An appraiser is analyzing the sale of a fourplex to develop a gross income multiplier. The nominal sale price was $1,000,000, and the seller paid $40,000 in loan points to an institutional lender as part of the buyer's financing. Potential gross income at the time of sale was $120,000. The subject fourplex has potential gross income of $110,000. What is the indicated value of the subject?
Correct Answer
A) $880,000
The seller received $40,000 less than the nominal price, so the cash-equivalent price is $960,000 and the multiplier is $960,000 ÷ $120,000 = 8.0. Applied to the subject's $110,000, that indicates $880,000. Using the nominal price gives $916,667, adding the points to the price gives $953,333, and stopping at the cash-equivalent price without applying the multiplier gives $960,000.
Why This Is the Correct Answer
Option A is correct because the seller received $960,000 after paying $40,000 in points, which makes the multiplier $960,000 ÷ $120,000 = 8.0. Applying 8.0 to the subject's $110,000 potential gross income gives $880,000.
Why the Other Options Are Wrong
Option B: $916,667
Option B, $916,667, uses the nominal price: $1,000,000 ÷ $120,000 × $110,000. That leaves the $40,000 of points in the multiplier; the correct calculation is $960,000 ÷ $120,000 × $110,000 = $880,000.
Option C: $953,333
Option C, $953,333, adds the points to the price: $1,040,000 ÷ $120,000 × $110,000. Points reduce what the seller actually receives, so the correct figure is $960,000 ÷ $120,000 × $110,000 = $880,000.
Option D: $960,000
Option D, $960,000, is the comparable's cash-equivalent price ($1,000,000 − $40,000) with no multiplier applied. The subject earns less income than the sale, so the correct step is 8.0 × $110,000 = $880,000.
Clean the price, then divide
Think of the sale price as dirty until financing effects are washed out. Only the clean price goes on top of the multiplier fraction.
How to use: Use this whenever a sale mentions seller-paid points or atypical financing before you compute a multiplier.
Exam Tip
Read a sale's financing facts before dividing. If the seller paid costs to obtain the buyer's third-party loan, deduct them from the nominal price first.
Common Mistakes to Avoid
- -Extracting the multiplier from the nominal sale price
- -Adding seller-paid points to the price instead of deducting them
- -Reporting the adjusted comparable price as the subject's value
Concept Deep Dive
Analysis
The problem tests whether the candidate cleans the sale price before extracting a multiplier. A multiplier is only as good as its numerator, so seller-paid points must come out first. The reasoning runs in order: find the cash-equivalent price, divide by the sale's income, then multiply by the subject's income.
Background Knowledge
A gross income multiplier relates a cash-equivalent price to potential gross income. Seller-paid points are a financing cost that inflates the nominal price relative to what the seller keeps, so an adjustment comes before any unit of comparison is extracted.
Real-World Application
A seller pays points so a buyer can qualify for a loan on a fourplex. An appraiser using that sale deducts the points before computing the multiplier, so the subject's indication does not carry a financing premium.
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 comparable sold for a cash-equivalent price of $640,000 and has annual EGI of $80,000. The subject property has annual EGI of $75,000. Market data indicate the subject would sell at the same price-to-income ratio, and no other adjustments are required. What value is indicated for the subject, to the nearest dollar?
Next Question
The subject property is a fourplex with potential gross income of $120,000. Stabilized vacancy/credit loss in its neighborhood is 10% of PGI. A similar fourplex in an adjoining neighborhood with lower vacancy sold for $855,000 cash equivalent, with PGI of $100,000 and stabilized vacancy/credit loss of 5% of PGI. What value does an effective gross income multiplier indicate for the subject?