Flaherty is considering an investment that, if paid for immediately, is expected to return $163,000 ten years from now. If Flaherty demands a 12% return, how much is she willing to pay for this investment? (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided. Round your “PV of a single amount” to 4 decimal places and final answer to the nearest whole dollar.)
Future Value × p (PV of a Single Amount) = Present Value × =
The Correct Answer and Explanation is:
To calculate how much Flaherty is willing to pay for an investment that will return $163,000 in 10 years with a 12% expected rate of return, we use the formula for the present value (PV) of a single amount: PV=FV×PV factor\text{PV} = \text{FV} \times \text{PV factor}
Where:
- FV is the future value = $163,000
- PV factor is the present value factor of a single amount for 12% interest over 10 years
- PV is the present value or how much Flaherty should be willing to pay today
Step 1: Locate the PV Factor
We need to use the Present Value of $1 table for 12% interest over 10 years.
From the table:
PV factor (12%, 10 years) = 0.3220
Step 2: Calculate Present Value
PV=163,000×0.3220=52,486\text{PV} = 163,000 \times 0.3220 = 52,486
✅ Final Answer:
Flaherty should be willing to pay: $52,486
📘 300-Word Explanation:
The concept of present value (PV) is fundamental in finance, as it helps assess the worth of future cash flows in today’s dollars. Money has a time value, meaning a dollar today is worth more than a dollar in the future due to its potential earning capacity. This principle is the basis for the present value calculation.
In this case, Flaherty is considering an investment that will pay $163,000 ten years from now. However, she expects a 12% annual return on her investment. To determine how much she should pay today for that future payoff, we discount the future value ($163,000) back to the present using the present value of a single amount formula.
We reference a present value of $1 table, which shows the present value of $1 to be received in the future, discounted at various interest rates and time periods. At 12% for 10 years, the PV factor is 0.3220, meaning $1 received in 10 years is worth only 32.20 cents today.
We multiply this factor by the future value: $163,000×0.3220=$52,486\$163,000 \times 0.3220 = \$52,486
This result represents the amount that, if invested today at 12% interest, would grow to $163,000 in 10 years.
Thus, if Flaherty pays more than $52,486, her return would be less than 12%. If she pays exactly $52,486, she earns exactly 12%. This calculation ensures she meets her investment return expectations.