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)?
The Correct Answer and Explanation is:
To calculate the present value (PV) of a cash inflow of $1,250 four years from now, using a required rate of return of 8%, we can use the Present Value formula:
[
PV = \dfrac{FV}{(1 + r)^n}
]
Where:
- ( PV ) = Present Value (what we are solving for)
- ( FV ) = Future Value = 1250 (the cash inflow expected in the future)
- ( r ) = interest rate = 8% or 0.08
- ( n ) = number of periods = 4 years
Step-by-step calculation:
[
PV = \dfrac{1250}{(1 + 0.08)^4}
]
[
PV = \dfrac{1250}{(1.08)^4}
]
[
PV = \dfrac{1250}{1.36049}
]
[
PV \approx 918.52
]
So, the present value is approximately $918.52.
Explanation:
The concept of present value (PV) is central in finance because it helps in determining the worth of a future cash inflow in today’s terms. Money has a time value, meaning that a dollar today is worth more than the same dollar received in the future because of its potential earning capacity. This principle forms the basis of discounted cash flow analysis, which is used to evaluate investment opportunities or financial decisions.
In this example, the future value of $1,250 represents a payment or inflow expected to be received four years from now. However, since money can earn interest, we discount this future sum to determine its value in today’s terms. The discounting process uses the required rate of return, which is 8% in this case. This discount rate reflects the opportunity cost of not having that money available for investment today.
As seen in the formula, the future value is divided by the compound factor ((1 + r)^n) to account for the time period and the rate of return. By discounting the future cash inflow, we estimate its current worth to be approximately $918.52, making this the present value of the expected payment after four years.