The net present value (NPV) is the present value of a series of cash flows over a specified period of time. In the world of corporate finance, NPV is used to determine whether or not investment decisions in machinery or projects will add or subtract from shareholder wealth.
We can solve for NPV using the following formula:
where:
Assume that a manufacturer was looking to expand production in order to meet the need for increases in product demand. The new machinery would have an initial cash investment of $10,000; additionally, management makes the following projections for the incremental increase in annual cash flows once the machine is running:
| 0 | 1 | 2 | 3 | 4 | 5 | |
| Cashflow | $ (10,000.00) | $ 3,000.00 | $ 3,250.00 | $ 3,500.00 | $ 3,750.00 | $ 4,000.00 |
Further, management expects that the required rate of return is 7%. Using these assumptions what is the NPV of the project? Utilizing the table above, we can discount each of the cash flows by the required return as follows:
| 0 | 1 | 2 | 3 | 4 | 5 | |
| Cashflow | $ (10,000.00) | $ 3,000.00 | $ 3,250.00 | $ 3,500.00 | $ 3,750.00 | $ 4,000.00 |
| PV | $ (10,000.00) | $ 2,803.74 | $ 2,838.68 | $ 2,857.04 | $ 2,860.86 | $ 2,851.94 |
In order to calculate NPV, we simply add all of the present values together then subject from the total the initial cash outlay:
| 0 | 1 | 2 | 3 | 4 | 5 | |
| Cashflow | $ (10,000.00) | $ 3,000.00 | $ 3,250.00 | $ 3,500.00 | $ 3,750.00 | $ 4,000.00 |
| PV | $ (10,000.00) | $ 2,803.74 | $ 2,838.68 | $ 2,857.04 | $ 2,860.86 | $ 2,851.94 |
| NPV | $ 4,212.26 |
Generally speaking, projects that have a positive NPV add to shareholder wealth, while projects that have a negative NPV are detrimental to shareholder wealth.
Additionally, projects that have an NPV of $0 neither add or subtract to shareholder wealth and merely generate enough return to cover the costs of capital. The rate of return associated with an NPV of $0 is also referred to as the internal rate of return (IRR). In the world of fixed income investing, IRR is referred to as the yield-to-maturity (YTM).
Investment decisions may also be made by comparing IRR to the weighted average cost of capital (WACC). If the IRR is greater than the WACC, then management should move forward with the project. In instances where the decision made with IRR conflicts with NPV, then defer to NPV over IRR.
Using an HP12c, we can calculate the NPV of the project above using the following keystrokes:
[10000][CHS][CF0]
[3000][CFj]
[3250][CFj]
[3500][CFj]
[3750][CFj]
[4000][CFj]
[7][i][f][NPV]
The Excel model used to calculate NPV can be found here.
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