An appraiser is developing a discounted cash flow analysis for an office building with a five-year holding period. The projected sale price at the end of year 5 is $1,250,000, selling costs are 4% of the price, and the mortgage balance at that date will be $600,000. The discount rate is 8%. What is the present value of the reversion to the total property?
Correct Answer
B) $816,700
Net proceeds are $1,250,000 × 0.96 = $1,200,000, and $1,200,000 ÷ 1.08^5 = $816,700. Discounting the gross price and ignoring costs gives $850,729. Subtracting the $50,000 of costs after discounting the gross price gives $800,729, which treats a year-5 cost as if paid today. Discounting the net amount at simple interest gives $857,143. The mortgage balance affects the equity reversion, not the reversion to the total property.
Why This Is the Correct Answer
Option B is correct because the seller nets $1,250,000 × 0.96 = $1,200,000 at the end of year 5. Discounting gives $1,200,000 ÷ 1.08^5 = $816,700.
Why the Other Options Are Wrong
Option A: $800,729
Option A, $800,729, discounts the gross price and then subtracts undiscounted costs: $850,729 − $50,000 = $800,729. The $50,000 is paid at year 5, so it must be discounted too, giving $816,700.
Option C: $850,729
Option C, $850,729, is $1,250,000 ÷ 1.08^5. It leaves out the 4% selling cost; the net amount of $1,200,000 discounts to $816,700.
Option D: $857,143
Option D, $857,143, uses simple interest: $1,200,000 ÷ (1 + 0.08 × 5) = $857,143. Discounting relies on compound interest, so the divisor is 1.08^5 and the result is $816,700.
Net first, then discount
Take selling costs off at the sale date, when they occur. Then discount that one figure back.
How to use: Use this order whenever a reversion carries selling costs in the same year as the sale.
Exam Tip
Match each cash flow to the date it occurs. A cost paid at the sale is discounted along with the sale proceeds.
Common Mistakes to Avoid
- -Discounting the gross sale price
- -Subtracting future selling costs without discounting them
- -Using simple rather than compound discounting
Concept Deep Dive
Analysis
A reversion enters a DCF net of the costs of selling. The selling costs fall due at the sale, so they share the same year-5 timing as the proceeds. The clean sequence is to net first, then discount the single remaining amount. The mortgage balance is a claim on the equity's share of the proceeds, so it stays out of a total property reversion.
Background Knowledge
The reversion is the value remaining at the end of the projection period, also called terminal value. Its contribution to present value depends on net proceeds, the discount rate and the number of periods.
Real-World Application
An appraiser modeling a five-year hold for an office property estimates brokerage and transfer costs at the projected sale. The net figure, not the headline price, goes into the final year of the DCF.
More Income Approach Questions
An undamaged but functionally inadequate system causes a supported $60,000 loss. Replacement costs $85,000 and restores only $60,000, with no other benefits. What loss classification and deduction fit?
The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
For an arithmetic illustration only, depreciate a historical $2,000,000 construction cost on a zero-salvage straight-line 40-year schedule for 10 years. What unindexed scheduled amount remains? This is not a conclusion of current market value or current replacement cost.
For an arithmetic illustration, allocate historical construction cost $2,400,000 over 40 years on a zero-salvage equal annual schedule. After 8 years, what scheduled unindexed amount remains? This is not a current market-value conclusion.
For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
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Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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