An appraiser extracted an 8% overall rate from sales of similar properties whose NOI was reported after reserves for replacement. The subject, a four-unit apartment building, has NOI of $39,200 before reserves. Reserves for similar properties are $300 per unit per year. Last year the owner spent $5,200 to replace a boiler, an outlay not reflected in the $39,200. What is the indicated value by direct capitalization?
Correct Answer
B) $475,000
The rate was extracted after reserves, so the subject's income must also be after reserves: 4 × $300 = $1,200, and $39,200 − $1,200 = $38,000. Then $38,000 ÷ 0.08 = $475,000. $425,000 deducts the one-year boiler outlay instead of the annualized reserve, $486,250 deducts $300 once rather than per unit, and $490,000 makes no deduction, which mismatches income and rate.
Why This Is the Correct Answer
Option B is correct because the subject's income must match the after-reserve basis of the 8% rate. The reserve is 4 × $300 = $1,200, leaving $38,000. Dividing $38,000 by 0.08 indicates $475,000.
Why the Other Options Are Wrong
Option A: $425,000
Option A, $425,000, deducts last year's $5,200 boiler outlay: $39,200 − $5,200 = $34,000, ÷ 0.08. Direct capitalization uses an annualized reserve, not one year's actual spending, so the deduction is $1,200 and the value $475,000.
Option C: $486,250
Option C, $486,250, deducts $300 once: $39,200 − $300 = $38,900, ÷ 0.08. The reserve is per unit, so the four units require $1,200, which leads to $475,000.
Option D: $490,000
Option D, $490,000, makes no deduction: $39,200 ÷ 0.08. This applies a rate extracted after reserves to income stated before them, which overstates value; the matched figure is $475,000.
Rate and income, same footing
Whatever came off the comparable's income before the rate was derived must come off the subject's income as well.
How to use: Use this check before dividing whenever you know how a rate was derived.
Exam Tip
Note how a rate was derived, because it tells you which level of income to capitalize. The subject's income may be stated at another level and need adjusting first.
Common Mistakes to Avoid
- -Applying an after-reserve rate to before-reserve income
- -Deducting a single year's capital spending instead of an annualized reserve
- -Forgetting to multiply a per-unit reserve by the number of units
Concept Deep Dive
Analysis
A rate and the income it capitalizes must be on the same footing. Because this rate came from income after reserves, the subject's income must take them as well. The facts also separate a smooth annual reserve from a lumpy single-year expenditure.
Background Knowledge
A replacement allowance annualizes the cost of components that wear out during an improvement's life, such as roof coverings or heating equipment. Whether it is deducted typically depends on market practice. What matters is treating it the same way when deriving the rate and when applying it.
Real-World Application
An appraiser's cap rate survey reports income after reserves, but the broker's package on the subject shows NOI before reserves. The appraiser deducts a market reserve from the broker's figure before applying the survey rate.
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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?