An appraiser trends a $420,000 historical construction cost by an appropriate index multiplier of 1.25, with the construction scope unchanged. Total depreciation of the improvements is $75,000, and site value is $95,000. What value is indicated?
Correct Answer
C) $545,000
420000×1.25−75000+95000 = 545000. Common errors: leaving out the site value gives $450,000; not trending the historical cost gives $440,000; adding the depreciation instead of deducting it gives $695,000.
Why This Is the Correct Answer
Option C is correct because the historical cost of $420,000 trended by 1.25 equals $525,000 of current cost. Deducting the $75,000 of supported depreciation leaves $450,000 for the improvements, and adding the $95,000 site gives $545,000.
Why the Other Options Are Wrong
Option A: $440,000
Option A, $440,000, results from skipping the index trend: $420,000 - $75,000 + $95,000 = $440,000. The historical cost must first be trended: $420,000 x 1.25 - $75,000 + $95,000 = $545,000.
Option B: $450,000
Option B, $450,000, is only the depreciated improvement figure: $420,000 x 1.25 - $75,000 = $450,000. It leaves out the $95,000 site value, which brings the indication to $545,000.
Option D: $695,000
Option D, $695,000, adds the depreciation instead of deducting it: $525,000 + $75,000 + $95,000 = $695,000. Depreciation reduces cost, so the correct result is $525,000 - $75,000 + $95,000 = $545,000.
Trend, Then Subtract, Then Add
Bring old cost to today first, take away the loss second, and add the land last. Think T-S-A: Trend, Subtract depreciation, Add site.
How to use: Use this sequence whenever a cost question gives an old cost and an index factor.
Exam Tip
When a question gives an index multiplier, check that your answer actually uses it. An answer that matches the untrended figure is a classic distractor.
Common Mistakes to Avoid
- -Using the historical cost without applying the index multiplier
- -Adding depreciation to cost new instead of subtracting it
- -Forgetting to add the site value to the depreciated improvements
Concept Deep Dive
Analysis
This question tests the trended historical cost method followed by the basic cost-approach summation. First convert the historical cost to a current figure with the index multiplier, then deduct depreciation and add the site value. Keeping the order of operations straight avoids the common slips of skipping the trend or the site.
Background Knowledge
The trended historical cost method updates an original construction cost to a current cost level by applying a cost index. Price indices only approximately measure cost change over time, and trending reflects the same historical scope rather than proving modern equivalent utility.
Real-World Application
An appraiser has the original construction contract for a 15-year-old custom home and a published cost index factor for the period. She trends the contract cost to the effective date, deducts her supported depreciation estimate, and adds a site value from vacant land sales.
More Cost Approach Questions
Why can equivalent-utility replacement cost be useful for an obsolete improvement?
An appraiser estimates the current replacement cost new of the improvements at $890,000, accrued depreciation from all causes at $170,000, and land value at $325,000. All necessary cost components and depreciation are included in those amounts. What is the indicated property value?
Improvement cost new is $595,000. Separately supported improvement depreciation deductions of $48,000, $27,000 are expressly nonoverlapping and not already excluded from cost new. Add supported site value of $155,000, already reflecting any site losses. What total indicated value results?
What best supports a claimed loss from a bathroom-layout deficiency?
Improvement cost new is $1,850,000. Separately supported improvement depreciation deductions of $310,000, $620,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
Which scenario most strongly supports giving the cost approach substantial weight?
A cost total $650,000 explicitly includes $40,000 of non-realty FF&E outside the appraised real-property interest. Exclude it. Supported realty-only total depreciation is $55,000. Add site $200,000, with no overlap. What real-property cost indication results?
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An external influence causes an annual net income loss of $9,600. The capitalization rate for the loss is 8%, and no other economic factors change. What is the indicated loss in value of the whole property, before allocation between site and improvements?
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