A building has cost new of $520,000, an effective age of 22 and total economic life of 55. Depreciated improvement value is:
Correct Answer
A) $312,000
Why this is correct: The correct answer is '$312,000.' The calculation uses the age-life method. Depreciation is calculated as the ratio of effective age to total economic life: 22 years / 55 years = 0.40 or 40%. This is the accrued depreciation ratio. The depreciated value is the cost new multiplied by the remaining life ratio (100% - 40% = 60%). So, $520,000 × 0.60 = $312,000. The original explanation warns against the common error of using the effective age percentage directly (22% of $520,000 = $114,400 depreciation, leaving $405,600). Why the other choices are wrong: '$208,000, the depreciation amount itself' is the dollar amount of depreciation ($520,000 × 0.40), not the depreciated value. '$364,000, using a 30% ratio' uses an incorrect, unsupported depreciation rate. '$405,600, applying a 22% ratio' mistakenly uses the effective age (22) as a percentage, not the age-life fraction. Exam tip: Depreciated Value = Cost New × (1 - (Effective Age / Total Economic Life)). Always compute the ratio first.
Why This Is the Correct Answer
Twenty-two years over a fifty-five-year total economic life is 0.40, so 40 percent of value has been consumed and 60 percent remains. Multiplying $520,000 by 0.60 gives $312,000 as the depreciated value of the improvements. Equivalently, $520,000 less $208,000 of accrued depreciation equals $312,000. That $312,000 is what gets added to land value in the cost approach.
Why the Other Options Are Wrong
Option B: $208,000, the depreciation amount itself
$208,000 is the accrued depreciation itself, 40 percent of cost new, not the value that remains. It is the intermediate figure, and the question asks for the depreciated improvement value that follows it. Handing in the deduction instead of the result is the most common error on this problem type.
Option C: $364,000, using a 30% ratio
$364,000 corresponds to a 30 percent depreciation ratio, which appears nowhere in the data. Twenty-two over fifty-five is 40 percent, and no rounding or convention converts it to 30 percent. The number is designed to look reasonable to anyone who estimates rather than divides.
Option D: $405,600, applying a 22% ratio
$405,600 comes from treating the effective age of 22 as a 22 percent depreciation rate, deducting $114,400. Effective age is a count of years, not a percentage, and it means nothing until it is divided by total economic life. This mistake always produces too little depreciation and too high a value.
Consumed Versus Left
The ratio tells you what has been consumed. One minus the ratio tells you what is left. Depreciation is the bite taken out; depreciated value is the sandwich that remains.
How to use: Underline the last four words of the stem. If it says depreciation, stop at the ratio times cost. If it says depreciated value, remaining value or contributory value of improvements, take the extra subtraction step.
Exam Tip
Compute the complement percentage first, then multiply once; it removes a subtraction step and the chance of turning in the deduction by mistake.
Common Mistakes to Avoid
- -Submitting the depreciation amount when the depreciated value was requested
- -Using effective age directly as a percentage
- -Estimating the ratio instead of dividing the two figures given
Concept Deep Dive
Analysis
This item adds one step to the age-life calculation: after computing accrued depreciation, you must subtract it from cost new to reach depreciated improvement value, which is the figure that actually enters the cost approach before land is added. Many candidates compute the ratio correctly and then hand in the depreciation amount as if it were the answer. The shortcut is to multiply cost new by one minus the ratio, which produces the depreciated value in a single step. The other trap embedded here is treating the effective age number itself as a percentage, a slip the distractor list rewards.
Background Knowledge
You need the age-life ratio and the follow-through step: depreciated improvement value equals cost new times one minus that ratio. You also need to keep straight which figure a question wants, the depreciation amount or the remaining value.
Real-World Application
Completing the cost approach on a small retail building, the appraiser deducts accrued depreciation from cost new to arrive at the depreciated contribution of the improvements, then adds site value and site improvements to reach the indicated value by the approach.
More Cost Approach Questions
In a cost approach for a proposed building, the appropriate cost basis is generally:
A warehouse cost $210,000 to build when the cost index stood at 105. The index is now 210. Its indicated current cost is:
The age-life method expresses depreciation as:
Market extraction of depreciation is limited by the fact that it:
Functional obsolescence caused by a deficiency is measured as curable when:
Curable physical deterioration is measured at cost to cure because:
A 2,050 sq ft dwelling is priced at $178 per square foot with a $34,000 detached garage and $21,500 of site improvements. Cost new is:
A house has three bedrooms sharing one bathroom, and adding a second bath is economically justified. This is:
Direct costs in a construction budget include:
An appraiser writes that a 40-year-old house has an effective age of 10 but describes original wiring, original kitchen and a 25-year-old roof. The report's problem is:
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Income Approach
8.2% of exam