Question

You are considering two independent projects that have differing requirements. Project A has a required return of 12 percent compared to Project B's required return of 13.5 percent. Project A costs $75,000 and has cash flows of $21,000, $49,000, and $12,000 for Years 1 to 3, respectively. Project B has an initial cost of $70,000 and cash flows of $15,000, $18,000, and $41,000 for Years 1 to 3, respectively. Based on the NPV, you should:

Answer 1

We will calculate the Net Present Value (NPV) of both the projects.

Net Present value (NPV) = Present value of future cash inflows - initial investment

For Project A:

We will calculate the present value of future cash flows by the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 12%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $21000 / (1 + 12%)+ $49000 / (1 + 12%)² + $12000 / (1 + 12%)³

PV = $21000 / (1 + 0.12)+ $49000 / (1 + 0.12)² + $12000 / (1 + 0.12)³

PV = $21000 / (1.12)+ $49000 / (1.12)² + $12000 / (1.12)³

PV = $18750+ ($49000 / 1.2544) + ($12000 / 1.404928)

PV = $18750 + $39062.5 + $8541.36

PV = $66353.86

Now, we will calculate the Net Present Value (NPV) as per below:

Net Present value (NPV) = Present value of future cash inflows - initial investment

Initial investment = $75000, Present value of future cash flows = $66353.86

Putting the values in the above equation, we get,

Net Present value (NPV) = $66353.86 - $75000  

Net Present value (NPV) = - $8646.14

For Project B:

We will calculate the present value of future cash flows by the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 13.5%, n= time period

For calculating the present value the given cash flows, we will calculate the present values of all the years and add them up. Now,putting the values in the above equation, we get,

PV = $15000 / (1 + 13.5%)+ $18000 / (1 + 13.5%)² + $41000 / (1 + 13.5%)³

PV = $15000 / (1 + 0.135)+ $18000 / (1 + 0.135)² + $41000 / (1 + 0.135)³

PV = $15000 / (1.135)+ $18000 / (1.135)² + $41000 / (1.135)³

PV = $13215.8590+ ($18000 / 1.288225) + ($41000 / 1.462135)

PV = $13215.8590 + $13972.7143 + $28041.1863

PV = $55229.7596

Now, we will calculate the Net Present Value (NPV) as per below:

Net Present value (NPV) = Present value of future cash inflows - initial investment

Initial investment = $70000, Present value of future cash flows = $55229.7596

Putting the values in the above equation, we get,

Net Present value (NPV) = $55229.7596 - $70000

Net Present value (NPV) = - $14770.24

Since the Net Present Value (NPV) of both the projects is negative, so, based on NPV, we should not accept either of the projects.