The subject property is a vacant lot with a net market ground rent of $30,000 per year. Since the prior appraisal, land capitalization rates for similar lots have risen from 6.0% to 7.5%, and the rent has not changed. How much has the indicated land value declined?
Correct Answer
C) $100,000
At 6.0% the value is $30,000 ÷ 0.06 = $500,000, and at 7.5% it is $30,000 ÷ 0.075 = $400,000, a decline of $100,000. Reporting the value at 7.5% gives $400,000, but that is the new value, not the change. Reading 1.5 points as 15% gives $75,000, and $30,000 is the unchanged annual rent.
Why This Is the Correct Answer
Option C is correct because capitalizing the same income at each rate gives $30,000 ÷ 0.06 = $500,000 and $30,000 ÷ 0.075 = $400,000. The difference between those values is $100,000.
Why the Other Options Are Wrong
Option A: $30,000
Option A, $30,000, is the annual net rent, which has not changed. The decline comes from capitalizing that income at two rates: $500,000 − $400,000 = $100,000.
Option B: $75,000
Option B, $75,000, is $500,000 × 0.15, which misreads a 1.5-point rate change as a 15% value loss. The actual decline is $500,000 − $400,000 = $100,000.
Option D: $400,000
Option D, $400,000, is the value at the new rate, $30,000 ÷ 0.075. The question asks for the decline, so compare it with the $500,000 value at 6.0%: $500,000 − $400,000 = $100,000.
Rates Up, Value Down
Income and value move together, but rate and value move opposite ways. To measure the change, compute the value at each rate.
How to use: Use this approach for any problem involving a change in a capitalization rate.
Exam Tip
Do not apply a percentage change in the rate directly to value. Work out both values and subtract.
Common Mistakes to Avoid
- -Reporting the new value instead of the change in value
- -Confusing percentage points with a percentage change
- -Treating the annual rent as the change in value
Concept Deep Dive
Analysis
Capitalization behavior is the point, not a single division. Value and rate move inversely, but a 25% rise in the rate does not produce a 25% fall in value. Calculating the value at each rate and comparing them is the reliable method.
Background Knowledge
Ground rent capitalization converts net land income into value by dividing by the land capitalization rate. With income held constant, a higher rate means a lower value. Because the rate is a divisor, the percentage change in value differs from the percentage change in the rate.
Real-World Application
A landowner receiving a level net ground rent hears that investors now expect higher land yields. An appraiser shows that the same rent supports a lower value at the higher rate, which explains the drop in offers.
More Land/Site Questions
How should an appraiser account for a site's access to public sewer compared with competing sites that require septic systems?
Which fact, if supported by competitive-market evidence, most directly supports a unit-price premium for an otherwise comparable site?
A rectangular site's frontage is doubled while its depth is halved, keeping area constant. What is the likely value effect in a retail district?
A downtown site's zoning height limit is reduced from six stories to three. Buyers in this market had been paying for six-story development potential. What effect on land value is most supportable?
A zoning change increases permitted density from four to eight units per acre. What is the likely effect on site value?
Using the allocation method, market evidence supports a typical land-to-total-property-value ratio of 28% for similar improved properties in the subject’s location. An improved comparable sold for $825,000. What land (site) contribution is indicated by applying that ratio?
An appraiser is valuing a vacant site near a landfill. A similar vacant site that is not affected by the landfill sold for $480,000. Paired land sales indicate that proximity to the landfill lowers site prices by $70,000. No other adjustments apply. What is the indicated value of the subject site?
An appraiser is extracting site value from a $600,000 cash sale. The seller's records show an original construction cost of $250,000 and a depreciated book value of $110,000. The appraiser estimates current replacement cost new at $400,000 and accrued depreciation from all causes at $100,000. What is the indicated site value?
Three parcels assembled under single ownership (standard appraisal guidance assemblage) support separate as-is values of $290,000, $340,000, and $250,000. After assemblage for a higher-utility use, the combined site is valued at $1,050,000. Assemblage costs (demolition, legal, holding, and related) total $55,000. What is the indicated net plottage (plottage increment after assemblage costs)?
A comparable commercial site with 65 front feet sold for a cash-equivalent price of $585,000. Per standard appraisal guidance, sale price per front foot is a vacant-land unit of comparison when frontage is a primary value determinant. The subject site has 72 front feet and is otherwise similar. What indicated land value does the front-foot unit support before other adjustments?
People Also Study
Real Estate Market
13.6% of exam
Property Description
11.8% of exam
Sales Comparison Approach
16.4% of exam
Cost Approach
13.6% of exam
Income Approach
8.2% of exam
Previous Question
An improved property has a value of $1,750,000. Sales of similar properties in the market area indicate that land accounts for 22% of total value. What is the indicated land value by allocation?
Next Question
An appraiser is valuing a vacant site exposed to highway traffic noise. A comparable vacant site that is not exposed to the noise or close to the highway sold for $435,000. Paired land sales indicate a $58,000 discount for traffic noise and highway proximity. No other adjustments apply. What land value is indicated for the subject?