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Sales ComparisonHARD16.4% of exam

Market data in a suburban area show buyers react to roof age in line with depreciated replacement cost. A comparable two-story colonial has a 2-year-old asphalt shingle roof. The subject's roof of the same type is 16 years old and in typical condition for its age. Shingle roofs in this market last about 20 years, and a new roof for either house costs $14,000. What roof adjustment applies to the comparable?

Correct Answer

C) -$9,800

Each roof is depreciated on an age-life basis: the comparable's has used 2 / 20 = 10% and the subject's 16 / 20 = 80% of its life, a difference of 70%. The difference in depreciated cost is $14,000 x 0.70 = $9,800, and because the comparable's roof is superior the adjustment is negative. The -$14,000 figure uses the full cost new, -$11,200 depreciates only the subject's roof and ignores the comparable's 2 years of wear, and -$8,820 applies the 70% to the comparable roof's depreciated $12,600 instead of to cost new.

Answer Options
A
-$14,000
B
-$11,200
C
-$9,800
D
-$8,820

Why This Is the Correct Answer

Option C is correct because the comparable's roof keeps 18 / 20 of its $14,000 cost, or $12,600, and the subject's keeps 4 / 20, or $2,800. The difference is $9,800, and since the comparable's roof is superior the adjustment is -$9,800.

Why the Other Options Are Wrong

Option A: -$14,000

Option A, -$14,000, adjusts by the full cost of a new roof. The subject's roof still has 4 years of life worth $2,800, and the comparable's roof is 2 years old, so the difference is $12,600 - $2,800 = $9,800.

Option B: -$11,200

Option B, -$11,200, depreciates only the subject's roof: $14,000 x 16 / 20 = $11,200. The comparable's roof has also used 2 of its 20 years, so the difference is $14,000 x 14 / 20 = $9,800.

Option D: -$8,820

Option D, -$8,820, applies the 70% age difference to the comparable roof's depreciated cost: $12,600 x 0.70 = $8,820. The age-life ratios are shares of cost new, so the difference is $14,000 x 0.70 = $9,800.

Compare what each roof has left

Work out the share of life left in each roof, take the difference, and multiply by cost new; the newer roof's owner gets the minus.

How to use: Use this for roof, furnace, water heater or other short-lived component adjustments.

Exam Tip

If both properties have the component, neither is worth cost new or zero; compare their remaining shares. Then set the sign by which property is better.

Common Mistakes to Avoid

  • -Adjusting by the full cost of a new roof
  • -Treating the comparable's roof as brand new when it has some age
  • -Applying the age-life difference to a depreciated figure instead of cost new

Concept Deep Dive

Analysis

The question tests a cost-based adjustment for a short-lived component when both properties have one at different ages. The adjustment is the difference between the two roofs' depreciated costs, not the cost of a new roof. The comparable has the younger, superior roof, so its price is adjusted down.

Background Knowledge

Short-lived components such as roof coverings have useful lives shorter than the remaining economic life of the house. Their depreciation is often measured with an age-life ratio applied to the cost new to replace them. When both properties have the component at different ages, the adjustment reflects the difference in their depreciated costs.

Real-World Application

An appraiser notes a comparable sold right after a reroof while the subject's roof is near the end of its life. Local sales show buyers discount for roof age about in line with depreciated cost, so the appraiser calculates the difference in remaining roof life and deducts it from the comparable.

short-lived componentroofage-life ratiodepreciated costremaining life
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