A lender asks an appraiser to review a 16-unit apartment building with annual PGI of $180,000, a stabilized vacancy and credit loss of 10%, and operating expenses of $54,000. The current mortgage payments of $60,000 per year will end when the existing loan is paid off at closing. The new loan requires a debt coverage ratio of 1.25 at an annual mortgage constant of 8%. What is the maximum loan amount?
Correct Answer
A) $1,080,000
NOI is $162,000 − $54,000 = $108,000, so the most debt service allowed is $108,000 ÷ 1.25 = $86,400, and $86,400 ÷ 0.08 = $1,080,000. Leaving out the vacancy loss gives $1,260,000. Ignoring the coverage requirement gives $1,350,000. Multiplying by 1.25 instead of dividing gives $1,687,500. The current mortgage payments end at closing and do not enter the calculation.
Why This Is the Correct Answer
Option A is correct because NOI of $108,000 divided by 1.25 allows $86,400 of debt service. At an 8% constant, $86,400 ÷ 0.08 = $1,080,000 of principal.
Why the Other Options Are Wrong
Option B: $1,260,000
Option B, $1,260,000, starts from income without the vacancy loss: $126,000 ÷ 1.25 ÷ 0.08 = $1,260,000. NOI after the 10% loss is $108,000, which supports $1,080,000.
Option C: $1,350,000
Option C, $1,350,000, divides NOI directly by the constant: $108,000 ÷ 0.08 = $1,350,000. That is a coverage ratio of 1.00; at 1.25 the loan is $1,080,000.
Option D: $1,687,500
Option D, $1,687,500, multiplies by the coverage ratio: $108,000 × 1.25 ÷ 0.08 = $1,687,500. Coverage requires NOI to exceed debt service, so the division gives $86,400 and $1,080,000.
Divide by coverage, divide by constant
NOI ÷ coverage gives the allowed payment. Payment ÷ constant gives the loan.
How to use: Use this pair of divisions when a lender's coverage requirement and a constant are given.
Exam Tip
Confirm the result by working forward: $1,080,000 × 0.08 = $86,400, and $108,000 ÷ $86,400 = 1.25.
Common Mistakes to Avoid
- -Multiplying NOI by the coverage ratio
- -Capitalizing NOI at the mortgage constant as though it were a value calculation
- -Using potential income instead of NOI
Concept Deep Dive
Analysis
A coverage ratio limits debt service to a fraction of NOI, and the mortgage constant converts that allowed debt service into principal. The path runs from PGI to NOI, then to debt service, then to the loan. The direction of the coverage step matters, because a ratio above 1 must shrink the available payment. The current mortgage payments end at closing, so they do not limit the new loan.
Background Knowledge
The debt coverage ratio compares NOI with annual debt service, and the mortgage constant compares annual debt service with loan principal. Together with the loan-to-value ratio they form the debt coverage formula, RO = DCR × RM × M, for an overall rate.
Real-World Application
An appraiser reviewing a commercial loan request sees that the proposed principal would break the lender's coverage test. Recalculating from stabilized NOI shows the principal the income can carry.
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
An appraiser is developing an overall capitalization rate for an apartment building. Typical financing for similar properties is a 75% loan-to-value loan at 6.0% interest with a 7.8% annual mortgage constant. Equity investors expect a 10% first-year cash-on-cash return and a 13% equity yield over the holding period. What overall capitalization rate is indicated by the band of investment?
Next Question
An appraiser is verifying the sale of a 12-unit apartment building. The broker will not release dollar income figures but reports that the price was 6.0 times EGI and 5.4 times PGI, and that the buyer's anticipated operating expenses were 55% of EGI. What overall capitalization rate does the sale indicate?