Debt funds 75% of value at an annual mortgage constant of 6.25%, and the remaining equity has a current annual dividend rate of 9%. What overall rate does the band of investment indicate, to two decimal places?
Correct Answer
A) 6.94%
Ro = 0.75 × 6.25% + 0.25 × 9% = 4.6875% + 2.25% = 6.9375%, or 6.94% to two decimals. Reversing the debt and equity weights gives 8.31%, an unweighted average of the two rates gives 7.63%, and omitting the equity component gives 4.69%. The band uses the mortgage constant and the equity dividend rate, not the loan interest rate or an equity yield.
Why This Is the Correct Answer
Option A is correct because Ro = 0.75 × 6.25% + 0.25 × 9% = 4.6875% + 2.25% = 6.9375%. Rounded to two decimal places, that is 6.94%.
Why the Other Options Are Wrong
Option B: 8.31%
Option B, 8.31%, comes from reversing the debt and equity weights: 0.25 × 6.25% + 0.75 × 9% = 1.5625% + 6.75% = 8.3125%. Debt funds 75%, so the correct rate is 0.75 × 6.25% + 0.25 × 9% = 6.94%.
Option C: 7.63%
Option C, 7.63%, comes from an unweighted average of the two rates: (6.25% + 9%) ÷ 2 = 7.625%. The band weights each rate by its share of value, giving 6.94%.
Option D: 4.69%
Option D, 4.69%, comes from omitting the equity component: 0.75 × 6.25% = 4.6875%. Adding the equity component of 0.25 × 9% = 2.25% gives 6.94%.
Loan share times constant, plus equity
Multiply the loan share by the mortgage constant, multiply the equity share by the equity dividend rate, and add the two products.
How to use: Use this to build an overall rate from financing and equity data.
Exam Tip
Pair each weight with its own rate and include both components; the result should fall between the two rates and closer to the rate with the larger weight.
Common Mistakes to Avoid
- -Swapping the loan and equity weights
- -Using the loan interest rate instead of the mortgage constant
- -Leaving out the equity component
Concept Deep Dive
Analysis
This question tests the mortgage-equity band of investment. The overall rate is the loan ratio times the mortgage constant plus the equity ratio times the equity dividend rate. The question stresses using cash-flow rates, not the loan coupon or an equity yield.
Background Knowledge
The band of investment derives an overall rate as a weighted average of the claims of lenders and equity investors on NOI. The mortgage component uses the annual mortgage constant, which includes principal and interest, and the equity component uses the equity dividend rate. The weights are the shares of value funded by debt and equity.
Real-World Application
An appraiser finds that typical financing for neighborhood shopping centers is 75% loan-to-value at a 6.25% annual constant, and investors expect a 9% cash return on equity. She builds a 6.94% overall rate and compares it with rates extracted from sales.
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Previous Question
Comparable income-property sales suggest capitalization rates from 6.2% to 7.8%. What should support selection of a rate for the subject property?
Next Question
A client has contracted to buy a fourplex for $550,000 and hopes to earn a 10% cash-on-cash return on equity. A similar fourplex recently sold for $750,000 with annual NOI of $60,000. At the overall rate indicated by that sale, what annual NOI would the subject need to justify the contract price?