A client is under contract to buy a triplex for $480,000. The appraiser's stabilized NOI is $36,000, and sales of similar triplexes indicate an overall rate of 7.5%. The client then learns that the owner must begin paying for trash collection at $200 per month, and rents will not change. The client's planned loan carries annual debt service of $24,000. At what overall rate would the revised NOI support the contract price?
Correct Answer
A) 7.00%
The new cost is $200 × 12 = $2,400 a year, so revised NOI is $36,000 − $2,400 = $33,600, and $33,600 ÷ $480,000 = 7.00%. That is below the 7.5% market rate, so the price needs a lower rate than sales indicate. Forgetting to annualize the cost gives 7.46%, and keeping the old NOI gives 7.50%. Adding the cost to NOI gives 8.00%. Debt service does not enter NOI.
Why This Is the Correct Answer
Option A is correct because the new owner-paid cost reduces NOI by $200 × 12 = $2,400, to $33,600. Dividing that income by the price gives the rate at which the price is still supported: $33,600 ÷ $480,000 = 7.00%.
Why the Other Options Are Wrong
Option B: 7.46%
Option B, 7.46%, deducts a single month of the cost: ($36,000 − $200) ÷ $480,000. The cost recurs monthly and NOI is annual, so $2,400 comes off and $33,600 ÷ $480,000 = 7.00%.
Option C: 7.50%
Option C, 7.50%, ignores the new cost: $36,000 ÷ $480,000. That matches the market rate but uses income the property will no longer produce; the revised NOI gives $33,600 ÷ $480,000 = 7.00%.
Option D: 8.00%
Option D, 8.00%, adds the cost to NOI: ($36,000 + $2,400) ÷ $480,000. A new expense lowers NOI, so the correct calculation is ($36,000 − $2,400) ÷ $480,000 = 7.00%.
Income Over Price Gives Rate
Cover the unknown in the income, rate and value triangle. With price and income known, income over price leaves the rate.
How to use: Use the triangle after first putting every income change on an annual basis.
Exam Tip
Convert monthly changes to annual figures before touching the rate. Then decide whether each listed figure, such as debt service, belongs above or below NOI.
Common Mistakes to Avoid
- -Deducting a monthly cost from annual NOI without annualizing it
- -Reporting the market rate instead of the rate implied by the revised NOI
- -Subtracting debt service from income before calculating an overall rate
Concept Deep Dive
Analysis
The unknown here is the rate, not the value. The candidate first restates NOI for the annualized new cost, then divides by the fixed contract price. Comparing the result with the market rate shows whether the price still holds up. Debt service and the market rate itself are not inputs to the calculation.
Background Knowledge
The capitalization relationship links income, rate and value, and any one can be found from the other two. Rearranged as rate equals income divided by value, it shows the rate a given price implies. A required rate below the market rate means the price is above the value the market rate would indicate.
Real-World Application
A buyer in contract on a small rental property discovers a new recurring cost shortly before closing. The appraiser shows the rate the price now implies, and at the 7.5% market rate the same income would indicate about $448,000, so the buyer can weigh renegotiating.
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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