An income stream of $10,000 per year for 10 years, discounted at 8%, has what present value? (PV factor for 10 years at 8% = 6.710)
Correct Answer
A) $67,100
Why this is correct: The present value of a level annual income stream (an annuity) is calculated as the annual payment multiplied by the present value factor for the given rate and term. Here, annual payment = $10,000, PV factor for 10 years at 8% = 6.710. Therefore, Present Value = $10,000 * 6.710 = $67,100. Why the other choices are wrong: $80,000 is simply the total undiscounted cash flow ($10,000 * 8 years). $100,000 is the total undiscounted cash flow over 10 years ($10,000 * 10). $46,320 might use a wrong factor or a different discount rate. Exam tip: PV of Annuity = Annual Payment * PV Factor. The factor accounts for discounting.
Why This Is the Correct Answer
Option B is correct because it properly applies the present value of annuity formula: PV = Annual Payment × PV Factor. The calculation is straightforward: $10,000 × 6.710 = $67,100. This represents the current worth of receiving $10,000 annually for 10 years when money can earn 8% annually. The PV factor of 6.710 already incorporates the discount rate and time period, making this a direct multiplication problem.
Why the Other Options Are Wrong
Option B: $80,000
$80,000 appears to be an arbitrary figure that doesn't correspond to any logical calculation method for this present value problem and significantly overvalues the income stream.
Option C: $100,000
$100,000 represents the total undiscounted payments ($10,000 × 10 years) without considering the time value of money, which ignores the fundamental principle that future money is worth less than present money.
Option D: $46,320
$46,320 might result from incorrectly using a present value factor for a different time period or discount rate, or from applying an incorrect formula altogether.
PAY × FACTOR = PV
Remember 'PAY × FACTOR = PV' - the annual PAYment times the PV FACTOR equals Present Value. Think of it as 'Pay Factor PV' - three simple words that represent the multiplication sequence.
How to use: When you see an annuity present value question, immediately identify the three components: annual payment amount, the given PV factor, and multiply them together for your answer.
Exam Tip
Always check if the PV factor is provided in the question - if so, it's a simple multiplication problem and you don't need to calculate the complex annuity formula.
Common Mistakes to Avoid
- -Using the total payments without discounting
- -Confusing present value factors with other financial factors
- -Attempting complex calculations when a simple PV factor is provided
Concept Deep Dive
Analysis
This question tests the fundamental concept of present value of an ordinary annuity, which is crucial in real estate appraisal for income capitalization approaches. The present value calculation determines what a series of future equal payments is worth in today's dollars, accounting for the time value of money through a discount rate. This concept is essential when valuing income-producing properties where rental income streams need to be converted to present value. The question provides the present value factor, which simplifies the calculation by eliminating the need to compute the complex annuity formula manually.
Background Knowledge
Present value of annuity calculations require understanding that equal periodic payments received over time must be discounted to reflect their current worth. The present value factor tables eliminate complex mathematical calculations by providing pre-computed factors based on specific discount rates and time periods.
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 property value using the income approach.
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