You want to invest in a project that costs $4125. The initial (Date 0) CF of the project is $75 which will grow at 10% each year forever. If the interest rate is 12% find the NPV of this project?

We know that NPV is the present value of cash inflow less the present value of cash outflow

Now, given that the initial cash flow is $4125

Annual cash inflow is $75

This is in the form of a growing perpetuity

The formula for present value of growing perpetuity is

A/(Re-g)

Where A is the cash flow in Year -1( Date-1)

Re is the interest rate or the discount rate

g is the growth rate

Hence, Present value of cash inflow is 75*(1.1)/(0.12-0.1)

82.5/0.02

4250

hence the NPV of the project is 4250 - 4125 = 125

Since the NPV of the project is positive we will accept the project.