To determine why the final value of the property under the cost approach is $525,000, let’s break down the calculation step-by-step using the cost approach method in real estate appraisal. The cost approach estimates the value of a property by calculating the cost to replace the building, adding the value of the site and site improvements, and adjusting for depreciation.
### Step-by-Step Explanation:
1. **Understand the Components Provided**:
– **Replacement Cost of the Building**: $375,000
– **Site Value**: $150,000
– **Site Improvements (landscaping and driveway)**: $75,000
– **Accrued Depreciation**: 20% (applied as a physical depreciation factor to the building)
2. **Cost Approach Formula**:
The cost approach value is calculated as:
\[
\text{Property Value} = (\text{Replacement Cost of Building} – \text{Depreciation}) + \text{Site Value} + \text{Site Improvements}
\]
3. **Apply Depreciation to the Building**:
– The replacement cost of the building is $375,000.
– The accrued depreciation is 20%, which applies to the building only (since physical depreciation typically affects the structure, not the land or site improvements unless specified otherwise).
– Calculate the depreciation amount:
\[
\text{Depreciation} = \text{Replacement Cost of Building} \times \text{Depreciation Rate}
\]
\[
\text{Depreciation} = 375,000 \times 0.20 = 75,000
\]
– Subtract the depreciation from the building’s replacement cost to get the depreciated value of the building:
\[
\text{Depreciated Building Value} = 375,000 – 75,000 = 300,000
\]
4. **Add the Site Value and Site Improvements**:
– The site value is given as $150,000.
– The site improvements (landscaping and driveway) are valued at $75,000.
– In the cost approach, the site value and site improvements are typically not depreciated unless explicitly stated, as land does not depreciate and site improvements like landscaping and driveways are often assumed to be in good condition or valued at current cost.
– Therefore, we use the full values:
– Site Value: $150,000
– Site Improvements: $75,000
5. **Calculate the Total Property Value**:
– Combine the depreciated building value, site value, and site improvements:
\[
\text{Property Value} = \text{Depreciated Building Value} + \text{Site Value} + \text{Site Improvements}
\]
\[
\text{Property Value} = 300,000 + 150,000 + 75,000 = 525,000
\]
6. **Verify the Calculation**:
– Depreciated Building Value: $300,000
– Site Value: $150,000
– Site Improvements: $75,000
– Total: $300,000 + $150,000 + $75,000 = $525,000
7. **Clarification on Depreciation**:
– The problem specifies a 20% physical depreciation factor applied to the building. Physical depreciation refers to the loss in value due to wear and tear, deterioration, or aging of the structure. Since the problem does not mention depreciation for the site or site improvements, we assume they are valued at their full cost ($150,000 and $75,000, respectively).
– If the site improvements were also subject to depreciation, the problem would explicitly state so, but here, only the building’s replacement cost is depreciated.
8. **Why $525,000?**:
– The final value of $525,000 reflects the sum of the depreciated building value ($300,000), the site value ($150,000), and the site improvements ($75,000).
– This matches the cost approach methodology, where the total property value accounts for the current cost to replace the building (adjusted for depreciation) plus the value of the land and improvements.
### Final Answer:
The final value of the property under the cost approach is $525,000 because:
– The building’s replacement cost ($375,000) is reduced by 20% depreciation ($75,000), resulting in a depreciated building value of $300,000.
– The site value ($150,000) and site improvements ($75,000) are added without depreciation, as they are not specified to be depreciated.
– Total: $300,000 + $150,000 + $75,000 = $525,000.
This calculation aligns with standard real estate appraisal practices for the cost approach.