Anne Appraiser is determining the value of a single family residential home that has an
actual age of 15 years, an estimated effective age of 10 years, and a remaining economic
life of 30 years. The replacement cost is $131,582. A two-car garage was added to the
property ten years ago and has an effective age of 7 years with a remaining economic life
of 18 years. The replacement cost is $29,581. An inground pool was installed 3 years
ago, with an effective age of 5 years and a remaining economic life of 12 years. The
replacement cost is $24,585. The home has an extensive wooden deck constructed 5
years ago, with an effective age of 5 years, and a remaining economic life of 15 years.
The replacement cost is $14,300. Wooden fencing completely encloses the rear yard area
and has an effective age of 3 years and a remaining economic life of 12 years. The
replacement cost is $8,748. Determine the total accrued depreciation.

  $53,734

Explanation:

When the "scrap value" of the asset is zero, the depreciation each year can be computed by dividing the replacement cost by the total economic life of the asset. Then the accumulated depreciation is that yearly depreciation multiplied by the effective age of the asset.

Here, we assume the total economic life is the sum of the effective age and the remaining economic life.

So, for example, the accumulated depreciation of the house would be calculated as ...

  ($131,582)(10 years)/(10 years +30 years) = $131,582(1/4) = $32,895.50

Here, values are shown in the attached spreadsheet rounded to the nearest dollar. The spreadsheet uses full precision values in its calculations.

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Depreciation is computed separately for each of the improvements, and the accumulated depreciation is the sum of the individual improvement depreciations. We have used a spreadsheet to do the arithmetic so as to minimize errors and avoid the tedium of repetitive calculations.

The total accrued depreciation is $53,734.

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