How much would an investor with a 12% required return be willing to invest in a project that will provide a cash flow of $2M every year for five years, five years from now, i.e. in years 6,7,8,9 and 10.
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To calculate how much an investor would be willing to invest in a project with a 12% required return, we need to use the present value formula. The present value formula is given by:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = interest rate
n = number of years
In this case, the cash flow is $2 million and it will be received every year for five years, starting from year 6. So, n = 5 and CF = $2 million.
The required return or interest rate is 12% or 0.12.
First, we need to calculate the present value of each cash flow using the formula above. Then, we sum up all the present values to get the total amount the investor would be willing to invest.
Let's calculate the present value of each cash flow:
PV year 6 = $2 million / (1 + 0.12)^5
PV year 7 = $2 million / (1 + 0.12)^6
PV year 8 = $2 million / (1 + 0.12)^7
PV year 9 = $2 million / (1 + 0.12)^8
PV year 10 = $2 million / (1 + 0.12)^9
Now, let's calculate the present value for each year:
PV year 6 = $2 million / (1.12)^5 = $1,186,587.99
PV year 7 = $2 million / (1.12)^6 = $1,057,927.16
PV year 8 = $2 million / (1.12)^7 = $944,544.20
PV year 9 = $2 million / (1.12)^8 = $844,717.32
PV year 10 = $2 million / (1.12)^9 = $756,164.23
Finally, we sum up all the present values to get the total amount of investment:
Total investment = PV year 6 + PV year 7 + PV year 8 + PV year 9 + PV year 10
Total investment = $1,186,587.99 + $1,057,927.16 + $944,544.20 + $844,717.32 + $756,164.23
Total investment = $4,789,940.90
Therefore, an investor with a 12% required return would be willing to invest approximately $4,789,940.90 in this project.