In the subject's market, lenders on fourplexes have lowered their typical loan-to-value ratio from 70% to 60%. The annual mortgage constant remains 5% and the equity dividend rate remains 10%. The subject's NOI has not changed. How does this affect the overall rate indicated by the band of investment and the indicated value?
Correct Answer
B) Rate rises from 6.50% to 7.00%; value falls
At 70% debt the band is 0.70 × 5% + 0.30 × 10% = 6.50%, and at 60% debt it is 0.60 × 5% + 0.40 × 10% = 7.00%. Less debt shifts weight to the higher equity rate, so the rate rises, and with NOI unchanged a higher rate lowers value. Swapping the weights produces the 8.50% to 8.00% decline, and a simple average produces the unchanged 7.50%. Saying that a higher rate raises value reverses the relationship between rate and value.
Why This Is the Correct Answer
Option B is correct because the band moves from 0.70 × 5% + 0.30 × 10% = 6.50% to 0.60 × 5% + 0.40 × 10% = 7.00%. Less debt puts more weight on the 10% equity rate. Since V = NOI ÷ R, a higher rate on unchanged NOI lowers the indicated value.
Why the Other Options Are Wrong
Option A: Rate falls from 8.50% to 8.00%; value rises
Option A says the rate falls from 8.50% to 8.00%. Those figures swap the weights: 0.30 × 5% + 0.70 × 10% = 8.50% and 0.40 × 5% + 0.60 × 10% = 8.00%. With debt correctly weighted, the rate rises from 6.50% to 7.00%.
Option C: Rate rises from 6.50% to 7.00%; value rises
Option C has the right rates, 6.50% and 7.00%, but says the higher rate raises value. In V = NOI ÷ R, the rate is in the denominator, so with NOI unchanged a higher rate lowers the indicated value.
Option D: Rate stays at 7.50%; value is unchanged
Option D says the rate stays at 7.50%. That is the simple average (5% + 10%) ÷ 2, which ignores the weights and so cannot respond to a change in loan-to-value ratio. The weighted rate moves from 6.50% to 7.00%.
Less debt, more equity weight
When equity is the pricier capital, moving weight toward equity pushes the blended rate up. A higher rate means a lower value on the same income.
How to use: Use this chain of reasoning when a problem changes the financing mix and asks about direction.
Exam Tip
For a two-scenario problem, work out the numbers for both scenarios and state the direction before you read the options. Then check the rate and value parts of each option separately.
Common Mistakes to Avoid
- -Applying the debt weight to the equity rate
- -Thinking that a higher capitalization rate raises value on the same NOI
- -Averaging the two rates so that a change in financing has no effect
Concept Deep Dive
Analysis
The problem compares two scenarios rather than producing one rate. You calculate the band at each loan-to-value ratio, note the direction of the change, and then apply the inverse relationship between rate and value. Each option requires both parts to be right.
Background Knowledge
The band of investment weights the capitalization rates for debt and equity by their typical shares of value, so a change in typical financing can change the indicated overall rate. When the equity rate exceeds the mortgage constant, a smaller debt share raises the weighted rate. Here the two component rates are unchanged, although actual market rates may also respond to credit conditions.
Real-World Application
After banks tighten underwriting, an appraiser updates a band-of-investment check on a stabilized apartment building. With the component rates held steady, the lower loan-to-value ratio raises the band rate. The appraiser notes that the result is a cross-check and compares it with rates from recent sales.
More Income Approach Questions
Which model describes yield capitalization of property benefits?
An appraiser is valuing a duplex. A market survey of recent duplex sales reports prices at 10.8 times potential gross income, with stabilized vacancy and credit loss of 10% of PGI and no other income. The subject's rent schedule is unavailable, but the property manager's records show collected income of $54,000 a year, in line with market rent and the 10% market loss. What value is indicated?
The subject property is a fourplex with annual EGI of $72,000 and operating expenses of $28,800. Of those expenses, $18,000 is fixed and $10,800 varies in direct proportion to EGI. The owner's annual mortgage payments are $21,000. An appraiser projects that EGI will fall 10% because of higher vacancy. What is the projected NOI?
Annual NOI available for debt service is $168,000 and total annual mortgage principal and interest debt service is $120,000. What is NOI ÷ debt service?
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?
Annual PGI is $360,000 and combined vacancy and collection loss is explicitly 8% of that same PGI base. There is no other income. What annual EGI remains?
Annual PGI is $640,000. Combined vacancy and collection loss is 6.25% of PGI. There is no other income. What EGI remains?
An appraiser is updating a prior appraisal of a triplex with potential gross income of $60,000 and no other income. The prior appraisal used vacancy and credit loss of 5% of PGI, and a new survey of competing rentals indicates 8%. The operating expenses of $24,000 are property taxes, insurance and contract services that do not vary with occupancy, and the market overall rate remains 7.5%. By what percentages do effective gross income and indicated value decrease?
Annual potential rental income is $600,000 and vacancy loss alone is $36,000. What percentage of potential rent does that loss represent?
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?
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