A project has an initial outlay of $2,087. The project will generate annual cash flows of $591 over the 5-year life of the project and terminal cash flows of $247 in the last year of the project. If the required rate of return on the project is 6%, what is the net present value (NPV) of the project?
Note: Enter your answer rounded off to two decimal points. Do not enter $ or comma in the answer box.
Net Present value (NPV) is the present value of future cash flows minus the initial investment.
First we will calculate the present value of future cash flows:
Present value of future cash flows = Present value of annual payments of $591 + Present value of terminal cash flow of $247 after 5 years.
Present value of annual payments of $591:
For the given project, the cash inflows of $591 will be same every year, so it is an annuity. For calculating the present value of annuity of $591, we will use the following formula:
PVA = P * (1 - (1 + r)-n / r)
where, P is the periodical amount = $591, r is the rate of interest = 6% and n is the time period = 5
Now, putting these values in the above formula, we get,
PVA = 591 * (1 - (1 + 6%)-5/ 6%)
PVA = 591 * (1 - (1 + 0.06)-5 / 0.06)
PVA = 591 * (1 - (1.06)-5 / 0.06)
PVA = 591 * (1 - 0.74725817286) / 0.06)
PVA = 591 * (0.25274182714 / 0.06)
PVA = 591 * 4.212363785666667
PVA = 2489.51
Present value of future cash flows = 2489.51
Present value of terminal cash flow of $247:
For calculating the present value of terminal cash flow of $247, we will use the following formula:
PV = FV / (1 + r)n
where, PV is the present value, r is the rate of interest = 6%, FV is future value = $247 and n is the time period = 5
Now, putting these values in the above formula, we get,
PV = 247 / (1 + 6%)5
PV = 247 / (1 + 0.06)5
PV = 247 / (1.06)5
PV = 247 / 1.3382255776
PV = 184.57
So, present value of terminal cash flow is 184.57.
Now,
Present value of future cash inflows = 2489.51 + 184.57 = 2674.08
Initial investment (given) = 2087
Net Present value (NPV) = Present value of future cash inflows - initial investment
Net Present value (NPV) = 2674.08 - 2087 = 587.08
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