A client planning a 24-unit apartment building asks what income the completed property must produce to be worth its $3,325,000 project cost. Overall capitalization rates for similar properties are 8%, operating expense ratios are 30% of EGI, and the vacancy/credit loss allowance is 5% of PGI. What PGI is required?
Correct Answer
C) $400,000
Work the income ladder backward: $3,325,000 × 0.08 = $266,000 NOI; $266,000 ÷ 0.70 = $380,000 EGI; $380,000 ÷ 0.95 = $400,000 PGI. Stopping at EGI gives $380,000. Grossing up by adding each percentage (× 1.30, then × 1.05) gives $363,090. Subtracting both percentages from one base ($266,000 ÷ 0.65) gives $409,231, but the two percentages apply to different bases.
Why This Is the Correct Answer
Option C is correct because $3,325,000 × 0.08 = $266,000 is the NOI the target value requires. Dividing by 0.70 recovers EGI of $380,000, since NOI is what remains after expenses of 30% of EGI. Dividing by 0.95 recovers PGI of $400,000, since EGI is what remains after a loss of 5% of PGI. As a check, $400,000 less 5% is $380,000, less 30% is $266,000, and $266,000 ÷ 0.08 = $3,325,000.
Why the Other Options Are Wrong
Option A: $363,090
Option A, $363,090, comes from adding the percentages on top of each figure: $266,000 × 1.30 = $345,800, then × 1.05 = $363,090. A percentage of the larger base cannot be recovered by marking up the smaller figure; the correct steps are $266,000 ÷ 0.70 = $380,000 and $380,000 ÷ 0.95 = $400,000.
Option B: $380,000
Option B, $380,000, is EGI ($266,000 ÷ 0.70), not PGI. It leaves out the vacancy and collection step, and $380,000 ÷ 0.95 = $400,000 is the income the building must be able to produce before that loss.
Option D: $409,231
Option D, $409,231, comes from combining the percentages into one 35% deduction: $266,000 ÷ 0.65 = $409,231. The 30% applies to EGI and the 5% applies to PGI, so they cannot be subtracted from one base; the correct result is $266,000 ÷ 0.70 ÷ 0.95 = $400,000.
Going up? Divide by the complement
Going down the ladder you multiply by what remains (0.95, then 0.70); going back up you divide by those same remainders. Marking up by the percentage is not the reverse of taking a percentage off.
How to use: Use this when value or NOI is known and the EGI or PGI behind it is needed.
Exam Tip
Note which base each percentage is stated on before you start. Prove the answer by running it forward through the ladder to the stated value.
Common Mistakes to Avoid
- -Multiplying NOI by 1.30 to recover EGI when expenses are 30% of EGI
- -Adding the expense and loss percentages although they apply to different bases
- -Stopping at EGI when the question asks for PGI
Concept Deep Dive
Analysis
Starting from a target value reverses the usual direct-capitalization sequence, so the skill is knowing which base each percentage belongs to. Value times the rate gives NOI. Because expenses are a percentage of EGI, NOI is 70% of EGI, and because loss is a percentage of PGI, EGI is 95% of PGI. Each step back up the ladder is a division by the complement of that step's percentage.
Background Knowledge
The income ladder runs from potential gross income, less vacancy and collection loss, to effective gross income, less operating expenses, to net operating income. Direct capitalization then divides NOI by the overall rate to indicate value. The same relationships can be run in reverse to find the income a given value requires.
Real-World Application
A client planning an apartment project knows the value needed to make the project work and asks what rent roll would support it. The appraiser's market capitalization rate, expense ratio and loss rate convert that value into a required gross income, which can then be compared with market rents.
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
Annual NOI for the subject property is $180,000, and the building is known to be worth $1,500,000. The land capitalization rate is 6% and the building capitalization rate is 9%. What total property value does the land residual technique indicate?
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Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?