An improvement had a historical cost of $280,000. A suitable cost index for the same scope of work has moved from 160 to 240. Total depreciation is 25% of the trended cost, and site value is $190,000. What value does the cost approach indicate?
Correct Answer
C) $505,000
280000×240÷160×0.75+190000 = 505000. Common errors: leaving out the site value gives $315,000; inverting the index ratio gives $330,000; not deducting the 25% loss gives $610,000.
Why This Is the Correct Answer
Option C is correct because $280,000 x 240 / 160 = $420,000 trended cost, $420,000 x 0.75 = $315,000 after the 25% loss, and $315,000 + $190,000 site = $505,000. This follows the correct sequence of trending first, applying the loss to the trended cost, and then adding the site.
Why the Other Options Are Wrong
Option A: $315,000
Option A, $315,000, comes from $280,000 x 240 / 160 x 0.75 = $315,000, which leaves out the site value. The correct total adds the $190,000 site: $315,000 + $190,000 = $505,000.
Option B: $330,000
Option B, $330,000, comes from $280,000 x 160 / 240 x 0.75 + $190,000 = $330,000, which inverts the index ratio and trends the cost down to $186,667. Trending up with 240 / 160 gives $420,000, so the correct total is $420,000 x 0.75 + $190,000 = $505,000.
Option D: $610,000
Option D, $610,000, comes from $280,000 x 240 / 160 + $190,000 = $610,000, which does not deduct the 25% loss. Deducting the loss gives $315,000 for improvements and $505,000 in total.
Trend, depreciate, add land
Multiply by current index over historical index, take off the improvement loss, then add the site. Land is added last because it is not depreciated.
How to use: Use this sequence on any cost-approach problem that combines index trending, depreciation and site value.
Exam Tip
Put the current index on top of the ratio when trending costs up. Check whether the loss is to be applied to the trended or untrended cost before calculating.
Common Mistakes to Avoid
- -Forgetting to add the site value
- -Skipping the index trending step and using the historical cost as current cost
- -Inverting the index ratio
Concept Deep Dive
Analysis
This calculation tests the steps in a trended historical cost analysis. First trend the historical cost with the index ratio, then deduct the 25% total improvement loss from the trended cost, then add the site value. The distractors leave out the site value (A), invert the index ratio (B) or leave out the loss (D).
Background Knowledge
The trended historical (original) cost method adjusts a past construction cost to current levels by multiplying it by the ratio of the current index to the index at the time of construction. Price indices only approximately measure cost change over time, so the result needs support. In the cost approach, depreciation is deducted from the improvement cost and site value is added separately.
Real-World Application
An appraiser has original construction records for a house and a cost index for its construction year and the effective date. The appraiser trends the recorded cost to current levels, deducts supported depreciation, and adds the land value from vacant lot sales. The appraiser also notes that the index is an approximate measure and checks the result against current cost data.
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?
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Previous Question
The cost new of the subject dwelling is $480,000, and total depreciation of the building is estimated at 25%. Site improvements, valued separately on an as-is basis, contribute $35,000, and the land, excluding those improvements, is valued at $150,000. None of these amounts overlap. What is the indicated value by the cost approach?
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