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 future cash inflow, the formula used is:
[
PV = \frac{FV}{(1 + r)^n}
]
Where:
- ( PV ) = Present Value (what we are solving for)
- ( FV ) = Future Value (the future cash inflow of $1,250)
- ( r ) = Required rate of return (8% or 0.08)
- ( n ) = Number of periods (in this case, 4 years)
Substituting the given values into the formula:
[
PV = \frac{1250}{(1 + 0.08)^4}
]
First, calculate the denominator:
[
(1 + 0.08)^4 = (1.08)^4 = 1.3605
]
Now, divide the future value by the result:
[
PV = \frac{1250}{1.3605} = 918.66
]
So, the present value of a cash inflow of $1,250 four years from now at an 8% rate of return is approximately $918.66.
Explanation:
The present value represents the amount you would need to invest today, at a given rate of return, to achieve a specific future cash inflow. The concept is based on the idea that money today is worth more than the same amount in the future due to its potential earning capacity—this is known as the time value of money.
In this case, if you expect to receive $1,250 four years from now, you want to know how much money you would need to invest today, assuming an 8% rate of return. By discounting the future value ($1,250) using the formula above, you adjust for the interest that could be earned over the four years.
The factor ( (1 + r)^n ), where ( r ) is the rate and ( n ) is the number of years, helps determine how much the future value decreases when converted to present value. For longer periods or higher rates of return, the present value will be smaller because the money has more time to grow or compound.
This calculation is important in financial decision-making, allowing investors to compare different investment options or assess the value of future cash flows today.