A property sold at a cash-equivalent price of $1,062,500. Its stabilized annual NOI is $85,000. What is the indicated overall rate?
Correct Answer
B) 8.00%
85000÷1062500×100 = 8. Common errors: reporting the price ÷ NOI multiplier as if it were the rate gives 12.50%; misplacing the decimal (×1,000 instead of ×100) gives 80.00%; misplacing the decimal (×10 instead of ×100) gives 0.80%.
Why This Is the Correct Answer
Option B is correct because the overall rate is NOI divided by the cash-equivalent sale price: $85,000 ÷ $1,062,500 = 0.08. Expressed as a percentage, 0.08 × 100 = 8.00%.
Why the Other Options Are Wrong
Option A: 0.80%
Option A, 0.80%, comes from misplacing the decimal: $85,000 ÷ $1,062,500 × 10 = 0.80. The correct conversion multiplies 0.08 by 100 to give 8.00%.
Option C: 12.50%
Option C, 12.50%, comes from inverting the ratio: $1,062,500 ÷ $85,000 = 12.5, which is a price-to-income multiplier, not a rate. The overall rate is $85,000 ÷ $1,062,500 = 8.00%.
Option D: 80.00%
Option D, 80.00%, comes from misplacing the decimal: $85,000 ÷ $1,062,500 × 1,000 = 80. The correct figure is 0.08 × 100 = 8.00%.
IRV: income over value
Income = Rate × Value, so Rate = Income ÷ Value and Value = Income ÷ Rate. Cover the unknown and the other two show the operation.
How to use: Use IRV to set up any rate, value or income problem in direct capitalization.
Exam Tip
A capitalization rate for typical income property is usually a single-digit or low double-digit percentage, so a result like 80% or 0.8% signals a decimal error. Recheck the arithmetic rather than relying only on the sense check.
Common Mistakes to Avoid
- -Dividing price by income and calling the result a rate
- -Misplacing the decimal when converting a ratio to a percentage
- -Using a price that has not been adjusted to cash equivalency
Concept Deep Dive
Analysis
This question tests extraction of an overall capitalization rate from a comparable sale. The overall rate is income divided by price, expressed as a percentage. The distractors come from inverting the ratio or misplacing the decimal when converting to a percent.
Background Knowledge
A market-derived overall rate is net income divided by sale price adjusted for cash equivalency. Rates extracted from comparable sales are a preferred source of capitalization rates. The income and price must be compatible, such as stabilized annual NOI against a cash-equivalent price.
Real-World Application
An appraiser verifies a sale of an apartment building at a cash-equivalent price and confirms its stabilized NOI. Dividing NOI by price gives an overall rate she compares with other sales to support the subject's capitalization rate.
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A cash-equivalent resale pair with all other relevant factors controlled moves from $280,000 to $294,000 in exactly 12 months. What annual percentage increase on the original price does this pair indicate?
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A client owns a fourplex with NOI of $36,000, and sales of similar fourplexes indicate an overall rate of 7.5%. The client is considering two plans. Plan A would raise NOI by $2,400 with no change in the overall rate. Plan B would leave NOI unchanged, but replacing the aging roof and building systems would lower buyers' perceived risk, and the appraiser concludes the overall rate would fall to 7%. Which plan adds more value, and by how much?