A lender will fund 70% of value at an annual mortgage constant of 8%. The remaining equity requires an annual equity dividend rate of 12%. Annual NOI is $92,000. Using the band of investment to develop the overall rate, what value is indicated, rounded to the nearest dollar?
Correct Answer
C) $1,000,000
Ro=0.7×0.08+0.3×0.12=0.092; 92000÷0.092=1000000. Common errors: capitalizing at the mortgage constant alone gives $1,150,000; capitalizing at an unweighted average of the two rates gives $920,000; swapping the debt and equity weights in the band gives $851,852.
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. Capitalizing NOI at that rate gives $92,000 ÷ 0.092 = $1,000,000. The overall rate is a weighted average of the claims of debt and equity on NOI.
Why the Other Options Are Wrong
Option A: $851,852
Option A, $851,852, comes from swapping the debt and equity weights: 0.30 × 0.08 + 0.70 × 0.12 = 0.108, and $92,000 ÷ 0.108 = $851,852. The correct weights give 0.092 and $1,000,000.
Option B: $920,000
Option B, $920,000, comes from using an unweighted average of the two rates: (0.08 + 0.12) ÷ 2 = 0.10, and $92,000 ÷ 0.10 = $920,000. The rates must be weighted 70/30, giving $92,000 ÷ 0.092 = $1,000,000.
Option D: $1,150,000
Option D, $1,150,000, comes from capitalizing at the mortgage constant alone: $92,000 ÷ 0.08 = $1,150,000. The equity portion must be included, giving Ro = 0.092 and $1,000,000.
Weight each rate by share
Multiply the mortgage constant by the loan share and the equity rate by the equity share, then add. The shares must total 100%. Use this to build Ro from financing data, and check that the loan-to-value ratio multiplies the mortgage constant, whichever share is larger.
How to use: Use this to build Ro from financing data and to check that the larger weight goes with the debt.
Exam Tip
Confirm that the loan ratio multiplies the mortgage constant and the equity ratio multiplies the equity dividend rate; swapping them is a common trap.
Common Mistakes to Avoid
- -Averaging the mortgage constant and equity rate without weighting
- -Applying the loan ratio to the equity rate and the equity ratio to the mortgage constant
- -Using the interest rate instead of the mortgage constant for the debt component
Concept Deep Dive
Analysis
This question tests the band of investment method for building an overall capitalization rate from mortgage and equity components. Each component rate is weighted by its share of value, and the weighted rates are added. The resulting overall rate is then used to capitalize NOI.
Background Knowledge
The band of investment treats the overall rate as a weighted average of the mortgage constant and the equity dividend rate, with weights equal to the loan-to-value ratio and the equity ratio. The mortgage constant is the annual debt service divided by the loan amount. The method reflects how investors and lenders each claim a share of NOI.
Real-World Application
An appraiser lacks enough comparable sales to extract an overall rate for a small industrial property. Using current lender terms and investor equity return expectations, the appraiser builds a band of investment rate. That rate is compared with any available market rates before capitalizing NOI.
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For a stabilized market-value income model, how should vacancy and collection loss be estimated?