An appraiser is valuing a fourplex with effective gross income of $110,000 and has found three cash-equivalent sales. Sale A sold for $720,000 with EGI of $90,000. Sale B sold for $820,000 with EGI of $100,000. Sale C sold for $850,000 with net operating income of $85,000; its EGI could not be verified. The appraiser averages the effective gross income multipliers available from the sales. What is the indicated value?
Correct Answer
A) $891,000
Sales A and B yield 8.0 and 8.2 on EGI, a mean of 8.1, and 8.1 × $110,000 = $891,000. Sale C's 10.0 is price divided by NOI, a different income level, so it does not belong with an EGI multiplier. Averaging all three gives $960,667, relying on Sale C alone gives $1,100,000, and using the higher usable multiplier instead of the mean gives $902,000.
Why This Is the Correct Answer
Option A is correct because only Sales A and B are measured on EGI, giving multipliers of 8.0 and 8.2 and a mean of 8.1. Applying 8.1 to the subject's $110,000 EGI gives $891,000.
Why the Other Options Are Wrong
Option B: $902,000
Option B, $902,000, applies Sale B's 8.2 alone: 8.2 × $110,000. The assignment calls for the mean of the usable multipliers, so the correct figure is 8.1 × $110,000 = $891,000.
Option C: $960,667
Option C, $960,667, averages Sale C into the set: (8.0 + 8.2 + 10.0) ÷ 3 × $110,000. Sale C's 10.0 is based on NOI, so including it inflates the mean; the correct figure is 8.1 × $110,000 = $891,000.
Option D: $1,100,000
Option D, $1,100,000, relies on Sale C alone: $850,000 ÷ $85,000 × $110,000. That applies a price-to-NOI ratio to EGI, which mismatches the income levels; the correct figure is $891,000.
Check the denominator first
Before averaging any ratios, ask what each denominator actually is. A ratio on a different income level is a different measure, however similar it looks.
How to use: Use this check whenever a list of sales reports income under more than one label.
Exam Tip
When one multiplier stands well above the others, look for a difference in income definition before including it in an average.
Common Mistakes to Avoid
- -Averaging ratios that use different income levels
- -Applying a price-to-NOI ratio to EGI
- -Choosing the highest usable multiplier without support
Concept Deep Dive
Analysis
The problem tests a screening judgment that comes before the arithmetic. Sale C's ratio looks like a multiplier, yet its denominator sits below EGI on the income ladder. Removing it leaves two matching sales, whose mean is applied to the subject's EGI.
Background Knowledge
Multipliers and rates are derived at a specific income level and must be used with that same level. NOI is lower than EGI because expenses have been deducted, so a price-to-NOI ratio runs higher than a price-to-EGI ratio for the same sale.
Real-World Application
A broker's sale sheet lists income for several buildings without consistent labels. The appraiser verifies each figure and sets aside a sale whose income turns out to be net, because mixing it in would overstate the subject's value.
More Income Approach Questions
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In a DCF using an explicitly forward-income terminal model, what income is normally capitalized at the end-of-hold sale?
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The subject property is a 20-unit apartment building being appraised in fee simple. Sales of similar properties indicate a gross income multiplier of 8.5. The current rent roll, at below-market rents, shows potential gross income of $200,000. The appraiser's rent survey indicates market potential gross income of $240,000. A prospective buyer's pro forma shows potential gross income of $260,000. What is the indicated market value?