A site produces stabilized annual net ground income of $28,800. A market-supported direct capitalization rate of 6% is appropriate for that income and the interest being valued, including applicable lease terms. What value does direct capitalization indicate?
Correct Answer
D) $480,000
Value = $28,800/0.06 = $480,000. The indicated result is $480,000. Common errors: multiplying by the rate instead of dividing gives $1,728; misplacing the decimal in the 6% rate gives $48,000; reporting the ground income as the value gives $28,800.
Why This Is the Correct Answer
Option D is correct because direct capitalization divides net income by the capitalization rate: $28,800 / 0.06 = $480,000. The rate is market-supported and compatible with the income and the interest being valued, so no further adjustment is needed. This follows the ground rent capitalization technique of capitalizing net market rent at the land capitalization rate.
Why the Other Options Are Wrong
Option A: $1,728
Option A, $1,728, results from multiplying the income by the rate instead of dividing: $28,800 x 0.06 = $1,728. The correct calculation is $28,800 / 0.06 = $480,000.
Option B: $28,800
Option B, $28,800, simply reports the annual net ground income as if it were the value. Income must be capitalized: $28,800 / 0.06 = $480,000.
Option C: $48,000
Option C, $48,000, comes from misplacing the decimal in the 6% rate and dividing by 0.6: $28,800 / 0.6 = $48,000. The rate of 6% is 0.06, so the value is $28,800 / 0.06 = $480,000.
IRV: Income over Rate
Picture the IRV triangle with Income on top and Rate times Value on the bottom. Cover V and you see Income divided by Rate.
How to use: Use the IRV triangle whenever a question gives income and a rate and asks for value.
Exam Tip
Before choosing an answer, check that the value is larger than the income when the rate is below 100%. A result smaller than the income usually signals you multiplied instead of divided.
Common Mistakes to Avoid
- -Multiplying income by the capitalization rate instead of dividing
- -Writing 6% as 0.6 instead of 0.06
- -Reporting the annual income as the value
Concept Deep Dive
Analysis
This question tests direct capitalization of net ground income into a land value. The income formula is Value = Income / Rate, so the stabilized net ground income is divided by the market-supported capitalization rate expressed as a decimal. Converting 6% to 0.06 and dividing $28,800 by it gives the indicated value.
Background Knowledge
Direct capitalization converts a single year's stabilized net income into a value indication using a capitalization rate derived from the market. In ground rent capitalization, the appraiser capitalizes market rent less any owner expenses at the land capitalization rate. The income and rate must be compatible with each other and with the property interest being appraised.
Real-World Application
An appraiser values a parcel leased to a fast-food operator under a ground lease paying market rent net of owner expenses. After confirming market ground rent and extracting a land capitalization rate from comparable ground-leased sales, the appraiser divides the net rent by that rate to indicate land value.
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Previous Question
A property has stabilized NOI of $217,000. The building value is $1,850,000 and the building capitalization rate is 8.0%. The land capitalization rate is 6.0%. Using the land residual technique, what is the indicated land value?
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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?