Find the future value at the end of year 3 of the following stream (appearing in the Table below) of cash flows received at the end of each year, assuming the firm can earn 17 percentage on its investments.year1 CF:6000year2 CF:3000year3 CF:9000
Question
Find the future value at the end of year 3 of the following stream (appearing in the Table below) of cash flows received at the end of each year, assuming the firm can earn 17 percentage on its investments.year1 CF:6000year2 CF:3000year3 CF:9000
Solution
To calculate the future value of a cash flow stream, we use the formula for future value (FV) which is:
FV = PV * (1 + r)^n
where:
- PV is the present value or the cash flow
- r is the interest rate
- n is the number of periods
Given that the interest rate is 17% or 0.17 and the cash flows are received at the end of each year, we can calculate the future value at the end of year 3 as follows:
For year 1 cash flow: FV1 = 6000 * (1 + 0.17)^3 = 6000 * 1.17^3 = 6000 * 1.6113 = $9667.8
For year 2 cash flow: FV2 = 3000 * (1 + 0.17)^2 = 3000 * 1.17^2 = 3000 * 1.3689 = $4106.7
For year 3 cash flow: FV3 = 9000 * (1 + 0.17)^1 = 9000 * 1.17 = 9000 * 1.17 = $10530
The total future value at the end of year 3 is the sum of these three values:
FV = FV1 + FV2 + FV3 = 4106.7 + 24304.5
So, the future value at the end of year 3 of the cash flow stream is $24304.5.
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