The subject property is a triplex with stabilized annual NOI of $33,000. The only sale of a similar triplex in its neighborhood closed three years ago at a 6.50% overall rate. A triplex in a nearby neighborhood where overall rates run higher has sold twice with no physical change: three years ago for $480,000 with annual NOI of $36,000, and this month for $600,000 with annual NOI of $42,000. Local brokers report that overall rates in the two neighborhoods have moved by the same amount. What is the indicated value of the subject by direct capitalization?
Correct Answer
C) $550,000
The resale pair shows rates moving from 7.50% ($36,000 ÷ $480,000) to 7.00% ($42,000 ÷ $600,000), a 50 basis point decline. Applied to the older 6.50% neighborhood rate, the current rate is 6.00%, and $33,000 ÷ 0.06 = $550,000. Leaving the old rate unadjusted gives $507,692. Using the other neighborhood's 7.50% rate from three years ago gives $440,000. Trending the old value by the pair's 25% price gain gives $634,615, but that gain includes income growth as well as the rate change.
Why This Is the Correct Answer
Option C is correct because the pair's rate fell from 7.50% ($36,000 ÷ $480,000) to 7.00% ($42,000 ÷ $600,000), a decline of 50 basis points. Taking that decline from the 6.50% neighborhood rate gives 6.00%. Capitalizing the subject's NOI gives $33,000 ÷ 0.06 = $550,000.
Why the Other Options Are Wrong
Option A: $440,000
Option A, $440,000, capitalizes at 7.50%: $33,000 ÷ 0.075. That is the other neighborhood's rate from three years ago, a level that runs higher than the subject's and is also out of date. The pair supplies only the half-point decline, applied to the local 6.50% rate to give 6.00% and $550,000.
Option B: $507,692
Option B, $507,692, is $33,000 ÷ 0.065, which applies the three-year-old rate as though the market had not moved. The resale pair shows a 50 basis point decline, so the current rate is 6.00% and the value is $550,000.
Option D: $634,615
Option D, $634,615, trends the old value by the pair's price gain: $33,000 ÷ 0.065 × 1.25. The 25% gain ($600,000 ÷ $480,000) reflects income growth as well as the rate change, so it overstates what the rate shift alone contributes. The correct calculation is $33,000 ÷ 0.06 = $550,000.
Borrow the move, not the level
From a resale pair in a different neighborhood, take how far the rate moved and leave its level behind. Then apply that move to the rate from the subject's own neighborhood.
How to use: Use this when a resale pair and an older local sale both appear in the facts.
Exam Tip
When price and NOI both change between two sales, compute a rate for each date before deciding which way rates moved. A rising price can accompany a falling or rising rate.
Common Mistakes to Avoid
- -Assuming a higher resale price means rates must have fallen by the same proportion
- -Using the resale property's rate level even though its neighborhood runs higher
- -Leaving the older local rate unadjusted for the market's move
Concept Deep Dive
Analysis
This tests whether a candidate can measure a market rate change from a resale pair and apply only that change to a rate from the subject's own neighborhood. Each sale of the pair needs its own rate, because both price and NOI changed between the two dates. The pair's rate level does not transfer since its neighborhood runs higher, but its movement does. The price rise is a distraction: rates fell by a half point, and the rest of the price gain came from higher income.
Background Knowledge
A resale of the same unchanged property holds physical and locational differences constant, so a change in its extracted rate points to a change in the market. Extraction divides anticipated net income by the sale price, and direct market evidence is the preferred source for rates. A rate level from one neighborhood may not fit another even when the direction and size of a market move are shared.
Real-World Application
An appraiser has one good but dated sale near a small rental property and no fresh local sales. A resale elsewhere in town shows how far investor rates have moved, so the appraiser updates the local rate by that amount and documents broker confirmation that the two areas move together.
More Income Approach Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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