Question

What is the net present value (NPV) of a project that has the following cash flows? The required return is 10.0%. Year 0 1 2 3 Cash Flow $(5,000) $2,000 $2,000 $2,000 $3,000 $ 1,000 $1,000 4 5 6 O $2,920 O None of these are correct. O $2,916 O $2,655 $ 3,208

Answer 1

Net Present value (NPV) is the present value of future cash inflows minus the initial investment.

First we will calculate the present value of cash inflows as per below:

Option (e) is correct

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value, PV = Present value, r = rate of interest = 10%, 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 = $2000 / (1 + 10%)+ $2000 / (1 + 10%)² + $2000 / (1 + 10%)³ + $3000 / (1 + 10%)⁴ + $1000 / (1 + 10%)⁵ + $1000 / (1 + 10%)⁶

PV = $2000 / (1 + 0.1)+ $2000 / (1 + 0.1)² + $2000 / (1 + 0.1)³ + $3000 / (1 + 0.1)⁴ + $1000 / (1 + 0.1)⁵ + $1000 / (1 + 0.1)⁶

PV = $2000 / (1.1)+ $2000 / (1.1)² + $2000 / (1.1)³ + $3000 / (1.1)⁴ + $1000 / (1.1)⁵ + $1000 / (1.1)⁶

PV = $1818.18+ $2000 / (1.21) + $2000 / (1.331)+ $3000 / (1.4641)+ $1000 / (1.61051) + $1000 / (1.771561)

PV = $1818.18+ $1652.89 + $1502.63+ $2049.04+ $620.92 + $564.47

PV = $1818.18+ $1652.89 + $1502.63+ $2049.04+ $620.92 + $564.47

PV = $8208

So, required present value is $8208

Initial investment = $5000

Net present value (NPV) = Present value of cash flows - Initial investment

Net Present value (NPV) = $8208 - $5000 = $3208