Tim recently invested $3,500 in a project that is promising to return 10.75 percent per year.
The cash flows are expected to be as follows:
End of Cash
Year Flow
1 $750
2 800
3 ???
4 950
Note that the 3rd year cash flow is unknown. Assuming the present value of this cash flow stream is
$3,500 (that is, CF0 = -3500), what is the missing cash flow value (that is, what is the cash flow at the
end of the 3rd year)?
To find the missing cash flow value at the end of the 3rd year, we need to calculate the present value of the cash flow stream considering the given information.
We know that the present value of the cash flow stream is $3,500. This means that the sum of the present values of each cash flow should equal $3,500.
To calculate the present value of each cash flow, we can use the formula:
PV = CF / (1 + r)^n
Where:
PV is the present value
CF is the cash flow
r is the interest rate (10.75% or 0.1075 in decimal form)
n is the number of years
Let's calculate the present value of each known cash flow:
PV1 = $750 / (1 + 0.1075)^1 = $750 / 1.1075 = $677.04
PV2 = $800 / (1 + 0.1075)^2 = $800 / 1.2321 ≈ $649.57
PV4 = $950 / (1 + 0.1075)^4 = $950 / 1.4049 ≈ $676.24
Now, subtract the sum of these present values from the total present value to find the missing cash flow:
Missing Cash Flow = Total Present Value - (PV1 + PV2 + PV4)
Missing Cash Flow = $3,500 - ($677.04 + $649.57 + $676.24)
Missing Cash Flow ≈ $3,500 - $2,002.85
Missing Cash Flow ≈ $1,497.15
Therefore, the missing cash flow at the end of the 3rd year is approximately $1,497.15.