An appraiser is developing the cost approach for a dwelling using replacement cost. A highly comparable dwelling recently sold for $390,000. At the sale date, its site was worth $110,000 and its improvement cost new was $350,000 on a replacement basis and $410,000 on a reproduction basis. What overall depreciation rate does this sale indicate for the subject?
Correct Answer
B) 20.0%
The cost type used on the comparable should match the subject's, so replacement cost new of $350,000 applies. The improvement contribution is $390,000 − $110,000 = $280,000, depreciation is $350,000 − $280,000 = $70,000, and $70,000 ÷ $350,000 = 20.0%. Using reproduction cost gives 31.7%, dividing by the contribution gives 25.0%, and dividing by the sale price gives 17.9%.
Why This Is the Correct Answer
Option B is correct because the subject uses replacement cost, so the comparable's $350,000 replacement cost new governs. The improvement contribution is $280,000, which leaves $70,000 of depreciation. Dividing by $350,000 gives 20.0%.
Why the Other Options Are Wrong
Option A: 17.9%
Option A shows 17.9%, from 70,000 ÷ 390,000. The dollar loss is right, but the sale price includes the site and is not the base; dividing by cost new of $350,000 gives 20.0%.
Option C: 25.0%
Option C shows 25.0%, from 70,000 ÷ 280,000. The dollar loss is right, but the base is the improvement contribution; dividing by cost new of $350,000 gives 20.0%.
Option D: 31.7%
Option D shows 31.7%, from (410,000 − 280,000) ÷ 410,000 = 130,000 ÷ 410,000. It uses reproduction cost, which does not match the subject's replacement-cost basis, so the correct rate is 20.0%.
Match the base, then divide
Use the cost type the subject uses, then divide the dollar loss by that cost new. Matching comes first and dividing second.
How to use: Use this when a comparable lists both replacement and reproduction cost and an extracted percentage is requested.
Exam Tip
Look for the subject's cost type before you calculate. A rate extracted on one basis does not transfer cleanly to the other.
Common Mistakes to Avoid
- -Using reproduction cost for a comparable when the subject uses replacement cost
- -Dividing the dollar loss by the improvement contribution
- -Dividing the dollar loss by the sale price
Concept Deep Dive
Analysis
This tests which figure to use before any arithmetic starts. The comparable has two cost estimates, and the extracted rate will be applied to a replacement-cost figure for the subject. The rate must come from the same type of cost, and its base is cost new.
Background Knowledge
Reproduction cost prices a replica, while replacement cost prices a property of equivalent utility, so the two can imply different depreciation for the same sale. Using the same cost type for comparables and subject keeps the extracted rate consistent with the figure it will be applied to.
Real-World Application
An appraiser's cost service provides both replacement and reproduction figures for an older comparable with dated construction. Since the subject's cost approach uses replacement cost, the appraiser extracts the comparable's loss on that basis. The higher reproduction-based rate is left out of the analysis.
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?
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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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Previous 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?
Next Question
The as-completed cost of the improvements is $540,000, and 80% of that cost is installed. A $22,000 loss applies to the installed portion, and the site value is $175,000. What total is indicated, before any consideration of completion risk or profit?