Cash-equivalent sale price is $400,000 and annual gross rent is $40,000. What is the annual gross-income multiplier, price ÷ annual rent?
Correct Answer
C) 10.0
400000÷40000 = 10. Common errors: inverting the ratio (annual rent ÷ price) gives 0.1; dividing by twelve months of the annual rent gives 0.8; multiplying the annual multiplier by 12 gives 120.0.
Why This Is the Correct Answer
Option C is correct because the annual gross income multiplier is price divided by annual rent: $400,000 ÷ $40,000 = 10.0. Both figures are on an annual basis, so no monthly conversion is needed.
Why the Other Options Are Wrong
Option A: 0.1
Option A, 0.1, comes from inverting the ratio and dividing rent by price: $40,000 ÷ $400,000 = 0.1. A gross income multiplier is price divided by rent, so $400,000 ÷ $40,000 = 10.0.
Option B: 0.8
Option B, 0.8, comes from multiplying the already annual rent by 12 before dividing: $400,000 ÷ ($40,000 × 12) = 0.83, rounded to 0.8. The $40,000 is already annual, so the correct multiplier is $400,000 ÷ $40,000 = 10.0.
Option D: 120.0
Option D, 120.0, comes from multiplying the annual multiplier by 12: $400,000 ÷ $40,000 × 12 = 120. That treats an annual result as if it needed a monthly conversion; the annual multiplier is 10.0.
Same period in, same out
An annual multiplier comes from annual income and is applied to annual income. A monthly multiplier is about 12 times larger because the income is 12 times smaller.
How to use: Use this check whenever a multiplier problem mentions rent amounts or periods.
Exam Tip
Put price on top: a multiplier is price divided by income. Then confirm whether the rent given is monthly or annual and whether the question asks for an annual or monthly multiplier.
Common Mistakes to Avoid
- -Inverting the ratio to rent divided by price
- -Multiplying an already annual rent by 12 before dividing
- -Mixing a monthly multiplier with annual income
Concept Deep Dive
Analysis
This question tests extraction of an annual gross income multiplier as price divided by annual rent. The challenges are dividing in the right direction and keeping the period consistent without mixing monthly and annual figures. A simple division of the two given annual-basis numbers gives the answer.
Background Knowledge
A gross income multiplier relates sale price to gross income as a factor. It can be annual or monthly, and the period used in extraction must match the period used in application. The multiplier is applied to the same level of income from which it was derived.
Real-World Application
An appraiser analyzing single-family rental sales divides each sale price by its annual gross rent. She then applies the supported annual multiplier to the subject's annual market rent.
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