What is the present value of a cash inflow of 1250 four years from now if the required rate of return is 8% (Rounded to 2 decimal places)?
Review Later
A. 918.79
B. 992.50
C. 938.75
D. 835.75
The Correct Answer and Explanation is:
To determine the present value (PV) of a cash inflow of $1,250 to be received four years from now, we can use the present value formula:
[
PV = \frac{FV}{(1 + r)^n}
]
Where:
- (PV) = Present Value (what we are solving for),
- (FV) = Future Value ($1,250),
- (r) = required rate of return (8%, or 0.08),
- (n) = number of periods (4 years).
Step-by-Step Calculation:
[
PV = \frac{1250}{(1 + 0.08)^4}
]
First, calculate (1 + 0.08 = 1.08). Then raise it to the power of 4 (since the cash inflow occurs 4 years from now):
[
PV = \frac{1250}{1.08^4}
]
Now, calculate (1.08^4):
[
1.08^4 \approx 1.3605
]
Next, divide $1,250 by 1.3605:
[
PV = \frac{1250}{1.3605} \approx 918.79
]
Thus, the present value is approximately $918.79.
Answer:
The correct answer is A. 918.79.
Explanation:
Present value (PV) is a concept used to determine the current worth of a future amount of money or cash inflow, considering a specific rate of return. It allows us to account for the time value of money—the idea that money received in the future is worth less than the same amount received today due to its earning potential. In this case, we used an 8% required rate of return, meaning that $1,250 received in four years is worth $918.79 today when discounted at that rate.
This calculation is crucial in finance for evaluating investment opportunities. If the calculated present value exceeds the cost of the investment, it may be considered a good investment. Conversely, if the present value is less than the investment cost, it may not be worth pursuing.