The historical cost of a structure was $380,000, and a suitable index multiplier for the same construction scope is 1.40. Total depreciation of the improvements is $95,000, and site value is $175,000. What is the indicated value?
Correct Answer
C) $612,000
380000×1.40−95000+175000 = 612000. Common errors: leaving out the site value gives $437,000; not trending the historical cost gives $460,000; adding the depreciation instead of deducting it gives $802,000.
Why This Is the Correct Answer
Option C is correct because $380,000 x 1.40 = $532,000 trended cost, less $95,000 depreciation gives $437,000, and adding the $175,000 site gives $612,000. This follows the cost approach sequence of cost, minus depreciation, plus site.
Why the Other Options Are Wrong
Option A: $437,000
Option A, $437,000, leaves out the site value: $380,000 x 1.40 - $95,000 = $437,000. Adding the $175,000 site gives the correct $612,000.
Option B: $460,000
Option B, $460,000, does not trend the historical cost: $380,000 - $95,000 + $175,000 = $460,000. The 1.40 multiplier must be applied first, giving $532,000 - $95,000 + $175,000 = $612,000.
Option D: $802,000
Option D, $802,000, adds the depreciation instead of deducting it: $532,000 + $95,000 + $175,000 = $802,000. Depreciation reduces cost, so the correct total is $532,000 - $95,000 + $175,000 = $612,000.
Trend, deduct, then add land
Think of three moves in order: bring old cost to today, take off the loss, then put the land back in.
How to use: Use this sequence for any trended-cost question that also gives depreciation and site value.
Exam Tip
Check that the multiplier is applied to the historical cost before depreciation is deducted, and that site value is added at the end.
Common Mistakes to Avoid
- -Applying depreciation to the untrended historical cost
- -Forgetting to add site value at the end
- -Adding depreciation instead of subtracting it
Concept Deep Dive
Analysis
This question tests the order of operations in a trended historical cost analysis: trend the historical cost with the index multiplier, deduct depreciation, then add site value. Each step must be applied once in the correct direction.
Background Knowledge
Trended historical cost adjusts an original construction cost to a current level using a cost index or multiplier. Price indices only approximately measure cost changes over time, so the result is an estimate that still needs depreciation and site value to reach a cost approach indication.
Real-World Application
An appraiser has original construction records for an older building and applies a published cost index multiplier to estimate current cost. Because the index only approximates change, the appraiser cross-checks with a current cost service before deducting supported depreciation and adding land value.
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?
A 2,200-sf dwelling costs $200 per square foot, and a separate 400-sf garage costs $75 per square foot. These costs are complete and do not overlap. Both have an effective age of 15 years and a total life of 50 years, with straight-line depreciation and no salvage value. No site value or other loss is involved. What is the combined depreciated cost of the dwelling and garage?
A new feature in the improvements has a current cost of $45,000 and a market contribution of $18,000. The entire difference is due to superadequacy, with no physical or external loss and no overlap. What is the loss from the superadequacy?
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?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Income Approach
8.2% of exam
Previous Question
The current cost of a building is estimated at $62 per square foot for 3,000 square feet. Site improvements not already included in that figure would cost an additional $45,000. What is the total cost of the improvements, excluding land and any other additions?
Next Question
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?