The subject property is a fourplex with annual NOI of $42,000. A similar fourplex recently sold for $650,000 with below-market seller financing. The appraiser estimates its cash-equivalent price at $600,000, and its annual NOI is $48,000. What is the indicated value of the subject by direct capitalization?
Correct Answer
A) $525,000
Extraction uses the cash-equivalent price because favorable financing inflates the nominal price. $48,000 ÷ $600,000 = 8%, and $42,000 ÷ 0.08 = $525,000. Using the nominal price gives $568,750. Carrying over the cash-equivalent price with no income adjustment gives $600,000, and inverting the income relationship gives $685,714.
Why This Is the Correct Answer
Option A is correct because the cash-equivalent price removes the effect of the below-market financing, so the rate is $48,000 ÷ $600,000 = 8%. Applying that to the subject gives $42,000 ÷ 0.08 = $525,000.
Why the Other Options Are Wrong
Option B: $568,750
Option B, $568,750, uses the nominal price: $42,000 ÷ ($48,000 ÷ $650,000), a rate of about 7.385%. That carries the value of the financing into the subject. The correct calculation is $42,000 ÷ 0.08 = $525,000.
Option C: $600,000
Option C, $600,000, carries over the comparable's cash-equivalent price. The subject earns less income, so the price must be scaled. The correct calculation is $42,000 ÷ 0.08 = $525,000.
Option D: $685,714
Option D, $685,714, inverts the income relationship: $600,000 × $48,000 ÷ $42,000. A subject with lower income should not be worth more on this measure. The correct calculation is $600,000 × $42,000 ÷ $48,000 = $525,000.
Cash price first, rate second
Clean the price to cash equivalent before you relate it to income. Financing perks are not part of the property's income-producing value.
How to use: Use this when a sale description mentions seller financing or a nominal price.
Exam Tip
If two prices appear for one sale, ask which is cash equivalent. Seller-financing language points to the lower, adjusted figure when the terms favored the buyer.
Common Mistakes to Avoid
- -Extracting a rate from a nominal price with favorable financing
- -Using the comparable's price with no adjustment for income
- -Inverting the income relationship when scaling to the subject
Concept Deep Dive
Analysis
The skill is choosing which price belongs in the extraction. The nominal price reflects the value of the financing as well as the real estate. Select the cash-equivalent price, extract the rate, and then apply it to the subject's income.
Background Knowledge
Rates and multipliers from sales are built on prices adjusted to cash equivalence. Seller financing at below-market terms typically lifts the nominal price above what an all-cash buyer would pay. Without that adjustment, extracted rates come out too low and multipliers too high.
Real-World Application
A comparable fourplex sold with a below-market seller carryback. The appraiser verifies the terms, estimates the cash-equivalent price, and uses that figure when extracting an overall rate for the subject.
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?
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Previous Question
A client plans to build a 10-unit apartment building and needs a completed value of $1,800,000. The overall rate for similar properties is 7.5%. Forecast operating expenses are $81,000, laundry income net of losses is $4,500, and vacancy and collection loss is 10% of potential rental income. The client paid $350,000 for the land. What annual potential rental income is required?
Next Question
A broker advertises the recent $950,000 cash sale of a 10-unit apartment building at a 9% capitalization rate, based on pro forma NOI of $85,500. While verifying the sale, an appraiser learns that the pro forma omitted vacancy and collection loss of $5,700 and a market management fee of $3,800. The buyer's partnership also pays $5,700 a year for its own accounting. What overall rate does this sale indicate?