A suitable cost index is used to trend a historical construction cost of $300,000, for the same scope of work, from index 180 to index 270. Total depreciation of the improvements is $85,000, and the site value is $120,000. What value does the cost approach indicate?
Correct Answer
D) $485,000
300000×270÷180−85000+120000 = 485000. Common errors: leaving out the site value gives $365,000; not trending the historical cost gives $335,000; inverting the index ratio (180 ÷ 270) gives $235,000.
Why This Is the Correct Answer
Option D is correct because the trended cost is $300,000 x 270 / 180 = $300,000 x 1.5 = $450,000. Subtracting $85,000 depreciation gives $365,000, and adding the $120,000 site gives $485,000.
Why the Other Options Are Wrong
Option A: $235,000
Option A, $235,000, inverts the index ratio: $300,000 x 180 / 270 = $200,000, then $200,000 - $85,000 + $120,000 = $235,000. Costs are trended forward with current index over historical index, giving $485,000.
Option B: $335,000
Option B, $335,000, skips the index trending: $300,000 - $85,000 + $120,000 = $335,000. The historical cost must first be trended to $450,000, which leads to $485,000.
Option C: $365,000
Option C, $365,000, leaves out the site value: $300,000 x 270 / 180 - $85,000 = $365,000. Adding the $120,000 site gives $485,000.
New index on top
To bring an old cost forward, divide the new index by the old index and multiply. The newer index goes on top.
How to use: Use new index on top whenever you trend a past cost to the present.
Exam Tip
If costs have risen, the trended figure should be higher than the historical cost. A smaller trended figure means the ratio was flipped.
Common Mistakes to Avoid
- -Inverting the index ratio
- -Using the historical cost without trending it
- -Forgetting to add site value
Concept Deep Dive
Analysis
This question tests trending a historical cost with a cost index and then completing the cost approach. Multiply the historical cost by the ratio of the current index to the historical index, subtract depreciation, and add site value. The key is putting the current index on top of the ratio.
Background Knowledge
The trended historical cost method adjusts original construction cost to current terms using a cost index ratio. Price indexes only approximately measure cost changes, so the result is an estimate. Trending original costs is a recognized part of cost analysis, but it reproduces the original scope rather than a modern replacement.
Real-World Application
An appraiser has the original construction contract for a building built years ago and a published cost index for that year and today. She trends the contract amount forward, subtracts supported depreciation and adds a current site value, noting that index trending is an approximation.
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
An appraiser is developing the cost approach for a dwelling built in 1920. Reproduction cost new is $780,000, which includes $90,000 for extra-thick masonry walls that add no value and no added cost of ownership. Replacement cost new is $690,000, which excludes those walls. Accrued depreciation, estimated against replacement cost, is $120,000. Site value is $230,000. What value does the cost approach indicate?
Next Question
The subject improvements have a cost new of $490,000, a remaining economic life of 33 years and a total economic life of 55 years. The site is valued at $171,000. Using straight-line age-life depreciation with no salvage value and no additional loss, what value does the cost approach indicate?