A property's NOI is fixed by lease at $80,000. If market cap rates move from 6.4% to 8.0%, its indicated value:
Correct Answer
C) Falls from $1,250,000 to $1,000,000
Why this is correct: The governing concept is that value using direct capitalization is calculated as Net Operating Income (NOI) divided by the capitalization rate (V = NOI / R). With NOI fixed at $80,000, value at 6.4% is $80,000 / 0.064 = $1,250,000. At 8.0%, value is $80,000 / 0.08 = $1,000,000. Thus, value falls by $250,000 (20%) when the cap rate increases by 1.6 percentage points. Why the other choices are wrong: "Falls by exactly the 1.6-point spread" is incorrect because value change is not a linear function of the rate spread; it depends on the base. "Rises from $1,000,000 to $1,250,000" is incorrect because a higher cap rate reduces value, not increases it. "Stays unchanged, since NOI is unchanged" is incorrect because value is sensitive to cap rate changes even with constant NOI. Exam tip: Cap rate changes have a leveraged effect on value; small rate errors can lead to large value errors.
Why This Is the Correct Answer
Option C is correct because the value falls from $1,250,000 to $1,000,000. At 6.4 percent, $80,000 divided by 0.064 equals $1,250,000; at 8.0 percent, $80,000 divided by 0.08 equals $1,000,000. The $250,000 decline is a 20 percent loss of value driven entirely by the rate, with the contractually fixed income unchanged. This is why lease-protected income does not protect an owner from repricing when the capital markets move.
Why the Other Options Are Wrong
Option A: Falls by exactly the 1.6-point spread
This treats a change in rate as if it translated directly into an equal percentage change in value, which the division does not support. The rate rose by 1.6 percentage points, but the value fell by 20 percent, because value responds to the ratio between the rates rather than their difference. Points and percentages of value are different units and cannot be equated.
Option B: Rises from $1,000,000 to $1,250,000
This has the direction backward: value rises when rates fall, not when they rise. The two dollar figures are correct but assigned to the wrong rates, since $1,250,000 corresponds to 6.4 percent and $1,000,000 to 8.0 percent. Selecting it usually means the candidate computed both values correctly and then reversed the mapping.
Option D: Stays unchanged, since NOI is unchanged
Stable income does not mean stable value, because value is a function of both the income and the rate at which the market capitalizes it. A fixed lease locks the numerator while leaving the denominator exposed to market movement, which is precisely the risk an investor in a long-term leased asset accepts. Owners of net-leased property learned this directly when rates rose while their rents stayed flat.
Seesaw at the division bar
Income sits on top and the rate sits below. Push the rate up and value drops; let the rate fall and value climbs. Points of rate and percent of value are never the same measurement.
How to use: Compute both values before reading the choices, then confirm that the option pairs the lower rate with the higher value. Distractors in this family usually swap the pairing or equate a rate change with a value change.
Exam Tip
Estimate the relative effect quickly: dividing the old rate by the new one gives the value ratio. Here 6.4 over 8.0 is 0.8, so the new value is 80 percent of the old.
Common Mistakes to Avoid
- -Equating a change in rate points with a percentage change in value
- -Reversing which rate produces the higher value
- -Assuming a long-term lease insulates value from rate movement
- -Adjusting the income to compensate for a rate change and double-counting the effect
Concept Deep Dive
Analysis
This tests the inverse relationship between capitalization rates and value, which is the mechanism behind most swings in income property values when the income itself is stable. Value equals net operating income divided by the overall rate, so with income held fixed by a lease, value moves inversely and non-linearly with the rate. Rising rates reflect investors demanding more return per dollar invested, whether because of higher interest rates, greater perceived risk, or weaker growth expectations, and the effect is a lower price for the same income stream. The non-linearity is what candidates miss: a rate change of 1.6 percentage points is not a 1.6 percent change in value. Here $80,000 divided by 0.064 gives $1,250,000, while $80,000 divided by 0.08 gives $1,000,000, so a rate increase of one quarter in relative terms produces a 20 percent value decline.
Background Knowledge
You need the direct capitalization relationship and comfort with the fact that value and rate move inversely and non-linearly. You should also understand what drives overall rates, including interest rates, perceived risk, expected growth, and lease quality, and why a long-term fixed lease insulates income without insulating value.
Real-World Application
A single-tenant building with twelve years remaining on a flat lease appraised at $1,250,000 two years ago. With investors now requiring 8 percent, you conclude $1,000,000 despite unchanged rent, and you explain to the client that the decline reflects the capital markets rather than any deterioration in the property or its tenant.
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A 50-unit apartment complex is subject to a 99-year ground lease with annual land rent fixed at $75,000, payable in perpetuity. The improvements were constructed by the leaseholder and will revert to the landowner at lease expiration. The appraiser is developing a market value opinion of the leasehold interest. Which statement BEST describes the appropriate income approach treatment?
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A property is subject to a ground lease with 40 years remaining. The tenant (improvements owner) pays $50,000 annually to the landowner, while current market rent for the land alone is $72,000 per year. The improvements are fully depreciated, and the tenant bears all maintenance, taxes, and insurance. Under the income approach, what is the indicated value of the leasehold interest assuming a 6% overall capitalization rate applied to the annual rent differential and a 40-year term?