A client has contracted to buy a fourplex for $550,000 and hopes to earn a 10% cash-on-cash return on equity. A similar fourplex recently sold for $750,000 with annual NOI of $60,000. At the overall rate indicated by that sale, what annual NOI would the subject need to justify the contract price?
Correct Answer
A) $44,000
The sale indicates $60,000 ÷ $750,000 = 8%, so the required NOI is $550,000 × 0.08 = $44,000. Applying the client's 10% equity return to the whole price gives $55,000. Reusing the comparable's NOI gives $60,000, and reading the sale's 12.5 price-to-NOI multiplier as a 12.5% rate gives $68,750.
Why This Is the Correct Answer
Option A is correct because the sale's rate is $60,000 ÷ $750,000 = 8%. A price of $550,000 at an 8% rate requires $550,000 × 0.08 = $44,000 of annual NOI.
Why the Other Options Are Wrong
Option B: $55,000
Option B, $55,000, is $550,000 × 10%, which applies the client's cash-on-cash goal to the whole price. That goal is a return on equity only, not an overall rate indicated by the market. The correct calculation is $550,000 × 0.08 = $44,000.
Option C: $60,000
Option C, $60,000, reuses the comparable's NOI. The subject's price is lower, so at the same rate its required income is lower too. The correct calculation is $550,000 × 0.08 = $44,000.
Option D: $68,750
Option D, $68,750, is $550,000 × 12.5%. The 12.5 is the sale's price-to-NOI multiplier, not a percentage rate; the matching rate is 1 ÷ 12.5 = 8%. The correct calculation is $550,000 × 0.08 = $44,000.
Cover the unknown
Think of income = rate × price, and cover the unknown. With a price and a rate, multiply to find income.
How to use: Use this when a client has a price and asks what income it requires.
Exam Tip
Identify the unknown before calculating, because value is not always what is being asked. A quick check is that a lower price at the same rate means lower income.
Common Mistakes to Avoid
- -Treating a price-to-income multiplier as a percentage rate
- -Assuming the subject needs the comparable's income
- -Applying a buyer's equity return to the whole price
Concept Deep Dive
Analysis
The usual calculation runs backward here, with income as the unknown. Extract the rate from the sale as usual. Then multiply the subject's price by the rate to find the income that price requires.
Background Knowledge
Price, income and rate form one relationship, so any one can be found from the other two. Lenders and buyers often ask what income a price requires. The same relationship can be stated as a multiplier, since a rate is the reciprocal of the matching multiplier.
Real-World Application
A buyer under contract asks whether in-place income justifies the price. The appraiser extracts a rate from a recent sale and calculates the NOI the price requires, then compares that with the income the fourplex can realistically produce.
More Income Approach Questions
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Debt funds 75% of value at an annual mortgage constant of 6.25%, and the remaining equity has a current annual dividend rate of 9%. What overall rate does the band of investment indicate, to two decimal places?
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The subject's annual PGI is $128,000. Sales in the market area indicate a price-to-income multiplier of 9.5, based on annual PGI. What is the indicated value?