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?
Correct Answer
C) 8.35%
An overall capitalization rate uses the cash-flow rates: 0.75 × 7.8% + 0.25 × 10% = 5.85% + 2.50% = 8.35%. Using the note rate and the equity yield gives 7.75%, which is an overall yield rate for discounting rather than a rate for capitalizing one year's NOI. Using the note rate with the dividend rate gives 7.00%, and the constant with the equity yield gives 9.10%; each mixes a cash-flow rate with a yield-type rate.
Why This Is the Correct Answer
Option C is correct because the overall capitalization rate weights the mortgage constant and the equity dividend rate: 0.75 × 7.8% + 0.25 × 10% = 5.85% + 2.50% = 8.35%. The constant reflects annual debt service relative to the loan, and the dividend rate reflects one year's cash flow relative to equity. Together they describe how one year's NOI is shared between lender and equity investor.
Why the Other Options Are Wrong
Option A: 7.00%
Option A, 7.00%, uses the note rate for debt: 0.75 × 6.0% + 0.25 × 10% = 7.00%. The note rate leaves out the principal repayment included in annual debt service, so the debt band should be 0.75 × 7.8% = 5.85%, which leads to 8.35%.
Option B: 7.75%
Option B, 7.75%, uses the note rate and equity yield: 0.75 × 6.0% + 0.25 × 13% = 7.75%. That is an overall yield rate, suited to discounting a stream of benefits, not a rate for capitalizing one year's NOI, which is 8.35% here.
Option D: 9.10%
Option D, 9.10%, pairs the constant with the equity yield: 0.75 × 7.8% + 0.25 × 13% = 9.10%. The 13% is a holding-period return that includes expected sale proceeds, so the equity band for a one-year capitalization rate should be 0.25 × 10% = 2.50%, giving 8.35%.
Cap with cash, yield with yield
A cap rate band uses the two cash-flow rates: constant and dividend. A yield rate band uses the two return rates: note rate and equity yield.
How to use: Use this when a band of investment comes with more rates than it needs.
Exam Tip
Before computing, ask whether the result will capitalize one year's income or discount a multi-year stream. That answer tells you which pair of rates to use.
Common Mistakes to Avoid
- -Using the note rate as the debt band in an overall capitalization rate
- -Treating a projected equity yield as the equity dividend rate
- -Mixing one cash-flow rate with one yield-type rate in the same band
Concept Deep Dive
Analysis
The arithmetic is simple; the test is choosing the right two of four rates. A rate applied to one year's NOI must be built from one-year cash-flow rates, which are the mortgage constant and the equity dividend rate. The note rate and equity yield rate belong to a different band, the one that builds an overall yield rate for discounting.
Background Knowledge
A band of investment weights the rates attributable to the components of a capital investment. Used for an overall capitalization rate, it combines the mortgage constant with the equity capitalization rate, also called the equity dividend or cash-on-cash rate. Used for an overall yield rate, it combines the loan interest rate with the equity yield rate.
Real-World Application
An appraiser surveying lenders and investors receives quotes showing note rates, constants, first-year cash-on-cash returns and projected equity IRRs. To support a direct-capitalization rate, the appraiser weights the constant and the cash-on-cash return, and keeps the note rate and IRR for any discounted cash flow 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?
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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 has stabilized annual real property NOI of $148,000 after operating expenses and property taxes. The overall capitalization rate is 8%. What value is indicated by direct capitalization, to the nearest dollar?
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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?