A lender requires a 1.25 debt coverage ratio on a loan with a 7.5% mortgage constant covering 70% of value. The implied cap rate by the DCR technique is:
Correct Answer
B) 6.6% before the equity share
Why this is correct: The governing concept is the Debt Coverage Ratio (DCR) technique to estimate a capitalization rate: Cap Rate = DCR × Mortgage Constant × Loan-to-Value Ratio. Here, DCR = 1.25, Mortgage Constant = 0.075, LTV = 0.70. Calculation: 1.25 × 0.075 × 0.70 = 0.065625, or 6.6% rounded. This reflects the minimum cap rate needed to satisfy the lender's requirements. Why the other choices are wrong: "7.1% from the lender's side" is incorrect because it does not match the calculation. "8.2% after rounding up" is incorrect as it's not the result of the formula. "9.4% including the equity residual" is incorrect because the DCR technique yields the overall cap rate before considering equity yield. Exam tip: The DCR-derived cap rate is a useful benchmark when sales data is scarce, reflecting lender underwriting standards.
Why This Is the Correct Answer
Multiplying the three inputs gives 1.25 times 0.075 times 0.70, which equals 0.065625, or approximately 6.6 percent. Each factor is essential: the coverage ratio scales income above debt service, the mortgage constant converts the loan balance into an annual payment, and the loan ratio scales the loan back to property value. Choice B is the only figure that results from applying all three, and its qualifying language about the equity share correctly signals that this rate is derived from lender requirements rather than from an equity return analysis.
Why the Other Options Are Wrong
Option A: 7.1% from the lender's side
This figure does not come out of the debt coverage formula at all, and it sits close enough to the 7.5 percent mortgage constant to suggest the error it represents, which is treating the lender's payment rate on the loan as though it were the property's overall rate. The mortgage constant applies to the loan balance, not to total value, and it takes no account of coverage or leverage. A rate borrowed straight from the debt terms cannot describe the whole property.
Option C: 8.2% after rounding up
This is in the range a band of investment produces when the mortgage component is weighted at 70 percent and an equity dividend rate of about 10 percent is assumed for the remaining 30 percent. The stem supplies no equity dividend rate, so any figure requiring one is being imported rather than derived. Band of investment and the debt coverage technique are different routes to a rate, and mixing them mid-problem produces an unsupported number.
Option D: 9.4% including the equity residual
This is 1.25 times 0.075, or 9.375 percent, which is the rate you get by dropping the loan-to-value factor and implicitly financing the property at 100 percent. Since only 70 percent of value carries debt, ignoring the loan ratio inflates the required income sharply. Forgetting the third factor is the most common arithmetic slip in this formula.
Coverage Times Constant Times Chunk
Three C's multiplied together. Coverage is the cushion the lender wants, constant is the payment rate on the loan, and chunk is the share of value the loan covers. Miss a C and the rate is wrong.
How to use: Write all three factors down before multiplying, and check that the loan ratio is present, since dropping it is the standard trap. If the stem gives an equity dividend rate instead of a coverage ratio, you are in a band of investment problem.
Exam Tip
Sanity check the size of your answer. The product of a coverage ratio near 1.2 and a constant near 8 percent at 70 percent leverage almost always lands in the 6 to 7 percent range, so a 9 percent answer signals a dropped factor.
Common Mistakes to Avoid
- -Omitting the loan-to-value factor and reporting the two-factor product
- -Confusing the mortgage constant with the mortgage interest rate
- -Blending band of investment inputs into the debt coverage formula
Concept Deep Dive
Analysis
The debt coverage technique, sometimes called the underwriter's method, derives an overall capitalization rate from the three numbers a lender actually underwrites: the debt coverage ratio, the annual mortgage constant, and the loan-to-value ratio. The formula multiplies them, Ro equals DCR times the mortgage constant times the loan ratio, and it follows directly from the definitions. Net operating income equals the debt coverage ratio times annual debt service, annual debt service equals the mortgage constant times the loan amount, and the loan amount equals the loan-to-value ratio times value, so dividing through by value leaves the product of the three. The rate this produces reflects the minimum income yield lenders are demanding on that class of property, which makes it a useful test of a rate extracted from thin sales data, though it is a lender's underwriting benchmark rather than a substitute for market-extracted evidence.
Background Knowledge
You need the definitions of debt coverage ratio, annual mortgage constant, and loan-to-value ratio, and the ability to derive Ro as their product rather than memorizing it blindly. You should also know the band of investment technique and how it differs, since it weights mortgage and equity components and requires an equity dividend rate, and you should understand that both are support techniques secondary to rates extracted from comparable sales.
Real-World Application
An appraiser valuing a small industrial building in a market with only two usable sales calls three lenders, learns they underwrite at a 1.25 coverage ratio and 70 percent loan to value with constants near 7.5 percent, computes a 6.6 percent benchmark, and uses it to test the 6.4 percent rate extracted from the sales.
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