An appraiser is estimating the market value of the fee simple interest in a four-unit apartment property. Each unit is leased at $1,050 per month, and similar units in competing properties rent for $1,200 per month. Stabilized vacancy and credit loss is 5% of PGI, market operating expenses are $19,720 a year, and the market overall rate is 8%. What is the indicated value?
Correct Answer
C) $437,500
A fee simple valuation capitalizes market income, so the $1,050 contract rent is set aside: PGI is 4 × $1,200 × 12 = $57,600. EGI is $57,600 × 0.95 = $54,720, NOI is $54,720 − $19,720 = $35,000, and $35,000 ÷ 0.08 = $437,500. $352,000 uses contract rent, $383,500 uses contract rent with no loss, and $473,500 uses market rent with no loss.
Why This Is the Correct Answer
Option C is correct because the fee simple interest is valued on market rent, not the rent in the existing leases. PGI is 4 × $1,200 × 12 = $57,600, EGI after the 5% loss is $54,720, and NOI after $19,720 of expenses is $35,000. Dividing by 0.08 gives $437,500.
Why the Other Options Are Wrong
Option A: $352,000
Option A, $352,000, applies the $1,050 contract rent: 4 × $1,050 × 12 = $50,400, × 0.95 = $47,880, − $19,720 = $28,160, ÷ 0.08. That figure measures income under the existing leases, not the market income of an unencumbered fee simple interest, which leads to $437,500.
Option B: $383,500
Option B, $383,500, uses contract rent and also drops the loss because the units are leased: $50,400 − $19,720 = $30,680, ÷ 0.08. It makes two errors, since a fee simple estimate calls for market rent and a market loss; the correct NOI of $35,000 gives $437,500.
Option D: $473,500
Option D, $473,500, starts correctly at market rent but omits the market loss: $57,600 − $19,720 = $37,880, ÷ 0.08. A market income estimate includes a vacancy and credit allowance, so EGI should be $54,720 and the value $437,500.
Interest first, then pick rent
Fee simple pairs with market rent; leased fee pairs with the lease terms. Name the interest before touching any figures.
How to use: Use this pairing whenever both a contract rent and a market rent appear.
Exam Tip
Identify the property interest before you start the math. When both rents are given, the interest named decides which one to capitalize.
Common Mistakes to Avoid
- -Using lease rents in a fee simple valuation because they are actual, documented income
- -Dropping the vacancy allowance because the units happen to be leased today
- -Selecting market rent but leaving out the market loss
Concept Deep Dive
Analysis
Two rents are available, and the skill is picking the one that matches the interest being appraised. A fee simple valuation looks at what the property would earn unencumbered, so market rent is the base even though tenants currently pay less. The contract rent would matter in a leased fee analysis, which is not the assignment here.
Background Knowledge
Market rent is the rent a property would command if offered on the market as of the appraisal date, while contract rent is the rent set by the terms of a lease. A fee simple valuation looks past the existing leases to market income. Income from a leased fee interest would instead reflect the lease terms.
Real-World Application
A lender orders a fee simple value on a small apartment building whose long-time tenants pay below the going rate. The appraiser reports the existing rents but capitalizes the rents shown by competing buildings, since those reflect the interest being valued.
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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An appraiser derives a multiplier from comparables using annual rents, then applies it to the subject's monthly rent. The result is:
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An appraiser is analyzing the cash sale of a fourplex for $645,000. At the time of sale, the buyer anticipated potential rental income of $60,000 per year and potential parking and laundry income of $4,500 per year, with vacancy and collection loss of 5%. What is the potential gross income multiplier indicated by this sale?