An appraiser is developing an overall rate for a small residential rental property by the band of investment. Lenders for similar properties have lengthened typical amortization from 25 years to 30 years, with no change in the interest rate or loan-to-value ratio. The equity dividend rate and the subject's NOI are unchanged. How does the change in loan terms affect the income approach?
Correct Answer
B) Mortgage constant falls, overall rate falls, and indicated value rises
The mortgage constant depends on the term as well as the interest rate. A longer amortization spreads repayment over more payments, so annual debt service per dollar of loan falls. With the same weights and equity rate, the band gives a lower overall rate, and the same NOI capitalized at a lower rate gives a higher value. Candidates who confuse the constant with the interest rate see no change, and those who think of total interest paid over the loan see the constant rising.
Why This Is the Correct Answer
Option B is correct because spreading repayment over 30 years lowers each year's payment per dollar of loan, so the mortgage constant falls. With the same weights and equity dividend rate, the weighted band rate falls too. The same NOI divided by a lower overall rate gives a higher indicated value.
Why the Other Options Are Wrong
Option A: Mortgage constant rises, overall rate rises, and indicated value falls
Option A says the mortgage constant rises because a longer loan costs more total interest. Total interest over the loan is a different measure: the constant is annual debt service over the loan amount, and it falls with a longer term.
Option C: Mortgage constant holds, overall rate holds, and indicated value holds
Option C says the mortgage constant holds, as though it followed the interest rate alone. The constant also depends on the term, so a change from 25 to 30 years moves it, and the overall rate and value move with it.
Option D: Mortgage constant falls, overall rate rises, and indicated value falls
Option D has the mortgage constant falling but the overall rate rising. In the band, the overall rate is a weighted sum that includes the constant, so with equity unchanged a lower constant gives a lower overall rate and a higher value.
Longer loan, lighter payment
A longer amortization means a lighter annual payment, which means a lower constant. Lower constant, lower band rate, higher value.
How to use: Use this when a question changes the loan term while holding the interest rate steady.
Exam Tip
Keep the note rate and the mortgage constant apart. The constant moves when the term changes, even if the interest rate does not.
Common Mistakes to Avoid
- -Treating the mortgage constant as if it equaled the interest rate
- -Confusing total interest over the loan with the annual constant
- -Reversing the link between the overall rate and value
Concept Deep Dive
Analysis
This tests the chain from loan terms to value. Term changes the constant, the constant is one weighted component of the band, and the band rate divides into NOI. Each link has its own direction: the constant falls, so the overall rate falls, so value rises. The interest rate holding steady is the trap, because the constant includes repayment of principal as well as interest.
Background Knowledge
The mortgage constant is the ratio of annual debt service to the loan amount, and it depends on the interest rate, payment frequency and term. In the band of investment, the overall rate is the loan-to-value ratio times the constant plus the equity share times the equity dividend rate. Value moves inversely with the overall rate when NOI holds.
Real-World Application
A lender program for small rental properties extends amortization by five years at the same note rate. An appraiser updating a band of investment recalculates the constant from the new payment and finds the indicated overall rate has eased.
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?
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Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
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Previous Question
The subject property has annual income before property tax of $80,000. Annual property tax is 0.5% of value. The capitalization rate, excluding the tax component, is 7.5%. What value is indicated by direct capitalization?
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