Two percentage adjustments, +10% and −5%, apply to a $300,000 comparable. What are the adjusted prices under the additive and the multiplicative methods?
Correct Answer
C) Additive $315,000; multiplicative $313,500
Additive: +10% − 5% = +5%, so $300,000 × 1.05 = $315,000. Multiplicative: 1.10 × 0.95 = 1.045, so $300,000 × 1.045 = $313,500. The two methods give different net adjustments.
Why This Is the Correct Answer
Option C is correct because the additive method sums +10% and −5% to get +5%, so $300,000 × 1.05 = $315,000. The multiplicative method multiplies 1.10 × 0.95 = 1.045, so $300,000 × 1.045 = $313,500. The two methods give different results.
Why the Other Options Are Wrong
Option A: Additive $313,500; multiplicative $315,000
Option A shows additive $313,500 and multiplicative $315,000. It reverses the labels: $313,500 comes from multiplying 1.10 × 0.95, and $315,000 comes from adding the percentages.
Option B: Additive $315,000; multiplicative $315,000
Option B shows $315,000 for both methods. It assumes the methods agree, but multiplying 1.10 × 0.95 gives 1.045 rather than 1.05, so the multiplicative result is $313,500.
Option D: Additive $345,000; multiplicative $313,500
Option D shows additive $345,000 and multiplicative $313,500. The $345,000 comes from $300,000 × 1.15, which adds the absolute values of 10% and 5% instead of netting +10% − 5% = +5%, which gives $315,000.
Add the rates, or chain the factors
Additive sums the percentages into one rate; multiplicative chains each as 1 plus the rate.
How to use: Use this to compute both versions when a question mixes percentage adjustments.
Exam Tip
Compute both methods yourself and match each figure to its label; a reversed-label distractor is common.
Common Mistakes to Avoid
- -Reversing which method gives which result
- -Assuming additive and multiplicative methods agree
- -Adding the absolute values of positive and negative percentages
Concept Deep Dive
Analysis
This question tests the difference between additive and multiplicative application of percentage adjustments. Additive sums the percentages first, while multiplicative chains them as factors. The two methods can produce different net adjustments.
Background Knowledge
When more than one percentage adjustment applies, they can be combined additively or multiplicatively, producing different net adjustment amounts. Appraisers should apply them consistently and in the manner supported by the market data. Understanding both methods helps check the arithmetic.
Real-World Application
An appraiser applies a +10% location adjustment and a −5% condition adjustment to a $300,000 comparable. She notes that applying them sequentially gives $313,500 while summing them gives $315,000 and states which method she used.
More Sales Comparison Questions
Supported adjustments are: non-market financing $10,000, GLA $36/sf, garage $3,500 per car, pool/spa $12,500. A comparable identical to the 2,800 sf subject sold for $267,000 with non-market financing. What is its adjusted price?
Using GLA $36/sf and non-market financing $10,000: a 3,100 sf comparable sold for $277,000 with non-market financing; the subject has 2,800 sf. Bath count differences are not adjusted. What is the adjusted price?
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A verified pair of cash-equivalent sales in the same market has C2 at $640,000 and C5 at $568,000. Rights, terms, time and other material characteristics are matched. A suitable comparable sold for $615,000. The subject is C5; the comparable is C2. Assume the observed contribution applies and no other adjustments. What signed condition adjustment and adjusted comparable price result?