An appraiser is deriving a monthly gross rent multiplier from the cash sale of a duplex that was listed at $525,000 and sold for $504,000. Its combined rent of $3,000 per month includes water, gas and electricity paid by the owner, and paired rentals show that this arrangement adds $200 to the combined monthly rent. The subject duplex rents for $2,600 per month, and its tenants pay their own utilities. What multiplier does the sale indicate on the subject's rent basis?
Correct Answer
C) 180.0
The subject's rent excludes utilities, so the sale's rent must be restated the same way: $3,000 − $200 = $2,800. The sale price then gives $504,000 ÷ $2,800 = 180.0. Using the unadjusted rent gives 168.0, and adding the $200 instead of removing it gives 157.5. Using the list price gives 187.5.
Why This Is the Correct Answer
Option C is correct because the sale's rent on a tenant-paid basis is $3,000 − $200 = $2,800. Dividing the $504,000 sale price by that rent gives 180.0, a multiplier that can be applied to the subject's tenant-paid rent.
Why the Other Options Are Wrong
Option A: 157.5
Option A, 157.5, adds the $200 to the rent: $504,000 ÷ $3,200. Owner-paid utilities are already in the $3,000, so they are removed, which gives $504,000 ÷ $2,800 = 180.0.
Option B: 168.0
Option B, 168.0, uses the unadjusted rent: $504,000 ÷ $3,000. That multiplier reflects rent including utilities and does not match the subject's rent basis; the matching figure is $504,000 ÷ $2,800 = 180.0.
Option D: 187.5
Option D, 187.5, uses the list price: $525,000 ÷ $2,800. A multiplier is derived from what the property sold for, so the correct figure is $504,000 ÷ $2,800 = 180.0.
Strip the Rent, Then Divide
Take out what the subject's rent does not include, then divide the sale price by what is left.
How to use: Use this order whenever a comparable's rent and the subject's rent cover different services.
Exam Tip
Check who pays utilities on both sides before deriving a rent multiplier. Keep to the price actually paid and ignore list prices.
Common Mistakes to Avoid
- -Deriving a multiplier from rent that includes owner-paid utilities and applying it to tenant-paid rent
- -Adding the utility amount to the rent rather than removing it
- -Using a list price instead of the sale price
Concept Deep Dive
Analysis
A gross rent multiplier compares price with rent, so the rent in the sale must mean the same thing as the rent it will be applied to. Here, the sale's rent includes utilities the subject's tenants pay themselves. The paired-rental difference allows the sale to be used by restating its rent on the subject's basis, and the sale price, not the list price, is the numerator.
Background Knowledge
Multipliers should come from sales with similar income streams. When a sale differs in who pays a cost and the market measures that difference in rent, the rent can be restated rather than the sale rejected. The result is applied to the subject's rent on the same basis.
Real-World Application
Few duplex sales are available, and the best one includes utilities in the rent while the subject does not. Paired rentals measure the rent difference, so the appraiser restates the sale's rent rather than losing the data point.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
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