Ten finished lots will sell at $120,000 each, five at the end of each of the next two years. Sales costs are 8% of price and developer incentive is 10% of price. At a 14% discount rate, what is the present value of the net proceeds?
Correct Answer
B) $810,157
Net per lot is $120,000 × (1 − 0.18) = $98,400, so each year nets $492,000. Discounting: $492,000 ÷ 1.14 + $492,000 ÷ 1.14² = $431,579 + $378,578 = $810,157.
Why This Is the Correct Answer
Option B is correct because each lot nets $120,000 × (1 − 0.18) = $98,400, so five lots net $492,000 per year. Discounting at 14% gives $492,000 ÷ 1.14 = $431,579 for year one and $492,000 ÷ 1.2996 = $378,578 for year two. The total present value is $810,157.
Why the Other Options Are Wrong
Option A: $984,000
Option A, $984,000, is the total net proceeds of $98,400 × 10 lots with no discounting at all. It ignores the time value of money; the correct figure discounts each year's $492,000 to $810,157.
Option C: $863,158
Option C, $863,158, results from discounting the full $984,000 for only one period ($984,000 ÷ 1.14). Year-two proceeds must be discounted for two periods, giving $431,579 + $378,578 = $810,157.
Option D: $1,052,632
Option D, $1,052,632, results from discounting the gross sales of $1,200,000 for one period ($1,200,000 ÷ 1.14). It ignores the 18% for sales costs and incentive and the second year of discounting; the correct answer is $810,157.
Net first, then discount
Take deductions off the gross price first, then divide each year's net by 1 plus the rate raised to the year number. Year two gets divided twice.
How to use: Use this sequence on any multi-year lot sell-out present value problem.
Exam Tip
Check each answer choice against common shortcuts such as no discounting or one-period discounting; the correct answer discounts each cash flow for its own year.
Common Mistakes to Avoid
- -Discounting all proceeds for only one period
- -Discounting gross prices before deducting costs and incentive
- -Reporting undiscounted net proceeds as present value
Concept Deep Dive
Analysis
This question tests a simple subdivision discounted cash flow analysis. Find the net proceeds per lot after sales costs and developer incentive, total the net proceeds for each year, and discount each year's amount back for the correct number of periods. The key is discounting year two for two periods, not one.
Background Knowledge
Subdivision development analysis is a specific application of discounted cash flow analysis used to value land. Projected lot sales are reduced by sales costs, development costs where applicable, and developer incentive, and the resulting net cash flows are discounted to present value at a rate reflecting the project's risk.
Real-World Application
A lender asks an appraiser to value a tract of approved finished lots that a builder expects to sell over two years. The appraiser projects annual lot sales, deducts selling costs and developer incentive, and discounts each year's net proceeds to estimate the bulk value today.
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