A property has annual NOI of $82,800. Debt funds 70% of value at an annual mortgage constant of 8%, and the remaining equity has a current annual dividend rate of 12%. What value is indicated using an overall rate from the band of investment, rounded to the nearest dollar?
Correct Answer
C) $900,000
0.7×0.08+(1−0.7)×0.12=0.092; 82800÷0.092=900000. Common errors: capitalizing at the mortgage constant alone gives $1,035,000; capitalizing at an unweighted average of the two rates gives $828,000; swapping the debt and equity weights in the band gives $766,667.
Why This Is the Correct Answer
Option C is correct because Ro = 0.70 × 0.08 + 0.30 × 0.12 = 0.056 + 0.036 = 0.092, and $82,800 ÷ 0.092 = $900,000. The weights match the 70% debt and 30% equity shares of value.
Why the Other Options Are Wrong
Option A: $766,667
Option A, $766,667, is wrong because it swaps the debt and equity weights (0.30 × 0.08 + 0.70 × 0.12 = 0.108; $82,800 ÷ 0.108 = $766,667). Debt is 70% of value, so the correct Ro is 0.092 and value is $900,000.
Option B: $828,000
Option B, $828,000, is wrong because it uses a simple unweighted average of the two rates ((0.08 + 0.12) ÷ 2 = 0.10; $82,800 ÷ 0.10 = $828,000). The band must weight each rate by its share of value, giving 0.092 and $900,000.
Option D: $1,035,000
Option D, $1,035,000, is wrong because it capitalizes at the mortgage constant alone ($82,800 ÷ 0.08 = $1,035,000). The equity portion must also be included, giving Ro of 0.092 and value of $900,000.
Weight each rate by share
Loan share times loan rate plus equity share times equity rate; the shares must add up to 100%.
How to use: Use this to set up any mortgage-equity band before dividing NOI by the result.
Exam Tip
Check that the larger weight goes with the debt when the loan-to-value ratio is above 50%.
Common Mistakes to Avoid
- -Swapping the debt and equity weights
- -Averaging the two rates without weighting
- -Using the mortgage constant alone as the overall rate
Concept Deep Dive
Analysis
This question tests the mortgage-equity band of investment. The overall rate is a weighted average: the loan share times the mortgage constant plus the equity share times the equity dividend rate. Once Ro is found, NOI is divided by it to produce value.
Background Knowledge
The band of investment builds an overall rate from the claims of the lender and equity investor on NOI. The mortgage constant is annual debt service divided by the loan amount, and the equity dividend rate is pre-tax cash flow divided by equity. Each is weighted by its proportion of total value.
Real-World Application
An appraiser lacking enough sales to extract an overall rate gathers current lender terms and typical equity dividend rates. Using a 70% loan-to-value ratio, the appraiser builds a weighted overall rate and applies it to the subject's NOI.
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The subject property's annual EGI is $450,000. The operating expense ratio, excluding debt service, is 32% of EGI. Using a 7.5% overall capitalization rate, what is the indicated value?
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