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# Discussion on: How can a positive NPV end up with negative NPV with the same set of cash flow and time horizon

DIPA_DHUNGANA

Net Present Value (NPV) is the difference between total present value of cash inflows and outflows. It iswidely used method for evaluating the desirability of the project as it considers the time value of money as well as timing of the cash flows (Moyer, McGuigan, Rao, & Kretlow, 2012).

Calculation of NPV

For the calculation of NPV, let us assume that the initial investment is Rs. 2,000,000 and the discount rate is 20%. In addition, the cash flows are uneven and no additional investments are made in following years.

Year Cash flow (CF) PV Factor @ 20% Discounted CF
1 800,000 0.8333 666,640
2 700,000 0.6944 486,080
3 650,000 0.5787 376,155
4 600,000 0.4823 289,380
5 800,000 0.4019 321,520
Total 2,139,775
Less: Initial Investment 2,000,000
NPV 139,775

If we increase the discount rate to 25% keeping the cash flows and time horizon constant, the NPV will be:

Year Cash flow (CF) PV Factor @ 25% Discounted CF
1 800,000 0.8000 640,000
2 700,000 0.6400 448,000
3 650,000 0.5120 332,800
4 600,000 0.4096 245,760
5 800,000 0.3277 262,160
Total 1,928,720
Less: Initial Investment 2,000,000
NPV -71,280

From the two different cases, we can see that the increase in discount rate leads to decrease in NPV of a project keeping other variables constant. In case of independent projects, the projects with positive NPV are accepted and project with highest NPV among the given alternatives is selected if the projects are mutually exclusive. Thus the projects with lower discount rate are more likely to be accepted as it results in higher NPV.

References
Moyer, R. C., McGuigan, J. R., Rao, R., & Kretlow, W. J. (2012). Contemporary Financial Management (12th ed.). Oklahoma: Cengage Learning.