Annual net market income attributable to the land is $27,000. The land capitalization rate is 6%. Using direct capitalization of the ground income, what land value is indicated?
Correct Answer
C) $450,000
Capitalize the annual net land income: $27,000 ÷ 0.06 = $450,000. The income and rate must be compatible. Gross contractual rent or a building income stream should not be substituted without the additional analysis those different inputs require.
Why This Is the Correct Answer
Option C is correct because $27,000 ÷ 0.06 = $450,000. The income is net income attributable to the land, and the rate is a land capitalization rate.
Why the Other Options Are Wrong
Option A: $27,000
Option A, $27,000, is the annual land income itself, not its capitalized value. Converting it to value requires dividing by the rate: $27,000 ÷ 0.06 = $450,000.
Option B: $1,620
Option B, $1,620, multiplies the income by the rate, $27,000 × 0.06, instead of dividing. Value is income divided by rate: $27,000 ÷ 0.06 = $450,000.
Option D: $45,000
Option D, $45,000, comes from writing 6% as 0.60 instead of 0.06: $27,000 ÷ 0.60 = $45,000. With the rate stated correctly, $27,000 ÷ 0.06 = $450,000.
IRV: divide to find value
Income equals Rate times Value, so Value equals Income divided by Rate; write the rate as a decimal before dividing.
How to use: Use IRV to set up any direct capitalization problem.
Exam Tip
Convert the percentage to a decimal carefully: 6% is 0.06, not 0.6. A value that is only ten times smaller than the correct figure points to a decimal slip.
Common Mistakes to Avoid
- -Multiplying income by the rate instead of dividing
- -Writing 6% as 0.6 instead of 0.06
- -Capitalizing gross rent with a net land rate
Concept Deep Dive
Analysis
This question tests direct capitalization of net land income. Land value equals the annual net income attributable to the land divided by the land capitalization rate. Dividing $27,000 by 6% written correctly as 0.06 gives $450,000.
Background Knowledge
Ground rent capitalization converts the net income a site earns, after any anticipated owner expenses, into value using a land capitalization rate. The income and rate must be compatible: land income goes with a land rate, and gross rent or building income requires additional analysis before use. The IRV relationship (Value = Income ÷ Rate) underlies the method.
Real-World Application
An appraiser values land leased to a restaurant operator that pays net ground rent of $27,000 a year. Using a market-derived land rate of 6%, the appraiser capitalizes the rent into a land value indication.
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