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I recently viewed a Youtube on Net Present Value (NPV), to gain a better understanding of the concept. Towards the end of the video the uploader makes the claim that the project has added value to the firm, above and beyond the 6% that they could have invested elsewhere.

But that doesn't make sense. If you could have invested the original 10,000 elsewhere at 6% per year you would get 10,000 ( 1 +.06)^5 = $13382.26 for a profit of $3328.26. This is greater than the calculated NPV of $3239 for the project.

I am also confused about how the discount rate is calculated. It seems that once you find a discount rate, it is always better to invest the money elsewhere than to undertake a given project whose cash flow you are discounting. For example in the problem above it makes more sense to invest the money elsewhere at 6% than to invest it in the project.

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  • You should include the relevant numbers in your question, rather than asking people to watch a video. What discount rate do they use? What's the nominal profit? Etc.
    – Acccumulation
    Commented May 8, 2018 at 22:00

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Your calculation of the 10,000 * (1+0.06)^5 = 13,382.26 does not take into account the time value of money. You wouldn't get that entire profit of $3328.26 today, you get it five years from now. Meaning you need to discount it by (1.06)^5 in the denominator to get the NPV.

[10,000 * (1.06)^5] / (1.06)^5 = exactly 10,000. -10,000 in year 1 + 10,000 in year 5 = exactly 0.

So the correct comparison here is $3239 > 0, not $3328.26.

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  • Thanks for the reply. What does NPV = 0 indicate. Is that what happens if you chose not to do the project and just invest it in a 6% investment , like a 6% cd that you cash in after 5 years? Though 6% seems pretty high.
    – john
    Commented Apr 9, 2018 at 3:18
  • Correct. Every year the 6% interest you gain is exactly canceled out by the 6% discount rate, so you're neither better nor worse off.
    – Casey L
    Commented Apr 9, 2018 at 3:22
  • Also it looks like the rate of return of the project can be calculated another way. If you add the cash-flows 2500 +4000 + 5000 + 3000 + 1000 = 15,500 , this is larger than the 10,000 * (1+0.06)^5 = 13,382.26. And 10000(1 + .092)^5 = 15,500. So the overall rate of return on the project is 9.2%
    – john
    Commented Apr 9, 2018 at 3:42
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    Nope. You can't just simplify like that. Every cash flow needs to be discounted based on when it's paid out.
    – Casey L
    Commented Apr 9, 2018 at 4:49
  • @john the 6% interest rate is very high but that's because it's chosen to make the maths interesting and a little bit easier rather than to be realistic. Its the finance version of Vikram buying 14 apples and 21 oranges in school textbooks.
    – MD-Tech
    Commented May 9, 2018 at 12:16

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