Debt funds 70% of value at an annual mortgage constant of 7.2%, and the remaining equity has a current annual dividend rate of 10.5%. What overall rate does the band of investment indicate?
Correct Answer
B) 8.190%
0.7×0.072+(1−0.7)×0.105=0.0819; percent=8.19. Common errors: averaging the two rates instead of weighting them gives 8.850%; swapping the debt and equity weights gives 9.510%; leaving out the equity component gives 5.040%.
Why This Is the Correct Answer
Option B is correct because Ro = M × Rm + (1 − M) × Re = 0.70 × 0.072 + 0.30 × 0.105 = 0.0504 + 0.0315 = 0.0819, or 8.190%. Each component rate is weighted by its share of value.
Why the Other Options Are Wrong
Option A: 5.040%
Option A, 5.040%, is wrong because it leaves out the equity component: 0.70 × 0.072 = 0.0504, or 5.040%. Adding the equity part, 0.30 × 0.105 = 0.0315, gives the correct 8.190%.
Option C: 8.850%
Option C, 8.850%, is wrong because it takes a simple average of the two rates instead of weighting them: (0.072 + 0.105) ÷ 2 = 0.0885, or 8.850%. Weighting by the 70% loan and 30% equity shares gives 8.190%.
Option D: 9.510%
Option D, 9.510%, is wrong because it swaps the debt and equity weights: 0.30 × 0.072 + 0.70 × 0.105 = 0.0951, or 9.510%. The loan carries the 70% weight, so the correct result is 8.190%.
Weight Each Band
Multiply each rate by its slice of value, then add the slices; the slices must total 100%.
How to use: Use this step-by-step weighting whenever a problem gives a loan ratio, a mortgage constant and an equity dividend rate.
Exam Tip
Check that the weights add to 1.00 and that the larger weight goes with the debt when the loan ratio is above 50%. The answer must fall between the two component rates.
Common Mistakes to Avoid
- -Averaging the two rates without weighting
- -Assigning the loan ratio to the equity rate
- -Using the loan interest rate instead of the mortgage constant
Concept Deep Dive
Analysis
This question tests the mortgage-equity band of investment for an overall rate. Each rate is weighted by its share of value: the mortgage constant by the loan ratio and the equity dividend rate by the equity ratio. The stated rates are cash-flow rates, which is what the formula requires.
Background Knowledge
The band of investment computes an overall rate as a weighted average of the claims on NOI by lenders and equity investors. The mortgage constant reflects annual debt service per dollar of loan, including principal and interest, and the equity dividend rate reflects the cash return to equity. Using a loan coupon rate or total equity yield instead of these cash-flow rates would not fit the formula.
Real-World Application
An appraiser surveys local lenders for typical loan-to-value ratios and mortgage constants and gathers investor equity dividend rates from comparable sales. A band-of-investment overall rate is then calculated as a cross-check on rates extracted directly from sales.
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?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
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?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Land or Site Valuation
4.5% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Previous Question
Potential base rent excludes other income. Loss is applied to base rent only; other income is already stated at effective collectible amounts. Which construction gives total EGI?
Next Question
Annual potential rent is $95,000. Apply 7% combined loss to rent only, then add $3,400 of other collectible real-estate income already stated after its losses. What EGI results?