An appraiser is deriving a land capitalization rate from the $450,000 cash sale of a vacant residential lot. Market ground rent for the lot is $43,000 per year, and the owner would pay $2,500 per year in expenses. What is the indicated land capitalization rate?
Correct Answer
A) 9.0%
Net ground income is market rent less the owner's expenses: $43,000 − $2,500 = $40,500. Dividing by the price gives the rate: $40,500 ÷ $450,000 = 9.0%. Using gross rent gives 9.6%, and adding the expenses gives 10.1%. The 11.1 figure comes from inverting the division, which produces a multiplier rather than a rate.
Why This Is the Correct Answer
Option A is correct because net ground income is $43,000 − $2,500 = $40,500, and dividing it by the $450,000 price gives 9.0%. That rate is on the same net basis as the income used in ground rent capitalization.
Why the Other Options Are Wrong
Option B: 9.6%
Option B, 9.6%, comes from $43,000 ÷ $450,000, which uses gross rent and skips the $2,500 of owner expenses. The net calculation is $40,500 ÷ $450,000 = 9.0%.
Option C: 10.1%
Option C, 10.1%, comes from ($43,000 + $2,500) ÷ $450,000, which adds the expenses instead of deducting them. The correct calculation gives 9.0%.
Option D: 11.1%
Option D, 11.1%, comes from $450,000 ÷ $40,500 = 11.1, which inverts the formula and produces a value-to-income multiplier rather than a rate. The rate is $40,500 ÷ $450,000 = 9.0%.
Income Over Value Equals Rate
Remember I = R × V, rearranged as R = I ÷ V. Use net income for I, and the result should look like a rate.
How to use: Use this rearrangement whenever a price and rent are known and the rate is the unknown.
Exam Tip
Check whether a stated rent is gross or net of the owner's expenses before dividing. Then check the result by capitalizing the income back to the price.
Common Mistakes to Avoid
- -Deriving the rate from gross rent and applying it to net income
- -Adding owner expenses to rent rather than deducting them
- -Dividing price by income and reading the result as a percentage
Concept Deep Dive
Analysis
Ground rent capitalization can be run in reverse. Value equals net income divided by the rate, so the rate equals net income divided by value. The income has to be net of the owner's expenses for the derived rate to be usable with net land income.
Background Knowledge
Ground rent capitalization requires an estimate of market rent, any expenses paid by the landowner and a market-derived land capitalization rate. A land rate can be derived from sales by relating net land income to price. Consistency between the income measure and the rate matters to the result.
Real-World Application
An appraiser needs a land capitalization rate for a ground lease assignment. The appraiser analyzes a recent vacant site sale and the market rent for similar land, deducting expected owner expenses to derive the rate on a net basis.
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