# Does the Net Present Value as a Financial Metric Fit Investment in Green Energy Security?

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Materials and Methods

## 4. Results and Discussion

#### 4.1. Current NPV as a Financial Metric and Interest Rates

_{n}—cash flows generated in particular years of investment exploitation; n—investment duration; I—investment outlay; and r

_{1}, r

_{2}… r

_{n}—discount rates for particular years of investment exploitation.

_{11}… r

_{1m}—annual interest rates from 1 to m in the first year of investment; t

_{11}… t

_{1m}—validity period of annual interest rates in the first calculation year of the investment calculated in days (the sum of t

_{11}to t

_{1m}equals 360 days); r

_{21}… r

_{2m}—annual interest rates from 1 to m in the second year of the implemented investment; t

_{21}… t

_{2m}—time of validity of annual interest rates in the second calculation year of the implemented investment calculated in days (the sum of t

_{21}to t

_{2m}equals 360 days); r

_{n}

_{1}… r

_{nm}—annual interest rates from 1 to m in the nth year of the implemented investment; and t

_{n}

_{1}… t

_{nm}—duration of annual interest rates in the nth year of the investment calculation (the sum of t

_{n}

_{1}to t

_{nm}equals 360).

#### 4.2. Towards a Modified NPV as a Financial Metric

_{f}—at a constant discount rate; and NPV

_{v}—at a variable discount rate.

_{f}measure, assuming the discount rate to be constant, and the NPV

_{v}containing the actual (variable) discount rates from the period under analysis, allows us to show the former’s disadvantages. The model, assuming that the interest rate changes once a year, is presented as follows:

_{1}, NCF

_{2}… NCF

_{n}—financial surpluses generated in the following years of investment’s exploitation; n—a consecutive year of the calculation period (investment’s lifetime); and r

_{1}, r

_{2}… r

_{n}—discount rates for each year. If the discount rate is changed more than once a year, the present value multiplier for one year takes the following form:

_{11}… r

_{1m}—annual interest rates in the first year of investment (from 1 to m); t

_{11}… t

_{1m}—duration of annual interest rates in the first calculation year of the investment (in days, the sum of t

_{11}to t

_{1m}equals 360); r

_{n}

_{1}… r

_{nm}—annual interest rate in the nth year of calculating the investment realized; and t

_{n}

_{1}… t

_{nm}—duration of annual interest rates in the nth year of the implemented investment (the sum of t

_{n1}to t

_{nm}equals 360).

## 5. Conclusions

- When deciding to carry out a given investment based on the traditional NPV model, which assumes a fixed interest rate, the investor is exposed to the lack of credibility of the calculations obtained; usage of the traditional NPV model creates a possibility of rejecting investment projects that may become profitable in the case of favourable changes in the price of money in later periods. Such a situation may lead to loss of future profit or even to the reduction of future market position.
- There is a risk of choosing a wrong project, which may lead to the company’s bankruptcy.
- Frequent changes of interest rates shaped by monetary institutions make it difficult to estimate their level in the medium and long term, which significantly reduces the financial rationality of investments; investors’ financial problems may be exacerbated by the negative interaction between interest rates and the level of cash flows. Realising the method of expressing the difference between the current cash inflows and their current outflows will allow for a better assessment of the investment effectiveness in the event of the volatility of interest rates.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Years | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|

Values | |||||||

NCF | 2,565,500 | 4,378,300 | 6,254,630 | 6,547,300 | 6,525,720 | 5,973,420 |

Years | 1 | 2 | 3 | 4 | 5 | 6 | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Interests Rate | ||||||||||||

interest rate (fixed) | 36% | 36% | 36% | 36% | 36% | 36% | ||||||

unfixed interest rate | 36% | 34% | 31% | 27% | 27% | 28% | 30% | 26% | 23% | 23% | 21% | |

number of days of interest rate validity | 150 | 210 | 197 | 163 | 256 | 104 | 167 | 193 | 360 | 62 | 298 |

Years | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|

PVIF | |||||||

PVIF r—fixed | 0.74 | 0.54 | 0.39 | 0.29 | 0.22 | 0.16 | |

PVIF r—variables | 0.72 | 0.55 | 0.43 | 0.33 | 0.27 | 0.22 |

**Table 4.**Value of updated financial surplus (PV) assuming fixed and unfixed interest rate (in EURO).

Years | 1 | 2 | 3 | 4 | 5 | 6 | |
---|---|---|---|---|---|---|---|

PV | |||||||

NCF | 2,565,500 | 4,378,300 | 6,254,630 | 6,547,300 | 6,525,720 | 5,973,420 | |

PV(NCF) R—fixed | 1,898,470 | 2,364,282 | 2,439,305 | 1,898,717 | 1,435,658 | 955,747 | |

PV(NCF) R—unfixed | 1,847,160 | 2,408,065 | 2,689,491 | 2,160,609 | 1,761,944 | 1,314,152 | |

Deviation value | 51,310 | 43,783 | 250,186 | 261,892 | 326,286 | 358,405 |

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## Share and Cite

**MDPI and ACS Style**

Dobrowolski, Z.; Drozdowski, G.
Does the Net Present Value as a Financial Metric Fit Investment in Green Energy Security? *Energies* **2022**, *15*, 353.
https://doi.org/10.3390/en15010353

**AMA Style**

Dobrowolski Z, Drozdowski G.
Does the Net Present Value as a Financial Metric Fit Investment in Green Energy Security? *Energies*. 2022; 15(1):353.
https://doi.org/10.3390/en15010353

**Chicago/Turabian Style**

Dobrowolski, Zbysław, and Grzegorz Drozdowski.
2022. "Does the Net Present Value as a Financial Metric Fit Investment in Green Energy Security?" *Energies* 15, no. 1: 353.
https://doi.org/10.3390/en15010353