A client is considering the purchase of a fourplex listed at $675,000. Stabilized NOI is $42,000, and recent sales of similar fourplexes indicate an overall rate of 7.2%. What overall rate does the list price represent, and how does the list price compare with the value indicated at the market rate?
Correct Answer
C) 6.22%, $91,667 above
The list price represents $42,000 ÷ $675,000 = 6.22%, below the 7.2% market rate. At market, value is $42,000 ÷ 0.072 = $583,333, so the list price is $91,667 too high. A lower rate means a higher price, which rules out a list price below value. The $6,600 figure is the annual NOI gap ($48,600 − $42,000), not a value gap, and 16.07 comes from dividing price by income.
Why This Is the Correct Answer
Option C is correct because $42,000 ÷ $675,000 = 6.22%, which is below the 7.2% market rate. Value at market is $42,000 ÷ 0.072 = $583,333. The list price exceeds that by $675,000 − $583,333 = $91,667.
Why the Other Options Are Wrong
Option A: 6.22%, $6,600 below
Option A has the right 6.22% but reports $6,600, which is $675,000 × 0.072 − $42,000, the extra annual NOI the price would need rather than a value difference. It also has the direction wrong: $675,000 is $91,667 above the $583,333 indicated value.
Option B: 16.07%, $91,667 below
Option B states 16.07%, which is $675,000 ÷ $42,000 read as a percent. That ratio is a multiplier, and the rate is $42,000 ÷ $675,000 = 6.22%. It also reverses the direction: $675,000 is above the $583,333 indicated value, not below it.
Option D: 16.07%, $6,600 above
Option D states 16.07%, which is $675,000 ÷ $42,000 read as a percent, when the rate is $42,000 ÷ $675,000 = 6.22%. Its $6,600 is $675,000 × 0.072 − $42,000, an annual NOI gap rather than a value difference, which is $675,000 − $583,333 = $91,667.
Low rate means high price
Rate and price move in opposite directions on the same income. An implied rate below market signals a price above market value.
How to use: Use this when a client has a price and the market gives a rate.
Exam Tip
State the direction before finalizing the answer. Also keep annual income differences separate from capital value differences.
Common Mistakes to Avoid
- -Reading a below-market implied rate as a bargain price
- -Inverting NOI and price when calculating an implied rate
- -Reporting an annual NOI shortfall as if it were a value difference
Concept Deep Dive
Analysis
The same relationship is used in both directions. First rearrange it to find the rate a price represents, then use it to find value at the market rate. The last step is reading the comparison correctly: a rate below market signals a price above the market-indicated value.
Background Knowledge
Value equals income divided by rate, and rate equals income divided by value. Comparing a price's implied rate with a market-derived rate is a quick test of pricing. A lower rate means buyers pay more for each dollar of income.
Real-World Application
A buyer's agent pitches a fourplex priced at about a 6.2% rate in a market trading near 7.2%. An appraiser capitalizes the NOI at the market rate and reports how far the list price sits above the indicated value.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
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Annual PGI is $250,000 and combined vacancy and collection loss is explicitly 12% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
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An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
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Previous Question
The subject property is an owner-managed fourplex. Market rent at full occupancy is $72,000 per year, and there is no other income. The owner's actual vacancy and credit loss is 2%, while competing fourplexes show a stabilized loss of 6%. The owner's statement lists $21,000 of operating expenses, $18,000 of mortgage payments and no management cost. Competing fourplexes pay management fees of 5% of EGI, and the overall rate is 8%. What is the indicated market value?
Next Question
The subject property is an office building with stabilized NOI of $123,000. Typical financing for similar properties is a 75% loan-to-value loan at 6.5% interest with a 7.6% annual mortgage constant. Equity investors expect a 10% equity dividend rate. At the value indicated by the band of investment, what is the annual pre-tax cash flow to equity?