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?
Correct Answer
D) Negative leverage would lower it to 6.6%
All cash, the return is $160,000 ÷ $2,000,000 = 8.0%. Debt service is $1,400,000 × 8.6% = $120,400, which leaves $39,600 on $600,000 of equity, or 6.6%, because the 8.6% constant exceeds the 8.0% overall rate. Using the 7.0% note rate for debt service gives 10.3% and the wrong direction. The 7.4% figure subtracts the 0.6-point spread without gearing it up for the debt-to-equity ratio, and 9.4% adds the geared spread instead of subtracting it.
Why This Is the Correct Answer
Option D is correct because debt service is $1,400,000 × 0.086 = $120,400, leaving $160,000 − $120,400 = $39,600 for equity. On $600,000 of cash, that is 6.6%, below the 8.0% return of an all-cash purchase. The loan's 8.6% annual cost exceeds the property's 8.0% rate, so the leverage is negative.
Why the Other Options Are Wrong
Option A: Positive leverage would raise it to 9.4%
Option A shows positive leverage raising the return to 9.4%, which is 8.0% + 0.6 × ($1,400,000 ÷ $600,000). The spread works against equity here because the constant is above the overall rate, so the geared 1.4 points are subtracted, giving 6.6%.
Option B: Positive leverage would raise it to 10.3%
Option B shows positive leverage raising the return to 10.3%, which is ($160,000 − $1,400,000 × 0.07) ÷ $600,000. The 7.0% note rate leaves out principal payments; actual debt service at the 8.6% constant is $120,400, and the return is 6.6%.
Option C: Negative leverage would lower it to 7.4%
Option C shows negative leverage lowering the return to 7.4%, which is 8.0% − 0.6. It has the right direction but ignores that $1,400,000 of debt rests on $600,000 of equity; the full calculation is $39,600 ÷ $600,000 = 6.6%.
Constant over rate: negative
If the mortgage constant is above the overall rate, a year's loan payments take more than the borrowed money earns.
How to use: Use this comparison to predict the direction of the equity dividend before doing the arithmetic.
Exam Tip
When the facts give both a note rate and a mortgage constant, use the constant for annual cash debt service. Check your answer by computing cash flow to equity divided by the cash invested.
Common Mistakes to Avoid
- -Comparing the overall rate with the note rate instead of the mortgage constant
- -Computing the equity return on the full purchase price instead of the cash invested
- -Overlooking how a small spread is magnified by the debt-to-equity ratio
Concept Deep Dive
Analysis
This tests whether financing helps or hurts the cash return to equity. The first-year comparison is between the overall rate and the mortgage constant, because the constant is what the loan costs in annual cash, principal and interest together. A note rate below the overall rate can make leverage look favorable when the cash return actually falls.
Background Knowledge
Financial leverage is the use of borrowed funds to finance an asset. Leverage is favorable when the return on the total investment exceeds the cost of borrowing and unfavorable when that cost is higher. The mortgage constant relates a year's debt service to the loan principal, and it is the debt rate used in the band of investment.
Real-World Application
A buyer assumes that a 7% loan will boost returns on a building priced at an 8% overall rate. The appraiser's rate analysis shows that the amortizing payments cost 8.6% of the loan each year. In the first year, the buyer's cash return on the down payment would be lower than if the buyer had paid all cash.
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Previous Question
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?
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