A certified general appraiser is valuing a 40-year-old office building affected by chronic noise and air pollution from a nearby airport. The appraiser estimates total external obsolescence at $620,000 using the sales comparison approach with paired sales. The site value, as confirmed by vacant land sales, is $380,000, and the reproduction cost new of the improvements is $1,850,000. Physical and functional depreciation total $310,000. What is the indicated value of the improvements after accounting for all forms of depreciation, including external obsolescence?
Correct Answer
A) $920,000
Why this is correct: The improvements are valued at reproduction cost new less all accrued depreciation: $1,850,000 - $310,000 physical and functional - $620,000 external = $920,000. The external obsolescence in this problem was measured by paired sales as the loss suffered by the improved property, and the $380,000 site value was independently confirmed by sales of vacant land that are subject to the same airport influence, so the site figure already carries whatever the noise and air pollution cost the land. Charging the full $620,000 against the improvements therefore does not double-count. The site value is added separately to reach total property value, but the question asks only for the depreciated value of the improvements. Why the other choices are wrong: '$1,230,000' deducts the external obsolescence but forgets the $310,000 of physical and functional depreciation. '$1,540,000' does the reverse, deducting the physical and functional depreciation and ignoring the external obsolescence the stem tells you to include. '$1,850,000' is reproduction cost new with no depreciation taken at all. Exam tip: In the cost approach, external obsolescence can burden both the land and the improvements. Trace where each figure came from: a site value drawn from comparable land already affected by the same influence has absorbed the land's share, so the measured improvement loss is deducted once, from the improvements.
Why This Is the Correct Answer
The arithmetic is $1,850,000 minus $310,000 minus $620,000, which equals $920,000. Every dollar of measured depreciation, regardless of category, comes out of the cost new before the improvements are stated at their depreciated value. The paired sales analysis produced an external obsolescence figure attributable to the improvements in this scenario, so it belongs in the same subtraction as the physical and functional loss. Site value stays outside the improvement calculation and is added afterward only when a total property value is requested.
Why the Other Options Are Wrong
Option B: $1,230,000
$1,230,000 is $1,850,000 minus only the $620,000 of external obsolescence, which silently drops the $310,000 of physical and functional loss. It reflects the reading error of treating the last depreciation figure mentioned as the only one that applies. All measured forms of depreciation are deducted, not just the one the stem spends the most words on.
Option C: $1,540,000
$1,540,000 is $1,850,000 minus only the $310,000 of physical and functional depreciation, omitting the airport-related external loss entirely. That would be right only if external obsolescence had already been captured elsewhere, which is not the case here since the site value came from vacant land sales stated as confirmed and separate. Ignoring a measured external loss overstates the improvements by the full $620,000.
Option D: $1,850,000
$1,850,000 is the reproduction cost new with no depreciation subtracted at all, which describes a brand-new building rather than a forty-year-old one under a flight path. It is the answer you get by reading the question as asking for cost rather than value. Cost new is an input to the cost approach, never its output.
Cost New Minus Everything
Say it as one line: cost new, minus physical, minus functional, minus external, equals depreciated improvements. Then a separate line: plus land, equals property. Keeping the two lines apart stops the site value from contaminating the improvement math.
How to use: Before computing, reread the last sentence of the stem and decide whether it asks for the improvements or for the whole property. Circle the site value only if the whole property is requested; otherwise mark it as a distractor and set it aside.
Exam Tip
List every depreciation figure in the stem before subtracting, then check each one off as you use it. Cost approach items are usually missed by omitting a number, not by miscalculating.
Common Mistakes to Avoid
- -Subtracting the site value from cost new instead of adding it to the depreciated improvements
- -Deducting only one category of depreciation when several are given
- -Assuming external obsolescence always attaches entirely to the improvements without checking how site value was derived
Concept Deep Dive
Analysis
This is a straight cost approach computation dressed up with an extra number designed to pull you off course. The improvement value indication equals reproduction cost new minus all accrued depreciation, and accrued depreciation is the sum of physical deterioration, functional obsolescence, and external obsolescence. Here the physical and functional components are already combined at $310,000 and external obsolescence is separately measured at $620,000 from paired sales, so total accrued depreciation is $930,000. Subtracting that from the $1,850,000 reproduction cost leaves $920,000 as the depreciated value of the improvements. The $380,000 site value is a distractor for this particular question because the stem asks only for the improvement indication; site value would be added later to reach the total property value of $1,300,000.
Background Knowledge
You need the cost approach formula, land value plus reproduction or replacement cost new minus accrued depreciation, and the three categories of depreciation. You should also know that paired sales analysis is a common way to measure external obsolescence, and that reproduction cost recreates a replica while replacement cost recreates equivalent utility with modern materials.
Real-World Application
An appraiser near a busy airport pairs sales of similar offices inside and outside the noise contour, isolates the price difference attributable to noise and air quality, and applies it as external obsolescence in the cost approach while cross-checking the same conclusion against sales comparison and income indications before reconciling.
More Cost Approach Questions
In a cost approach for a proposed building, the appropriate cost basis is generally:
A warehouse cost $210,000 to build when the cost index stood at 105. The index is now 210. Its indicated current cost is:
The age-life method expresses depreciation as:
Market extraction of depreciation is limited by the fact that it:
Functional obsolescence caused by a deficiency is measured as curable when:
Curable physical deterioration is measured at cost to cure because:
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A house has three bedrooms sharing one bathroom, and adding a second bath is economically justified. This is:
Direct costs in a construction budget include:
An appraiser writes that a 40-year-old house has an effective age of 10 but describes original wiring, original kitchen and a 25-year-old roof. The report's problem is:
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