By Yuriy Smirnov Ph.D.

The net present value (NPV) method is widely used in capital budgeting and investment decisions. It is also considered as the best single screening criterion to reject or accept a project because the NPV method takes into account the time value of money concept. Its value reflects an expected change in shareholders’ value caused by a project.

The net present value of a project is the sum of the present value of each expected cash flow (both inflows and outflows) discounted at a discount rate. The equation of NPV is as follows:

NPV = CF_{0} + |
CF_{1} |
+ | CF_{2} |
+ … + | CF_{N} |

(1 + r)^{1} |
(1 + r)^{2} |
(1 + r)^{N} |

or

NPV = | N | CF_{t} |

Σ | ||

(1 + r)^{t} |
||

t = 0 |

Here, CF is an expected cash flow at the end of designated year t, r is discount rate, and N is life of the project in years.

It is important to remember that the discount rate takes into account not only the time value of money concept but also the risk of uncertainty of expected cash flows! That is the reason why the project’s weighted average cost of capital (WACC) should be used as the discount rate. In other words, a project’s WACC is the required rate of return on capital invested in the project. Accordingly, the greater the risk of uncertainty of expected cash flows, the higher the discount rate, and vice versa.

The decision rule in using the NPV method is rather straightforward. The threshold value of zero indicates that a project’s cash flows exactly cover the cost of invested capital and provide the required rate of return on invested capital. The general rules can be stated as follows:

- A stand-alone project should be accepted if its NPV is positive, rejected in case it is negative, and stay indifferent if zero.
- In the case of considering a number of independent projects, all those that have a positive NPV should be accepted.
- Among several mutually exclusive projects, the one with the highest positive net present value should be accepted.

A company is considering two projects with the same initial cost of $20,000,000. They are equally risky, have the same cost of capital of 11.5%, and the same total expected cash flows. The only difference is that cash flows from Project Y come in relatively sooner and relatively later from Project Z. The detailed information about expected cash flows is presented in the table below.

Initial Cost, CF_{0} |
Cash flows at the end of relevant year, CF_{t} |
|||||

0 | 1 | 2 | 3 | 4 | 5 | |

Project Y | -$20,000,000 | $10,000,000 | $8,000,000 | $6,000,000 | $4,000,000 | $2,000,000 |

Project Z | -$20,000,000 | $2,000,000 | $4,000,000 | $6,000,000 | $8,000,000 | $10,000,000 |

Let’s put all the data available in the formula above or use the calculator. So the net present value of Project Y is $3,480,385.27 and $318,148.89 for Project Z.

NPV of Project Y = -$20,000,000 + | $10,000,000 | + | $8,000,000 | + | $6,000,000 | + | $4,000,000 | + | $2,000,000 | = $3,480,385.27 |

(1 + 0.115)^{1} |
(1 + 0.115)^{2} |
(1 + 0.115)^{3} |
(1 + 0.115)^{4} |
(1 + 0.115)^{5} |

NPV of Project Z = -$20,000,000 + | $2,000,000 | + | $4,000,000 | + | $6,000,000 | + | $8,000,000 | + | $10,000,000 | = $318,148.89 |

(1 + 0.115)^{1} |
(1 + 0.115)^{2} |
(1 + 0.115)^{3} |
(1 + 0.115)^{4} |
(1 + 0.115)^{5} |

Discounted cash flows of both projects are schematically presented in the figure below.

If the projects are independent, the company should accept both because of positive NPV. If the projects are mutually exclusive, the company should reject Project Z and accept Project Y because it has a higher net present value.

The net present value of a project can also be calculated in Excel as in the example below.

- Select output cell
**H6**. - Click
button, select*fx***All**category, and select**NPV**function from the list. - In field
**Rate**, select cell**B1**. - In field
**Value1**, select the data range**C6:G6**, leave field**Value2**empty, and press the**OK**button.

We didn’t take into account the initial cost of Project Z. Select output cell **H6**, and add cell **B6** to the formula in the **Formula Bar**.

The advantage of NPV among other project valuation techniques is that it uses a discounted cash flows approach. Thus, it helps to estimate the additional shareholders’ value taking into account the time value of money concept.

Despite the obvious advantages of the NPV method, some disadvantages should be taken into account during project valuation.

__Sensitivity to discount rate__. One of the basic assumptions is that all of the project’s cash flows are reinvested at the discount rate. Actually, interest rates fluctuate over time, depending on the changes in economic conditions and inflation fears. Moreover, these fluctuations may be significant, especially in a long-term outlook. So, the actual change in the shareholders’ value can be quite different from the initial estimation.__Cash flows beyond the lifetime of the project__. Some projects can provide cash flows after the initial expected lifetime. These cash flows can provide additional shareholder value to the initial estimation, but they are ignored by the NPV method.__Real options__. During the lifetime of the project, management can undertake some actions influencing its timing or scale in response to changes in market conditions. These actions may change both the time of occurrence and the amount of cash flows, which, in turn, will lead to the change in shareholder value provided by the project. Traditional discounted cash flow analysis does not take such changes into account.

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