An appraiser verifying the sale of a 20-unit apartment building finds a price of $1,000,000, financed with a 75% loan at a 6.5% interest rate and a 7.2% annual mortgage constant. The buyer paid the balance in cash. Projected first-year NOI is $78,000. What is the buyer's first-year equity dividend rate?
Correct Answer
C) 9.60%
The loan is $750,000, so debt service is $750,000 × 0.072 = $54,000 and cash flow to equity is $78,000 − $54,000 = $24,000. Equity is $250,000, and $24,000 ÷ $250,000 = 9.60%. Using the 6.5% interest rate for debt service gives 11.70% because it leaves out principal. NOI ÷ price gives the 7.80% overall rate, and dividing cash flow by the loan gives 3.20%.
Why This Is the Correct Answer
Option C is correct because debt service is $750,000 × 0.072 = $54,000, leaving $24,000 of cash flow to equity. Dividing by equity of $250,000 gives 9.60%.
Why the Other Options Are Wrong
Option A: 3.20%
Option A, 3.20%, divides cash flow by the loan: $24,000 ÷ $750,000 = 3.20%. The denominator should be the $250,000 of equity, which gives 9.60%.
Option B: 7.80%
Option B, 7.80%, is NOI over price: $78,000 ÷ $1,000,000 = 7.80%. That is the overall rate for the whole property; equity earns $24,000 ÷ $250,000 = 9.60%.
Option D: 11.70%
Option D, 11.70%, computes debt service at the interest rate: $750,000 × 0.065 = $48,750, leaving $29,250, and $29,250 ÷ $250,000 = 11.70%. The constant captures the full loan payment, so the correct cash flow is $24,000 and the rate is 9.60%.
Constant pays, coupon doesn't
Debt service comes from the constant because it includes principal. The interest rate alone understates the payment on an amortizing loan.
How to use: Use this phrase when a problem gives both an interest rate and a mortgage constant.
Exam Tip
If both an interest rate and a constant appear, ask which one the calculation needs. Debt service on an amortizing loan uses the constant.
Common Mistakes to Avoid
- -Computing debt service from the interest rate on an amortizing loan
- -Dividing equity cash flow by the price or the loan
- -Reporting NOI over price as the equity return
Concept Deep Dive
Analysis
Neither the cash flow nor the equity is given, so both must be built. The key judgment is that debt service comes from the mortgage constant, which covers principal and interest, not from the interest rate. Cash flow after debt service then goes over the cash equity.
Background Knowledge
The equity dividend rate, also called the cash-on-cash or equity capitalization rate, relates one year of pre-tax cash flow to the equity investment. The mortgage constant relates annual debt service to loan principal, which is why it differs from the interest rate on an amortizing loan.
Real-World Application
An appraiser verifying the financing on a sale needs the buyer's first-year cash return for a band-of-investment check. The loan summary shows both the note rate and the annual payment, and the appraiser uses the annual payment to find cash flow to equity.
More Income Approach Questions
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Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
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For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
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