An appraiser is developing an overall rate from market financing. Debt funds 75% of value at an annual mortgage constant of 6.5%, and the remaining equity has a current annual dividend rate of 12%. What overall rate does the band of investment indicate?
Correct Answer
B) 7.875%
0.75×0.065+(1−0.75)×0.12=0.07875; percent=7.875. Common errors: averaging the two rates instead of weighting them gives 9.250%; swapping the debt and equity weights gives 10.625%; leaving out the equity component gives 4.875%.
Why This Is the Correct Answer
Option B is correct because 0.75 × 0.065 = 0.04875 and 0.25 × 0.12 = 0.03, which sum to 0.07875, or 7.875%. The overall rate is a weighted average of the component claims on NOI, as Ro = M × Rm + (1 − M) × Re shows.
Why the Other Options Are Wrong
Option A: 4.875%
Option A, 4.875%, leaves out the equity component: 0.75 × 0.065 = 0.04875. The equity share of 25% at 12% adds 0.03, so the overall rate is 7.875%.
Option C: 9.250%
Option C, 9.250%, averages the two rates without weighting them: (6.5% + 12%) ÷ 2 = 9.25%. Debt funds 75% of value, so the rates must be weighted, 0.75 × 0.065 + 0.25 × 0.12 = 7.875%.
Option D: 10.625%
Option D, 10.625%, swaps the debt and equity weights: 0.25 × 0.065 + 0.75 × 0.12 = 0.10625. Debt is the 75% component, so the correct calculation is 0.75 × 0.065 + 0.25 × 0.12 = 7.875%.
Weight Each Slice
Multiply each slice of the capital stack by its own rate, then add the slices. The bigger slice carries more weight.
How to use: Use this when building an overall rate from debt and equity components.
Exam Tip
Confirm that the loan-to-value ratio is paired with the mortgage constant and the equity ratio with the equity dividend rate before multiplying.
Common Mistakes to Avoid
- -Averaging the debt and equity rates without weighting
- -Swapping the debt and equity weights
- -Using the loan interest rate instead of the mortgage constant
Concept Deep Dive
Analysis
This question tests the band-of-investment formula for an overall rate. Each component's rate is weighted by its share of value: debt at 75% times the mortgage constant plus equity at 25% times the equity dividend rate. Distractors average the rates, swap the weights or drop the equity component.
Background Knowledge
The band-of-investment technique builds an overall capitalization rate from the financial components of a typical purchase. The mortgage constant is weighted by the loan-to-value ratio and the equity dividend rate by the equity ratio, and the two products are summed.
Real-World Application
An appraiser lacking enough comparable sales to extract an overall rate surveys lenders and investors for typical loan terms and equity return expectations. The appraiser weights the mortgage constant and equity dividend rate by their shares of value to derive the overall rate.
More Income Approach Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
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).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
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.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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
Related Tools
Previous Question
The subject property is a commercial site under a ground lease with five level annual payments of $60,000 remaining. Each payment is due at the beginning of the lease year, and the next one is due today. The discount rate is 8%. What is the present value of the remaining rent payments?
Next Question
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?