An income stream of $10,000 per year for 10 years, with a discount rate of 8%, has what present value? (Use PV factor of 6.71)
Correct Answer
B) $67,100
Present value of an annuity = Annual payment × PV factor: $10,000 × 6.71 = $67,100.
Why This Is the Correct Answer
Option B is correct because it properly applies the present value of annuity formula: Annual Payment × PV Factor = Present Value. The calculation is straightforward: $10,000 × 6.71 = $67,100. The PV factor of 6.71 already incorporates the 8% discount rate over the 10-year period, eliminating the need for complex calculations. This factor represents the cumulative present value of $1 received annually for 10 years at 8% discount rate.
Why the Other Options Are Wrong
Option A: $100,000
Option A ($100,000) represents the total undiscounted cash flows ($10,000 × 10 years) without considering the time value of money, which ignores the fundamental principle that money received in the future is worth less than money received today.
Option C: $80,000
Option C ($80,000) appears to apply an incorrect discount factor or methodology, possibly confusing this with a different type of present value calculation or using an wrong interest rate or time period.
Option D: $46,320
Option D ($46,320) likely results from incorrectly applying present value calculations, possibly using the wrong formula or confusing this with a present value of a lump sum calculation rather than an annuity.
PAP Formula
PAP = Payment × Annuity factor = Present value. Remember 'PAP' like patting yourself on the back for getting the right answer - just multiply the Payment by the Annuity Present value factor.
How to use: When you see an annuity present value question, immediately think 'PAP' and look for the annual payment amount and the given PV factor, then simply multiply them together.
Exam Tip
Always check if a PV factor is provided in the question - if so, you don't need to calculate it manually using complex formulas, just multiply the annual payment by the given factor.
Common Mistakes to Avoid
- -Using the total undiscounted cash flows instead of applying the present value factor
- -Confusing present value of annuity with present value of a single lump sum
- -Attempting to manually calculate the PV factor when it's already provided in the question
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value of an ordinary annuity, which is crucial in real estate valuation for income-producing properties. The present value calculation determines what a series of future cash flows is worth today, accounting for the time value of money through a discount rate. This concept is essential for the income approach to valuation, where appraisers must convert future rental income streams into current market value. The question provides the present value factor (6.71) which represents the sum of individual present value factors for each year, simplifying the calculation from a complex multi-step process to a simple multiplication.
Background Knowledge
Present value of annuity calculations are fundamental to the income approach in real estate appraisal, used to convert future income streams into current value. The concept relies on the time value of money principle, where future cash flows are discounted back to present value using an appropriate discount rate that reflects risk and opportunity cost.
Real-World Application
Appraisers use this calculation when valuing rental properties with long-term leases, determining the present value of future rent payments to establish the property's income-based value for mortgage lending or investment analysis.
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