Two hypothetical projects have identical cost cash flows and identical positive net sale receipts. One receives each sale receipt earlier and finishes in three years; the other finishes in six. Use the same positive discount rate and identical risk. Which has the higher present residual for land?
Correct Answer
D) The three-year tract indicates the higher land value
With unchanged cost cash flows and the same positive discount rate, receiving the same positive net sale receipts earlier gives a higher present value. A numeric rate is unnecessary to rank that controlled comparison. Actual projects require their full receipt, expense and risk schedules.
Why This Is the Correct Answer
Option D is correct because at a positive discount rate, the same positive receipts received earlier are discounted less and therefore have a higher present value. With identical costs and risk, the three-year project's faster receipts produce the higher present residual for land. Net cash flows over the absorption period are discounted to estimate land value.
Why the Other Options Are Wrong
Option A: Both indicate the same value, as totals are equal
Option A, that both indicate the same value because totals are equal, ignores discounting. Equal nominal totals received at different times have different present values when the discount rate is positive.
Option B: The six-year tract is worth more for its longer run
Option B, that the six-year tract is worth more for its longer run, reverses the principle. Receiving the same receipts later lowers their present value, so the longer project indicates less.
Option C: Neither can be valued without a discount rate given
Option C, that neither can be valued without a given discount rate, misses that the question asks only for a ranking. With the same positive rate, identical costs and risk, earlier receipts produce a higher present value whatever the specific rate.
Sooner money is bigger money
A dollar received sooner is worth more today than the same dollar received later, at any positive discount rate.
How to use: Use this phrase to rank projects with equal totals but different timing.
Exam Tip
When all else is identical, the project receiving cash sooner has the higher present value; you do not need the exact rate to rank them.
Common Mistakes to Avoid
- -Treating equal nominal totals as equal present values
- -Thinking a longer project adds value
- -Assuming a ranking requires a specific discount rate
Concept Deep Dive
Analysis
This question tests the time value of money in a land residual or subdivision development analysis. When cost cash flows, total net receipts, discount rate and risk are identical, receiving the receipts sooner produces a higher present value. Ranking the two projects requires only that principle, not a numeric rate.
Background Knowledge
In the subdivision development method, projected sales revenues and development costs over the absorption period are discounted at a market-extracted rate. The total net present value of those cash flows indicates the land value. Faster absorption, other factors equal, increases present value because money received sooner is worth more.
Real-World Application
An appraiser values raw acreage for a subdivision. Market data show lots in one area sell out in three years and in another in six, so the faster-absorbing project yields a higher discounted residual land value.
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