An older building nets $30,000 a year until redevelopment in two years. The land will then be worth $800,000, but removing the building will cost $60,000 at that time. At 9% (2-year annuity factor 1.7591; reversion factor 0.8417), what is the present value of the transitional property?
Correct Answer
D) $675,631
Value is the present worth of interim net income plus the present worth of the future land value net of removal cost: $30,000 × 1.7591 = $52,773, and ($800,000 − $60,000) × 0.8417 = $622,858. The total is $675,631.
Why This Is the Correct Answer
Option D is correct because interim income is worth $30,000 × 1.7591 = $52,773 today, and the net reversion is ($800,000 − $60,000) × 0.8417 = $622,858. Adding them gives $52,773 + $622,858 = $675,631.
Why the Other Options Are Wrong
Option A: $726,133
Option A, $726,133, ignores the removal cost: $52,773 + ($800,000 × 0.8417) = $52,773 + $673,360 = $726,133. The $60,000 demolition cost must be deducted from the reversion, giving $675,631.
Option B: $622,858
Option B, $622,858, is only the present value of the net reversion, ($800,000 − $60,000) × 0.8417. It omits the $52,773 present value of interim income; the total is $675,631.
Option C: $860,000
Option C, $860,000, adds the removal cost to the land value without discounting: $800,000 + $60,000 = $860,000. Removal cost reduces the reversion, and both income and reversion must be discounted, giving $675,631.
Income now plus land later
Discount the interim income and discount the future land value after demolition cost, then add the two.
How to use: Use this to structure any transitional or interim-use valuation problem.
Exam Tip
Subtract removal cost from the future land value before applying the reversion factor, and do not forget the interim income.
Common Mistakes to Avoid
- -Ignoring the cost to remove the building
- -Leaving out the present value of interim income
- -Adding future amounts without discounting
Concept Deep Dive
Analysis
This question tests valuing a property in transition to a new use. Value equals the present worth of interim income plus the present worth of the future land value net of the cost to remove the building. Both the income and the reversion must be discounted with the given factors.
Background Knowledge
When an existing improvement is in transition to a new highest and best use, its value reflects interim income until redevelopment plus the discounted land value, less the present worth of removal costs if they exceed salvage. This is a common way to value properties with short remaining economic lives.
Real-World Application
An appraiser values an aging strip center expected to be demolished in two years for apartments. The appraiser discounts the remaining rental income and the expected land value net of demolition costs to estimate present value.
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Previous Question
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?
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