The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Correct Answer
A) $512,000
The comparable's improvements contributed $580,000 − $150,000 = $430,000, so depreciation is $500,000 − $430,000 = $70,000, or 14% of cost new and 2% a year over 7 years. Ten years at 2% is 20%, and $640,000 × 0.80 = $512,000. Using sale price as the percentage base gives $529,655, applying the overall 14% without annualizing gives $550,400, and deducting the comparable's $70,000 gives $570,000.
Why This Is the Correct Answer
Option A is correct because the comparable's $70,000 loss is 14% of its $500,000 cost new, or 2% a year over 7 years. The subject's 10 years at 2% gives 20% depreciation. Applying that to $640,000 leaves $512,000.
Why the Other Options Are Wrong
Option B: $529,655
Option B shows $529,655, which uses sale price as the base: 70,000 ÷ 580,000 = 12.069%, or 1.7241% a year, and 640,000 × (1 − 0.17241) = $529,655. The percentage belongs on cost new, which gives 2% a year and $512,000.
Option C: $550,400
Option C shows $550,400, which applies the comparable's overall 14%: 640,000 × 0.86. That ignores the subject's age of 10 years; at 2% a year the correct loss is 20%, leaving $512,000.
Option D: $570,000
Option D shows $570,000, which subtracts the comparable's $70,000 from the subject's $640,000. Dollar depreciation reflects the comparable's own cost and age, so the correct figure uses 20% and gives $512,000.
Dollars to percent to years
Convert the comparable's dollar loss into a percent of its cost new, then into a percent per year. Carry the annual rate, not the dollars, to the subject.
How to use: Use this when a comparable and a subject differ in age or cost new and an annual extracted rate is requested.
Exam Tip
Check the base and the age. The percentage is figured on cost new, and the annual rate is multiplied by the subject's age.
Common Mistakes to Avoid
- -Transferring the comparable's dollar depreciation to the subject
- -Applying the overall percentage to a subject of a different age
- -Dividing depreciation by sale price rather than cost new
Concept Deep Dive
Analysis
This tests the last stage of market extraction, where the comparable's result is converted into a form that fits the subject. A dollar amount does not transfer between properties of different cost and age. Convert the loss to a percentage of cost new, annualize it, and then apply it to the subject's age and cost.
Background Knowledge
Market extraction subtracts site value from a comparable's price to find the improvement contribution, then compares it with cost new to measure depreciation. The percentage may be used as an overall rate or an annual rate. Annualizing introduces the assumption that depreciation occurs on a straight-line basis over time.
Real-World Application
An appraiser values a 10-year-old house using a 7-year-old model that sold recently in the same subdivision. Because the two differ in age and size, the appraiser annualizes the extracted loss and applies it to the subject's own cost new. The straight-line assumption is noted in the workfile.
More Cost Approach Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
Improvement cost new is $500,000. Separately supported improvement depreciation deductions of $125,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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