An appraiser develops a band of investment rates using mortgage-equity analysis for a proposed 100-unit apartment project. She estimates a mortgage constant of 6.25% on a 75% loan-to-value mortgage at 5.5% interest amortized over 30 years, and an equity dividend rate of 9.0% based on investor surveys and comparable equity investments. Using the band-of-investment method, what is the overall capitalization rate (Ro) indicated for the property?
Correct Answer
A) 6.94%
Band-of-investment Ro = (Mortgage Weight × Mortgage Constant) + (Equity Weight × Equity Dividend Rate). Mortgage weight = 75% = 0.75; Equity weight = 25% = 0.25. Ro = (0.75 × 6.25%) + (0.25 × 9.0%) = 4.6875% + 2.25% = 6.9375%, which rounds to 6.94%. This calculation follows the standard band-of-investment formula in the Income Approach (as outlined in the Appraisal Institute's *The Appraisal of Real Estate*, 14th ed., Ch. 17) and is required under USPAP Standards Rule 1-5 for developing supportable capitalization rates when market extraction is limited.
Why This Is the Correct Answer
Multiplying 0.75 by 6.25 percent gives 4.6875 percent, multiplying 0.25 by 9.0 percent gives 2.25 percent, and the sum is 6.9375 percent, which rounds to 6.94 percent. The weights sum to one, which is a quick structural check that the calculation was set up correctly. Because the mortgage constant exceeds the interest rate by the amortization component, using the interest rate instead would understate the result. The band of investment is most useful when comparable sales are too few to extract a rate directly.
Why the Other Options Are Wrong
Option B: 7.44%
7.44 percent is half a point above the correct figure and does not follow from the stated weights and rates. It may arise from mis-weighting the components or from blending in the interest rate partially. Recomputing with the weights written out catches it immediately.
Option C: 7.94%
7.94 percent is a full point high and appears to come from weighting the equity component too heavily, for instance by reversing the weights or by using a 50-50 split. Reversing the weights would give 0.25 times 6.25 plus 0.75 times 9.0, or 8.31 percent, which is close enough to make this family of errors plausible. Confirming which component carries 75 percent prevents it.
Option D: 8.44%
8.44 percent lies well above the range the inputs support and is closer to what a heavily equity-weighted structure would produce. With three quarters of the capital costing 6.25 percent, the blended rate must sit much nearer that figure than the 9.0 percent equity rate. A weighted average always falls between its components and closer to the heavier one, which rules this out on inspection.
Constant, Not Interest
The mortgage side of the band uses the constant, which includes principal repayment, never the bare interest rate. If a problem hands you both, the interest rate is bait. Weight each component by its share, and check that the shares sum to one.
How to use: Write the two products on separate lines before adding, labeling each with its weight. Then verify the result falls between the two rates and nearer the more heavily weighted one.
Exam Tip
A weighted average always lies between its inputs. Any answer outside the 6.25 to 9.0 range here can be eliminated without computing anything.
Common Mistakes to Avoid
- -Substituting the mortgage interest rate for the mortgage constant
- -Reversing the debt and equity weights
- -Treating the resulting overall rate as a yield rate for multi-year discounting
Concept Deep Dive
Analysis
The band of investment builds an overall capitalization rate from the weighted return requirements of the two capital sources funding a typical purchase. The mortgage component contributes the annual mortgage constant, which is total annual debt service divided by the original loan amount and therefore already embeds both interest and amortization. The equity component contributes the equity dividend rate, the before-tax cash flow divided by the equity investment. Each is weighted by its share of value, so the formula is Ro equals the loan-to-value ratio times the mortgage constant, plus the equity-to-value ratio times the equity dividend rate. Here the weights are 0.75 and 0.25, and the rates are 6.25 percent and 9.0 percent. Notice the trap embedded in the fact pattern: the stem supplies a 5.5 percent interest rate alongside the 6.25 percent constant, and only the constant belongs in the calculation. The interest rate is given so that a candidate who does not know the difference will use it.
Background Knowledge
You need the band of investment formula and the definitions of mortgage constant, loan-to-value ratio, equity-to-value ratio, and equity dividend rate. You should also know why the mortgage constant exceeds the interest rate on an amortizing loan, and the alternative methods of developing an overall rate including extraction and the debt coverage ratio formula.
Real-World Application
An appraiser valuing a proposed apartment project with too few comparable sales interviews three lenders for current terms, computes the mortgage constant from the quoted rate and amortization, surveys investors for equity dividend expectations, builds the rate from the weighted components, and discloses each source in the report.
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Previous Question
An appraiser is estimating a market capitalization rate for a Class B office building in a stable but maturing submarket. She analyzes five recent, comparable sales of similar properties with fee-simple ownership and typical lease structures. The indicated overall capitalization rates (Ro) range from 6.2% to 7.8%. To derive a credible Ro, the appraiser adjusts each comparable’s Ro for differences in lease-up risk, tenant credit quality, and near-term lease rollover exposure—then selects a rate within the adjusted range. Which USPAP Standard explicitly governs the selection and justification of this final Ro?
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A small commercial building has potential gross income of $120,000 annually. The appraiser analyzes three comparable properties, which have stabilized vacancy and collection losses of 8%, 9%, and 7.5%. The subject property's owner provides records showing a 5% vacancy rate over the past three years due to long-term tenants. What is the appropriate stabilized vacancy and collection loss rate to use in estimating effective gross income?