finance - Compute the (Net) Present Value

Let's have a project where we invest 1000 at the beginning of year 1 and 1000 at the beginning of year 2. At the end of year 2 the income is 2200 and the project is closed.

Person A discounted with 5%.

Person B discounted with 10%.

Now I want to calculate the present value and net present value for both of them.

Person A: $PV = \frac{2200}{1.05^2} = 1995.46$

Person A: $NPV =$ Present value of the income - investments $= 1995,46 - (1000 + 1000) = -4.54$

Person B: $PV = \frac{2200}{1.10^2} = 1818.18$

Person B: $NPV = 1818.18 - (1000 + 1000) = -181.82$

Is this correct?

This is a part of a multiple choice question where is no option that the (N)PV of both is positive or negative at the same time. So I guess something is wrong.

Answer

No, it's not correct. The 1000 you invest at the beginning of the second year should also be discounted, That 1000 also has a present value. This gives:

$$NPV = \frac{2200}{(1+R)^2} - \frac{1000}{(1+R)} - 1000$$

with $R$ the annual rate.

Remember, you cannot simply add incoming or outgoing cash flows that occur at different times.