A comparable sold at a cash-equivalent price of $500,000 exactly 8 months before the effective date. Prices in the market have risen at a simple, non-compounded rate of 6% per year. No other adjustments apply. What is the time-adjusted price, to the nearest dollar?
Correct Answer
B) $520,000
500000×(1+0.06×(8/12))=520000. Common errors: adjusting downward instead of upward gives $480,000; dividing the annual rate by 8/12 instead of multiplying gives $545,000; applying the full annual rate to an 8-month interval gives $530,000.
Why This Is the Correct Answer
Option B is correct because eight months is 8/12 of a year, so the change is 6% × 8/12 = 4%. Applying it to the cash-equivalent price gives $500,000 × 1.04 = $520,000.
Why the Other Options Are Wrong
Option A: $480,000
Option A, $480,000, adjusts downward: $500,000 × (1 − 0.06 × 8/12) = $500,000 × 0.96. The market change is an increase, so the result is $500,000 × 1.04 = $520,000.
Option C: $530,000
Option C, $530,000, applies the full annual 6% to an 8-month interval: $500,000 × 1.06. Only 8/12 of the year has passed, so the change is 4%, giving $520,000.
Option D: $545,000
Option D, $545,000, divides the annual rate by 8/12 instead of multiplying: 0.06 ÷ (8/12) = 9%, and $500,000 × 1.09 = $545,000. The correct change is 0.06 × 8/12 = 4%, giving $520,000.
Prorate the year
For part of a year, multiply the annual rate by months divided by 12.
How to use: Use this whenever an annual rate is applied to a period shorter than a year.
Exam Tip
A partial-year change must be smaller than the full annual rate, which quickly rules out results at or above 6%.
Common Mistakes to Avoid
- -Applying the full annual rate to a partial year
- -Dividing by the fraction of the year instead of multiplying
- -Adjusting downward in a rising market
Concept Deep Dive
Analysis
This question tests converting a simple annual rate to a partial-year time adjustment. Multiply the annual rate by the fraction of the year that has passed, then apply that change to the price. The increase means the adjustment is upward.
Background Knowledge
Market conditions adjustments are often stated as an annual or monthly rate. With simple interest, the change is earned only on the original amount, so the rate is multiplied by the time elapsed. Time adjustments, or the lack of them, must be supported by evidence.
Real-World Application
An appraiser has evidence of about 6% annual appreciation in a stable suburban market. A comparable that closed eight months ago is adjusted upward 4% to bring it to the effective date.
More Sales Comparison Questions
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Which two depreciation categories may each be classified as curable or incurable by comparing the cost to remedy a deficiency with the value gained?
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When reconciling value indications from the three approaches to value, an appraiser should:
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A comparable sold for $324,000 exactly 18 months before the effective date. Market prices have increased at a simple, non-compounded rate of 0.35% per month. The comparable also requires a −$11,000 physical adjustment stated in effective-date dollars. What is the adjusted price?