Discounting Each Cash Flow Correctly in Net Present Value
Summary
The example compares an investment’s net present value for two discount rates. It initially discounts only the income received at the end, while subtracting both investments at their undiscounted amounts. That mixes cash flows from different dates and produces incorrect NPVs.
The corrected method discounts each cash flow according to when it occurs: the initial investment remains at present value, the investment made at the start of the second year is discounted by one year, and the final income is discounted by two years. In the example, this gives a positive NPV at the lower rate and a negative NPV at the higher rate. The discussion illustrates the timing principle for NPV, but it is a small example rather than a broader treatment of project valuation or uncertainty.
Key ideas
- Cash flows at different dates cannot be added without adjusting them to a common date.
- Discount an investment made at the start of the second year by one year when calculating present value at the project start.
- Discount income received at the end of the second year by two years.
- A higher discount rate can change the sign of a project’s NPV.
Tags
Full text
# Compute the (Net) Present Value
# 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 by Olaf (score 3, accepted)
https://quant.stackexchange.com/a/17354
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.
## Answer by Kas (score 1)
https://quant.stackexchange.com/a/58796
As Olaf said you are not correct. The correct answers for NPV problem are:
Person A: $NPV = \frac{2200}{(1+0,05)^2} - \frac{1000}{(1+0,05)} - 1000 = 43,08$
Person B: $NPV = \frac{2200}{(1+0,1)^2} - \frac{1000}{(1+0,1)} - 1000 = - 90,91$
Person A should carry on with investment, but person B should not as the investment yields negative present value and wont be reasonable.
## Answer by GeaR (score 0)
https://quant.stackexchange.com/a/59218
The NPV calculation is the following:Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.