What is the present value of $100,000 to be received in 5 years, assuming a 7% discount rate?
Correct Answer
A) $71,299
Present value = Future Value ÷ (1 + discount rate)^years. $100,000 ÷ (1.07)^5 = $100,000 ÷ 1.4026 = $71,299.
Why This Is the Correct Answer
Option A ($71,299) correctly applies the present value formula: PV = FV ÷ (1 + r)^n. Substituting the given values: $100,000 ÷ (1.07)^5 = $100,000 ÷ 1.4026 = $71,299. This calculation properly discounts the future value back to present terms using the compound discount factor. The mathematical computation is accurate and follows standard financial principles used in real estate valuation.
Why the Other Options Are Wrong
Option B: $76,290
$76,290 appears to use an incorrect discount factor, possibly from miscalculating the compound interest or using a different time period or interest rate in the denominator.
Option C: $93,000
$93,000 suggests simple interest discounting rather than compound discounting, or possibly using only one year instead of five years in the calculation.
Option D: $140,255
$140,255 represents a future value calculation rather than present value, likely calculated as $100,000 × (1.07)^5, which moves in the wrong direction.
PV-FD: Present Value Future Divided
Remember 'PV-FD': Present Value equals Future Divided by (1 + rate)^years. Think 'Present Value - Future Divided' to recall that you divide the future amount by the compound factor.
How to use: When you see a present value question, immediately think 'PV-FD' and set up the division: Future Value on top, compound factor (1 + rate)^years on bottom.
Exam Tip
Always double-check that you're dividing (not multiplying) for present value calculations, and ensure you're raising the compound factor to the correct power equal to the number of years.
Common Mistakes to Avoid
- -Multiplying instead of dividing (calculating future value instead of present value)
- -Using simple interest instead of compound interest
- -Forgetting to raise the discount factor to the power of years
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value, which is crucial in real estate appraisal for income capitalization approaches and discounted cash flow analysis. Present value calculations allow appraisers to determine what a future sum of money is worth in today's dollars, accounting for the time value of money and investment risk. The formula requires understanding that money received in the future is worth less than the same amount received today due to opportunity cost and inflation. This concept is essential for valuing income-producing properties and comparing investment alternatives.
Background Knowledge
Present value is a core financial concept that measures the current worth of money to be received in the future, discounted at a specific rate of return. In real estate appraisal, this principle underlies the income approach to value, where future rental income streams are discounted to present value to determine property worth.
Real-World Application
An appraiser valuing a commercial property uses present value to determine what a $100,000 lease payment due in 5 years is worth today when analyzing the income approach, helping establish the property's current market value for lending or sale purposes.
More Math & Stats Questions
What is the area of a triangular lot with a base of 120 feet and a height of 80 feet?
An irregular lot has the following measurements: Side A = 100', Side B = 150', Side C = 120', Side D = 180'. If the lot can be divided into two rectangles (100' × 150' and 120' × 30'), what is the total area?
A property has a potential gross income of $180,000, vacancy and collection loss of 7%, and operating expenses of $65,000. What is the NOI?
A property generates $120,000 in net operating income and is valued at $1,500,000. What is the capitalization rate?
A building has potential gross income of $180,000, vacancy and collection loss of 8%, and operating expenses of $54,000. What is the net operating income?
People Also Study
Valuation Principles & Procedures
25% of exam
Property Description & Analysis
20% of exam
Market Analysis & Highest/Best Use
15% of exam
USPAP (Ethics & Standards)
15% of exam
Report Writing & Compliance
10% of exam