# Question on Net Present Value, Discount rate, and Opportunity Cost

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.

• 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. May 8, 2018 at 22:00

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.

• 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
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. 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
Apr 9, 2018 at 3:42
• Nope. You can't just simplify like that. Every cash flow needs to be discounted based on when it's paid out. 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. May 9, 2018 at 12:16