The subject property is a retail building owned in fee simple, with annual NOI of $127,500. A similar nearby retail building stands on leased land. An investor recently paid $1,400,000 for the leasehold interest in that building, which earns annual NOI of $170,000 before a ground rent of $30,000 per year. The ground rent is at market. At about the same time, the landowner sold the leased fee interest for $600,000. What is the indicated value of the subject by direct capitalization?
Correct Answer
B) $1,500,000
With ground rent at market, the two interests together approximate the fee simple: $1,400,000 + $600,000 = $2,000,000. The fee simple rate is the income before ground rent over that total, $170,000 ÷ $2,000,000 = 8.5%, so the subject is $127,500 ÷ 0.085 = $1,500,000. The leasehold buyer's 10% ($140,000 ÷ $1,400,000) is a leasehold rate and gives $1,275,000. Averaging the 10% and the land's 5% gives $1,700,000, and setting income after ground rent against the total price gives $1,821,429.
Why This Is the Correct Answer
Option B is correct because the leasehold and leased fee together make up the whole bundle of rights: $1,400,000 + $600,000 = $2,000,000. The income to that whole is $170,000 before ground rent, for an 8.5% fee simple rate. The subject's value is $127,500 ÷ 0.085 = $1,500,000.
Why the Other Options Are Wrong
Option A: $1,275,000
Option A, $1,275,000, uses the leasehold rate: ($170,000 − $30,000) ÷ $1,400,000 = 10%, then $127,500 ÷ 0.10. That rate comes from a different interest and level of income, so it does not transfer to a fee simple subject. The correct rate is 8.5%, giving $1,500,000.
Option C: $1,700,000
Option C, $1,700,000, averages the 10% leasehold rate and the 5% land rate ($30,000 ÷ $600,000) to get 7.5%, then $127,500 ÷ 0.075. A simple average ignores that the leasehold makes up 70% of the total value. The value-weighted result is 8.5%, giving $1,500,000.
Option D: $1,821,429
Option D, $1,821,429, divides income after ground rent by the total price: $140,000 ÷ $2,000,000 = 7%, then $127,500 ÷ 0.07. The $2,000,000 includes the land, so the income must include the $30,000 that goes to the land. The correct rate is 8.5%, giving $1,500,000.
Whole price, whole income
Put the whole property's income over the whole property's price for a fee simple rate. A part of the income over a part of the price gives a rate for that part.
How to use: Use this when a sale involves a building on leased land and the subject is owned outright.
Exam Tip
When a comparable sits on a ground lease, identify which interest sold and whether its NOI is before or after ground rent before dividing anything.
Common Mistakes to Avoid
- -Applying a leasehold rate to a fee simple subject
- -Dividing income after ground rent by a price that includes the land
- -Averaging the rates of two interests without weighting them by value
Concept Deep Dive
Analysis
A rate must match the interest and the income level it came from. The investor bought only the leasehold and receives income after ground rent, so that sale gives a leasehold rate. The subject is owned in fee simple, so its rate has to reflect the whole property. Because the ground rent is at market, the fee simple rate can be rebuilt from income before ground rent and the sum of the two interests.
Background Knowledge
A lease divides the bundle of rights into the leased fee held by the lessor and the leasehold held by the lessee. The type of rate derived varies with the level of income processed, and a rate should be applied to the same level from which it came. When contract rent is at market, the interests together approximate the fee simple value.
Real-World Application
An appraiser finds a recent sale of a retail building on leased land while valuing a similar owned building. The appraiser confirms the land interest sale, combines the two prices, and derives a whole-property rate instead of using the buyer's reported leasehold return.
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Cash-equivalent sale price is $396,000 and matching monthly gross rent is $2,200. What monthly gross-rent multiplier is price ÷ monthly rent?
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The subject property is a mixed-use building with annual NOI of $60,000 from ground-floor retail and $40,000 from upper-floor offices. An appraiser is valuing the two components separately. A retail building in the same district recently sold for $1,000,000 with NOI of $80,000. An office building nearby recently sold for $900,000 with NOI of $90,000. What total value is indicated?