Question 72

The depreciated value of the building is $76,800.

To calculate the depreciated value of the building, first determine the total replacement cost by finding the volume of the building and multiplying it by the cost per cubic foot. The volume is 20' x 40' x 15' = 12,000 cubic feet, leading to a replacement cost of $96,000. After applying the 20% depreciation, this results in a depreciated value of $76,800.

A) $76,800

This option correctly reflects the calculation of the depreciated value. Starting with the total replacement cost of $96,000, applying the 20% depreciation results in a value of $76,800, which is consistent with the calculations based on the building's volume and cost per cubic foot.

B) $81,920

This option is incorrect as it suggests a lower depreciation than what has been calculated. If the building suffered a 20% depreciation, the value after depreciation should not exceed $76,800, making this option incompatible with the provided data.

C) $85,333

This choice is also incorrect. It implies a lesser depreciation than the stated 20%, leading to a value that does not align with the calculations based on the overall replacement cost. The correct depreciation would yield a lower value than $85,333.

D) $96,000

This option represents the original replacement cost of the building before any depreciation is applied. Since the question specifically asks for the depreciated value, this option is not valid, as it fails to account for the 20% depreciation that affects the value.

Conclusion

The correct answer of $76,800 accurately represents the building's depreciated value after applying a 20% reduction to the total replacement cost. All other options either miscalculate the depreciation or fail to consider the effect of the stated depreciation percentage, confirming that $76,800 is the only viable choice based on the given data.