The subject property is an office building with stabilized NOI of $123,000. Typical financing for similar properties is a 75% loan-to-value loan at 6.5% interest with a 7.6% annual mortgage constant. Equity investors expect a 10% equity dividend rate. At the value indicated by the band of investment, what is the annual pre-tax cash flow to equity?
Correct Answer
C) $37,500
The band gives 0.75 × 7.6% + 0.25 × 10% = 8.2%, so value is $123,000 ÷ 0.082 = $1,500,000 and the loan is $1,125,000. Debt service is $1,125,000 × 7.6% = $85,500, leaving $123,000 − $85,500 = $37,500, which is also 10% of the $375,000 equity. Using the note rate for debt service gives $49,875. Taking a 25% share of NOI gives $30,750, and applying the constant to the equity gives $28,500.
Why This Is the Correct Answer
Option C is correct because the band rate of 8.2% indicates $123,000 ÷ 0.082 = $1,500,000, so the loan is $1,125,000 and debt service is $1,125,000 × 7.6% = $85,500. Cash flow to equity is NOI less debt service: $123,000 − $85,500 = $37,500. That figure equals 10% of the $375,000 equity, which confirms the band reconciles.
Why the Other Options Are Wrong
Option A: $28,500
Option A, $28,500, applies the mortgage constant to equity: $375,000 × 7.6% = $28,500. The constant measures debt service relative to the loan, while equity earns its 10% dividend rate, which gives $375,000 × 10% = $37,500.
Option B: $30,750
Option B, $30,750, gives equity its 25% capital share of NOI: 0.25 × $123,000 = $30,750. Equity receives what remains after debt service, and because debt and equity carry different rates, its share of NOI differs from its share of capital; $123,000 − $85,500 = $37,500.
Option D: $49,875
Option D, $49,875, computes debt service at the note rate: $1,125,000 × 6.5% = $73,125, and $123,000 − $73,125 = $49,875. The note rate leaves out principal repayment, so annual debt service should be $1,125,000 × 7.6% = $85,500, leaving $37,500.
NOI pays lender, equity gets rest
Debt service comes off NOI first, using the constant on the loan, and the rest is the equity dividend. If that remainder equals the dividend rate times the equity, the band reconciles.
How to use: Use this to check any band of investment answer that involves dollars of debt service or equity cash flow.
Exam Tip
When both an interest rate and a constant are given, annual debt service comes from the constant. A quick check is to multiply the equity by the dividend rate and compare.
Common Mistakes to Avoid
- -Computing annual debt service at the note rate rather than the mortgage constant
- -Assuming equity's share of NOI equals its share of capital
- -Computing debt service on the full value rather than on the loan
Concept Deep Dive
Analysis
The band of investment is more than a weighted average of two rates. The overall rate is built so that the value it indicates pays the lender the constant on the loan and pays equity its dividend rate on the equity. Solving requires the rate, the value, the loan and the debt service in sequence. The dividend rate on equity then gives an independent check on the result.
Background Knowledge
The mortgage constant is the ratio of annual debt service to the loan amount, and the equity capitalization rate is the ratio of pre-tax cash flow to equity to the equity investment. Weighting them by the debt and equity proportions gives an overall rate. NOI at the indicated value is therefore fully divided between debt service and cash flow to equity.
Real-World Application
An appraiser who has used a band of investment for an office building wants to test the conclusion before signing. Debt service on a typical loan at the indicated value is subtracted from NOI, and the remainder is compared with what equity investors expect on their cash investment.
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