Answer:
To calculate the net present value of this project using the Equivalent Annual Annuity approach, we first need to calculate the present value of each cash flow. We can use the following formula to calculate the present value of each cash flow:
PV = CF / (1 + r)^n
Where:
PV = Present Value
CF = Cash Flow
r = Discount Rate
n = Number of Years
Using a discount rate of 12%, we can calculate the present value of each cash flow as follows:
Year 0: PV = -5000 / (1 + 0.12)^0 = -5000
Year 1: PV = 2000 / (1 + 0.12)^1 = 1785.71
Year 2: PV = 1600 / (1 + 0.12)^2 = 1262.62
Year 3: PV = 1400 / (1 + 0.12)^3 = 1006.22
Year 4: PV = 1200 / (1 + 0.12)^4 = 831.99
Year 5: PV = 1000 / (1 + 0.12)^5 = 680.58
Next, we can calculate the net present value (NPV) of the project by summing up the present values of all cash flows:
NPV = -5000 + ∑PV
Where:
∑PV = Sum of Present Values
NPV = -5000 + (1785.71 + 1262.62 + 1006.22 + 831.99 + 680.58) = **$767.12**
Finally, we can use the Equivalent Annual Annuity approach to determine the constant annual cash flow generated by this project over its lifespan if it was an annuity . We can use the following formula to calculate the Equivalent Annual Annuity:
EAA = NPV / ((1 - (1 / (1 + r)^n)) / r)
Where:
EAA = Equivalent Annual Annuity
NPV = Net Present Value
r = Discount Rate
n = Number of Years
Using a discount rate of 12% and a project life of five years, we can calculate the Equivalent Annual Annuity as follows:
EAA = $767.12 / ((1 - (1 / (1 + 0.12)^5)) / 0.12) ≈ **$287.25**
Therefore, the net present value of this project using the Equivalent Annual Annuity approach is **$287.25** per year.