fourplex and a smaller, newer one with lower vacancy. An appraiser shows that their net incomes are nearly equal, but the market's lower rate for the newer building gives it the higher value.
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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