A broker tells an appraiser that fourplexes in the market area are selling at 12.5 times NOI. A lender’s survey of the same market reports a 7.5% overall rate. What overall rate does the broker’s figure represent, and how does its value indication compare with that of the lender’s rate?
Correct Answer
D) 8.0%; lower value
A factor is the reciprocal of a rate, so 12.5 times NOI equals 1 ÷ 12.5 = 8.0%. Value equals income divided by rate, so a higher rate means a lower value on the same NOI. Reading the multiple itself as 12.5% misses the conversion, and 0.8% is a decimal slip. Pairing 8.0% with a higher value reverses the inverse relationship between rate and value.
Why This Is the Correct Answer
Option D is correct because a factor is the reciprocal of a rate: 1 ÷ 12.5 = 8.0%. Since value equals income divided by the rate, an 8.0% rate yields less value than a 7.5% rate on the same income. On $100,000 of NOI, the figures would be $1,250,000 and about $1,333,333.
Why the Other Options Are Wrong
Option A: 12.5%; lower value
Option A reads the multiple as a percentage, but 12.5 times NOI is not a 12.5% rate. The reciprocal is 1 ÷ 12.5 = 8.0%, so although the option's direction is right, its rate is wrong.
Option B: 8.0%; higher value
Option B has the rate right at 1 ÷ 12.5 = 8.0% but the direction wrong. A higher rate in the denominator gives a lower value, so 8.0% points below the 7.5% indication, not above it.
Option C: 0.8%; higher value
Option C's 0.8% misplaces the decimal, since 0.08 equals 8.0%, not 0.8%. The correct conversion is 1 ÷ 12.5 = 8.0%, which is above the lender's 7.5% and so points to a lower value.
Flip It to Switch
Flip a multiple to get a rate and flip a rate to get a multiple. Bigger rate, smaller multiple, smaller value.
How to use: Use the flip when market quotes mix net income multiples and capitalization rates.
Exam Tip
Before comparing a multiple with a rate, convert them to the same form. Then remember that a higher rate and a lower multiple move value the same way.
Common Mistakes to Avoid
- -Reading a net income multiple directly as a percentage rate
- -Thinking a higher capitalization rate implies a higher value
- -Misplacing the decimal when converting a reciprocal to a percentage
Concept Deep Dive
Analysis
A multiplier and a rate are two ways of expressing one relationship between income and value. Converting one into the other lets different market quotes be compared. The second step is direction: value falls as the rate rises, because the rate is in the denominator.
Background Knowledge
Direct capitalization can be written with a rate, V = I ÷ R, or with a factor, V = I × F. The two forms are equivalent because the factor equals one divided by the rate.
Real-World Application
During a market interview, one broker quotes price in multiples of NOI while a lender's survey reports overall rates. The appraiser converts the broker's figure to a rate so both can be weighed together in the income analysis.
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?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
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?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
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?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
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Previous Question
The subject property is a fourplex with six detached garages that are rented separately. Potential rent from the apartments is $72,000 a year, with stabilized vacancy and credit loss of 5%. Potential garage rent is $7,200 a year, and similar garages in the area experience 25% vacancy and credit loss. Annual operating expenses are $25,800, and the market overall rate is 8%. What is the indicated value by direct capitalization?
Next Question
An appraiser is valuing a newly built retail building that cost $1,100,000 to construct and is in lease-up. There is no cash flow in year 1. NOI is projected at $100,000 at the end of year 2 and $120,000 at the end of year 3, when net sale proceeds of $1,500,000 are also expected. The discount rate is 10%. What is the present value of these benefits?