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, we use the formula:
[
PV = \frac{FV}{(1 + r)^n}
]
Where:
- (FV) is the future value of the cash inflow (1250),
- (r) is the required rate of return (8%, or 0.08),
- (n) is the number of years until the cash inflow (4 years).
Substituting the 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 calculated denominator:
[
PV = \frac{1250}{1.3605} = 918.43
]
So, the present value of a cash inflow of 1250 four years from now, with a required rate of return of 8%, is 918.43 (rounded to two decimal places).
Explanation:
Present value (PV) is a key concept in finance that allows us to determine how much a future amount of money is worth today, given a certain interest or discount rate. It is based on the time value of money principle, which states that a dollar today is worth more than a dollar in the future due to its earning potential. In this case, we are trying to determine how much 1250, which will be received four years from now, is worth today if the required rate of return is 8%.
The higher the discount rate or rate of return, the lower the present value will be. This is because the money is being discounted over time, meaning future cash flows are worth less in today’s terms due to the lost opportunity to earn interest or invest elsewhere. Conversely, the closer the time period (n), the higher the present value, since the money is discounted for fewer years.
In this example, the present value of 1250 received four years from now is 918.43. This means if you were offered 918.43 today or 1250 in four years with an 8% return, they would be equivalent.