A ground lease requires $60,000 a year and land capitalization rates are 6 percent. What value does the leased fee indicate?
Correct Answer
C) $1,000,000
Why this is correct: The leased fee interest is valued by capitalizing the contract rent. The formula is Value = Income / Rate. Here, the annual ground rent (income) is $60,000 and the cap rate is 6% (or 0.06). Calculation: $60,000 / 0.06 = $1,000,000. Why the other choices are wrong: "$360,000" is wrong; this might come from multiplying $60,000 by 0.06 ($60,000 * 0.06 = $3,600). "$600,000" is wrong; this might come from $60,000 / 0.10. "$1,000,000" is correct. "$1,200,000" is wrong; this might come from $60,000 / 0.05. Exam tip: For direct capitalization: Value = Annual Income / Cap Rate. Double-check your decimal placement for the rate.
Why This Is the Correct Answer
Sixty thousand dollars divided by 0.06 equals $1,000,000, applying the value equals income over rate relationship. Using a land capitalization rate is appropriate because the income is ground rent on land. The clean result signals the item is testing the formula and decimal handling rather than any refinement. Verifying in reverse confirms it: $1,000,000 times 6 percent returns the $60,000 of rent.
Why the Other Options Are Wrong
Option A: $360,000
$360,000 comes from multiplying $60,000 by 0.06 rather than dividing, which inverts the operation. The result is not a value at all but a fraction of one year's income. Any answer smaller than several years of rent should trigger suspicion in a capitalization problem.
Option B: $600,000
$600,000 results from dividing by 0.10 rather than 0.06, using a rate the stem does not supply. It is also implausible as a land rate, since land rates run below overall rates and well below 10 percent in most markets. Reading the rate directly out of the stem prevents the substitution.
Option D: $1,200,000
$1,200,000 results from dividing by 0.05, again a rate not given. Its proximity to the correct figure makes it attractive to a candidate estimating rather than dividing. The inverse relationship is worth noting: a lower rate produces a higher value, which is why rate selection matters so much.
Income Over Rate
Value equals income divided by rate. The rate is always the small number, so it belongs on the bottom. If your answer is smaller than the income, you multiplied when you should have divided.
How to use: Write the formula before touching the numbers, convert the percentage to a decimal, and divide. Then verify by multiplying your value by the rate to see whether you recover the income.
Exam Tip
Land capitalization rates are lower than building or overall rates because land does not depreciate and needs no recapture. A question implying otherwise is testing that point.
Common Mistakes to Avoid
- -Multiplying income by the rate instead of dividing
- -Using an overall rate where a land rate is required
- -Capitalizing a short-remaining-term ground rent in perpetuity without valuing the reversion
Concept Deep Dive
Analysis
Direct capitalization converts a single year's income into a value indication through the relationship value equals income divided by rate. A ground lease produces an unusually clean application of that formula because the income is contractual ground rent and the asset is land, which does not depreciate and therefore requires no recapture in the rate. Here $60,000 of annual ground rent divided by a 6 percent land capitalization rate gives $1,000,000. Two refinements matter in practice. Capitalizing the rent in perpetuity is an approximation appropriate for a very long or perpetual ground lease; where the term is finite, the leased fee should be modeled as the present value of the rent for the remaining term plus the present value of the reversion, which will include the improvements if they revert to the landlord. And the rate must be a land rate rather than an overall rate, since land rates are lower precisely because no recapture component is needed.
Background Knowledge
You need the IRV relationships and direct capitalization, the definition of a ground lease and the leased fee interest it creates, and the reason land capitalization rates sit below building or overall rates. You should also know that a finite-term leased fee is properly valued as the present value of the rent stream plus the reversion.
Real-World Application
An appraiser valuing a leased fee under a long-term ground lease on a corner retail pad capitalizes the contract ground rent at a land rate drawn from other ground lease sales, then tests the result against nearby fee simple land sales to confirm the indication is reasonable.
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