The subject is a single-family residence whose improvements have a current cost new of $720,000, an effective age of 18 years, and a total economic life of 72 years. The site value of $248,000 already reflects any site influences. Using the straight-line age-life method, with no salvage value or other deductions, what is the total indicated value, including the site?
Correct Answer
C) $788,000
Age-life depreciation=720000×18÷72=180000; remainder=720000−180000−0+248000=788000. Common errors: leaving out the site value gives $540,000; not deducting the age-life depreciation gives $968,000; adding the depreciation, rather than the depreciated cost, to the site gives $428,000.
Why This Is the Correct Answer
Option C is correct because age-life depreciation is 18 ÷ 72 = 25% of cost new, or $720,000 × 18 ÷ 72 = $180,000. Then $720,000 − $180,000 = $540,000, plus the $248,000 site value equals $788,000.
Why the Other Options Are Wrong
Option A: $428,000
Option A, $428,000, adds the depreciation amount rather than the depreciated cost to the site ($180,000 + $248,000). The depreciated improvements are $540,000, so the total is $540,000 + $248,000 = $788,000.
Option B: $540,000
Option B, $540,000, is the depreciated improvement value only ($720,000 − $180,000). It leaves out the $248,000 site value; adding it gives $788,000.
Option D: $968,000
Option D, $968,000, adds site value to undepreciated cost ($720,000 + $248,000). The $180,000 age-life depreciation must be deducted, giving $788,000.
Effective age over economic life
EA divided by EL gives the depreciation share. Multiply by cost new, subtract, then add land.
How to use: Use EA over EL to set up any age-life depreciation calculation.
Exam Tip
Use effective age, not actual age, and total economic life, not remaining life, unless the question says otherwise. Check whether the answer asks for value with or without site.
Common Mistakes to Avoid
- -Adding the depreciation amount to site value instead of the depreciated cost
- -Using actual age instead of effective age
- -Forgetting to add the site value
Concept Deep Dive
Analysis
This question tests the age-life method. Depreciation equals effective age divided by total economic life, times cost new. Subtract that depreciation from cost new and add site value.
Background Knowledge
In the straight-line or age-life method, depreciation is estimated by dividing effective age by total economic life. That ratio is applied to cost new to find the dollar depreciation. The depreciated cost of the improvements is then added to the separately estimated site value.
Real-World Application
An appraiser judges a home to have an effective age of 18 years and a 72-year economic life. Applying 25% depreciation to cost new and adding a site value from land sales produces the cost approach indication.
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