A property's replacement cost new is estimated at $450,000. Physical depreciation is $45,000, functional obsolescence is $25,000, and external obsolescence is $15,000. If the land value is $125,000, what is the indicated value by the cost approach?
Correct Answer
D) $490,000
Why this is correct: The cost approach formula is: Value = (Replacement Cost New - Total Depreciation) + Land Value. Step 1: Sum depreciation: $45,000 + $25,000 + $15,000 = $85,000. Step 2: Depreciated cost of improvements: $450,000 - $85,000 = $365,000. Step 3: Add land value: $365,000 + $125,000 = $490,000. Why the other choices are wrong: "$450,000" is the replacement cost new, ignoring depreciation and land. "$575,000" incorrectly adds land to the replacement cost without subtracting depreciation. "$365,000" is the depreciated cost of improvements only, missing the land value. Exam tip: Cost approach = (Cost - Depreciation) + Land. Always include land at the end.
Why This Is the Correct Answer
Option A ($490,000) correctly applies the cost approach formula by starting with the replacement cost new of $450,000, subtracting total depreciation of $85,000 ($45,000 + $25,000 + $15,000), which yields $365,000 for the depreciated improvement value. The final step adds the land value of $125,000 to reach the total indicated value of $490,000. This follows the standard cost approach sequence: Replacement Cost New - Total Depreciation + Land Value = Indicated Value.
Why the Other Options Are Wrong
Option A: $450,000
Option A ($450,000) represents only the replacement cost new without any adjustments for depreciation or land value, making it an incomplete calculation that ignores the fundamental components of the cost approach.
Option B: $575,000
Option B ($575,000) appears to incorrectly add the total depreciation to the replacement cost instead of subtracting it, then add land value, resulting in a value that's significantly overstated and mathematically incorrect.
Option C: $365,000
Option C ($365,000) represents only the depreciated cost of improvements ($450,000 - $85,000) but fails to add the land value of $125,000, which is a critical component that must be included in the final indicated value.
RLD Formula
Remember 'RLD': Replacement cost minus (Less) Depreciation plus (Dirt) Land = Value. Think 'Really Love Dirt' to remember the sequence.
How to use: When you see a cost approach question, immediately write 'RLD' and fill in: R (replacement cost) - L (total depreciation) + D (land value) = Answer. This prevents formula confusion and calculation errors.
Exam Tip
Always double-check that you've added all three types of depreciation together before subtracting from replacement cost, and never forget to add back the land value as the final step.
Common Mistakes to Avoid
- -Forgetting to add the land value to the depreciated improvement value
- -Adding depreciation instead of subtracting it from replacement cost
- -Using only one type of depreciation instead of summing all three types
Concept Deep Dive
Analysis
This question tests the fundamental cost approach formula, which is one of the three primary valuation methods in real estate appraisal. The cost approach estimates property value by calculating what it would cost to replace the improvements, then subtracting all forms of depreciation, and finally adding the land value. This method is particularly useful for newer properties, special-use properties, or when comparable sales data is limited. Understanding the three types of depreciation (physical, functional, and external) and how they cumulate is essential for accurate cost approach calculations.
Background Knowledge
The cost approach is based on the principle of substitution, which assumes a rational buyer will not pay more for a property than the cost to acquire land and construct improvements of equal utility. Appraisers must understand that depreciation comes in three forms: physical (wear and tear), functional (design deficiencies), and external (location or market factors), and these are additive when calculating total depreciation.
Real-World Application
Appraisers commonly use the cost approach for insurance purposes, new construction, special-use properties like churches or schools, and as a check against other valuation methods. Accurate depreciation estimation requires field observation and market analysis to support the final value conclusion.
More Cost Approach Questions
A property generates $85,000 in Net Operating Income and sells for $1,062,500. What is the overall capitalization rate?
A property has potential gross income of $180,000, vacancy and collection loss of $15,000, and operating expenses of $65,000. What is the Net Operating Income?
A comparable sale occurred 8 months ago for $425,000. Market conditions indicate property values have increased 0.5% per month since that time. What is the adjusted sale price?
A property generates $150,000 in potential gross income. Market data indicates a 7% vacancy rate and operating expenses of 35% of effective gross income. If the cap rate is 9.5%, what is the indicated value?
A property sold for $320,000 one year ago. If market conditions have improved by 6% since that sale, what is the time-adjusted sale price for comparison purposes?
A commercial building cost $2,500,000 to construct. The land value is $600,000. If the building has suffered 15% physical deterioration and 8% functional obsolescence, what is the depreciated cost of the improvements?
A building's gross rent multiplier (GRM) is 120. If the monthly rent is $2,500, what is the indicated value?
In the cost approach, economic obsolescence is characterized as:
The concept of regression in property values means that:
A commercial property has potential gross income of $120,000, vacancy and collection loss of 8%, and operating expenses of $35,000. Using a cap rate of 9.5%, what is the indicated value?
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