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.
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