Annual NOI for the subject is $85,800. Typical financing covers 70% of value at an annual mortgage constant of 6%, and the remaining equity has a current annual dividend rate of 12%. Using the band of investment to develop the overall rate, what value is indicated, rounded to the nearest dollar?
Correct Answer
C) $1,100,000
0.7×0.06+(1−0.7)×0.12=0.078; 85800÷0.078=1100000. Common errors: capitalizing at the mortgage constant alone gives $1,430,000; capitalizing at an unweighted average of the two rates gives $953,333; swapping the debt and equity weights in the band gives $841,176.
Why This Is the Correct Answer
Option C is correct because Ro = 0.70 × 0.06 + 0.30 × 0.12 = 0.042 + 0.036 = 0.078. Dividing NOI by that rate gives $85,800 ÷ 0.078 = $1,100,000.
Why the Other Options Are Wrong
Option A: $841,176
Option A, $841,176, comes from swapping the debt and equity weights: 0.30 × 0.06 + 0.70 × 0.12 = 0.102, and $85,800 ÷ 0.102 = $841,176. Debt funds 70%, so the correct rate is 0.078 and the value is $1,100,000.
Option B: $953,333
Option B, $953,333, comes from an unweighted average of the two rates: (0.06 + 0.12) ÷ 2 = 0.09, and $85,800 ÷ 0.09 = $953,333. The band weights each rate by its share of value, giving 0.078 and $1,100,000.
Option D: $1,430,000
Option D, $1,430,000, comes from capitalizing at the mortgage constant alone: $85,800 ÷ 0.06 = $1,430,000. The equity component must be included, giving Ro of 0.078 and a value of $1,100,000.
Weight each rate by its share
Multiply the mortgage constant by the loan share and the equity rate by the equity share, then add. Divide NOI by that blended rate.
How to use: Use this for any band of investment problem that gives loan and equity shares and rates.
Exam Tip
Match each rate to its own weight: the loan ratio goes with the mortgage constant and the equity ratio goes with the equity dividend rate.
Common Mistakes to Avoid
- -Swapping the debt and equity weights
- -Averaging the two rates without weighting
- -Using the loan interest rate instead of the mortgage constant
Concept Deep Dive
Analysis
This question tests the mortgage-equity band of investment and its use in direct capitalization. The overall rate is the loan ratio times the mortgage constant plus the equity ratio times the equity dividend rate. That rate is then divided into NOI to indicate value.
Background Knowledge
The band of investment computes an overall rate as a weighted average of the claims of debt and equity on NOI. The mortgage component uses the annual mortgage constant, and the equity component uses the equity dividend rate. The weights are the loan-to-value ratio and the equity ratio.
Real-World Application
An appraiser learns that typical financing for a small industrial building is 70% loan-to-value at a 6% annual constant, and investors expect a 12% cash return on equity. She builds a 7.8% overall rate and capitalizes the subject's NOI to reach value.
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Previous Question
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?
Next Question
The subject property is an office building under contract for $2,000,000 with NOI of $160,000. A lender offers a $1,400,000 loan at 7.0% interest with an 8.6% annual mortgage constant, and the buyer would pay the balance in cash. Compared with an all-cash purchase, how would this financing affect the buyer's first-year cash return on the cash invested?