# Evaluation of Investment in Renovation to Increase the Quality of Buildings: A Specific Discounted Cash Flow (DCF) Approach of Appraisal

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{0}), the NPV is described as follows:

_{OT}), expressed as follows:

_{1}is the value generated by F

_{0}during a period of 20 years, considering F

_{0}as outflow and FIe as inflow, where FIe is energy savings for every year of the investment effect period, from year 1 to year 20 (OT); FIe values are inflated at a 1.0% inflation rate per year; F

_{0}is the amount of cash required to finance investment in energy savings of the building at year 0; IRR

_{1}is the rate of return of the investment, as in case (1). To consider the time effect of monetary values, all financial flows are discounted using a discount rate, i, which is the same for all flow values. This hypothesis could be relaxed in further applications of the model, for example, by considering the weighted average cost of capital approach, thus considering the different financial fund strategies that are applied to finance the investment. In our model, the discount rate (i) is equal to a sample rate price of an Italian long-term treasury bond, as risk-free investment, that actually could be estimated in 2.50% per year in Italy. The second-model equation could be expressed as follows:

_{2}is the value generated by F

_{0}during a period of 20 years, considering F

_{0}as outflow and FIe and Tb as inflow; in Equation (8), in addition, Tb is the tax benefit (65%) of F

_{0}in 10 equal payments, 6.5% of F

_{0}per year, for a 10-year period of fiscal allowance: Tb = 0.065F

_{0}. To achieve Tb, a person must have an income and pay taxes, to which, via a tax benefit, a tax payment reduction (deduction) can be applied. IRR

_{2}is the rate of return of the investment as in case (2). The third-model equation could be expressed as follows:

_{3}is the value generated by F

_{0}during a period of 20 years, considering F

_{0}as outflow and FIe, Tb and TV as inflow; in Equation (9), in addition, TV is the terminal value as the increased value of the building, which is the amount of F

_{0}investment (TV

_{20}= F

_{0}) discounted at time zero; TV is the estimated increase in value of the building obtainable by selling the building at year 20 thanks to the investment for energy savings issued at year 0; IRR

_{3}is the rate of return of the investment as in case (3). The discount rate (i) is again 2.50% per year. The Equation (7) model calculates NPV

_{1}and IRR

_{1}considering FIe as the only positive effects for building owners, while the Equation (8) model calculates NPV

_{2}and IRR

_{2}even considering the positive effect of Tb for building owners and the Equation (9) model calculates NPV

_{3}and IRR

_{3}, then considering even the positive effects of TV for building owners. Particularly, the Equation (9) model specification is useful to ensure that the use of public resources is efficient given the positive externalities, thus ensuring efficient use of public resources. In every equation model, the tax benefit (Tb) is given to consumers given the effects of sustainable construction techniques on public goods production; the environmental effects of construction techniques are, in fact, considered to be a public good. The reduced emissions of pollutants and energy-saving investments are defined as externalities because they are freely accessible and do not pass through price mechanisms. The formulation given by Equations (7)–(9) could be applied to calculate the average NPV per year, as follows:

_{1,y}, NPV

_{2,y}and NPV

_{3,y}equations are respectively NPV per year, calculating NPV via Equations (7)–(9); we call, generically, NPV

_{y}every NPV per year calculated by applying one of the equations in Equation (10). The NPV approach proposed in Equation (10) is useful to compare alternative options of investment in private housing investment, by comparing different NPV

_{y}values of different property investment options and then choosing, ceteris paribus, the investment with the higher NPV

_{y}(under the hypothesis of same risk, same OT and same capital absorption at the beginning of the investment plan to overcome the case of financial constraint). At the same time, under the same conditions, the IRR approach is applied to compare the same investments and then to choose, again ceteris paribus, the investment with the higher IRR. The DCF approach is considered the main approach to the valuation of the investments, although it is not without its critics. In fact, some authors [27] show that the DCF approach, in particular the calculation of IRR, does not take into account, among other criticalities, that: (a) multiple real-value IRRs may arise; (b) complex-valued IRRs may arise; (c) IRR ranking is generally different from NPV ranking; (d) IRR criterion is not applicable with variable cost of capital; (e) the IRR does not measure the return on initial investment; and (f) the IRR does not signal the loss of entire capital. To overcome these limits [28,29,30,31] a development of IRR’s approach defined as the “average internal rate of return” (AIRR) with the aim of achieving a conceptual shift where the rate of return does not depend on cash flows but on the invested capital is suggested.

## 3. Case Study

^{2}per year. In Italy, the classification used by law considers ten energy classes (from 4A up to G) with intervals depending on overall energy performance, a physical value measured in kWh per m

^{2}per year. In northern Italy, characterized by temperatures lower than central and southern Italy, energy certifications issued indicate that low-energy buildings are prevalent. Data from the Piemonte region [52] indicate that of 298,622 buildings, 58,375 are in class G (19.54%) and 42,592 are in class F (14.26%). In Emilia Romagna region [53], of 633,331 buildings, 230,860 are in class G (36.45%) and 103,106 are in class F (16.27%). In Lombardia region [54], of 1,484,424 surveyed buildings, 757,472 are in class G (50.99%) and 203,708 are in class F (13.71%). The buildings within the case study are expressive of a significant proportion of Italian buildings, particularly those located in the regions of northern Italy, which, on average, are still characterized by very low energy performance at minimum on the scale of energy efficiency (classes G and F).

## 4. Results

_{1}and IRR

_{1}. Approach 2 considers the initial investment with a negative sign and the energy savings and tax benefits with a positive sign; the assessment applies Equation (8) for the calculation of NPV

_{2}and IRR

_{2}. Approach 3 considers the initial investment with a negative sign and the energy savings, tax benefits and terminal value with a positive sign; the assessment applies Equation (9) for the calculation of NPV

_{3}and IRR

_{3}. For the purpose of calculating the energy savings, a cost of natural gas of €0.07 per kWh was considered. To analyze a building’s performance is considered its feasibility study. For each project alternative, we assume full equity coverage, and, therefore, the values in Table 1 involve an immediate financial output, without a gradual repayment with debt servicing.

_{0}) is €138,450 for every analyzed case. In the total investment, major costs were for the purchasing of materials (€39,550), drainage and insulation (€14,500), and labor (€27,500). The company that carried out the work was a small firm with 18 workers, as is often the case among Italian construction firms, and therefore it was not equipped with tools to allow a reduction of labor costs. The firm was also not able to enjoy economies of scale in the shipyard and economies of size in the purchasing of materials. The cost savings of heating and cooling (FIe) is €11,022, (Table 2), which is inflated at an annual rate of 1.00% and discounted at a rate of 2.50% per year. The choice of the rate of discount has a great impact on the evaluation of projects, especially those with a long-term time horizon, as is typical of investments in buildings [55]. To reduce the subjectivity of our assessment of the discount rate (k), that is equal to the emissions of long-term treasury bonds from the Italian State in 2015 (BTP), that is 2.50% per year, we have applied an approach that considers the financial evaluation in terms of net present value (NPV), with an explicit discount rate, and even in terms of internal rate of return (IRR), where the IRR (the result of the analysis) should be compared to the given cost of capital use, the discount rate, to verify that the IRR > k. Frequently, in fact, it is difficult to properly calculate the value of the discount rate, as it depends on the financing choices of those who make the investment, using equity or debt, and on the levels of investment risk and investor risk tolerance. Regarding the effect of the tax deduction, it is limited only to final consumers, not firms, and aims to facilitate investment in renovation with public funds, that being a tax reduction in this case. Moreover, the tax deduction, in this case study, has a significant effect (as indicated by the comparison between IRR

_{1}and IRR

_{2}) in determining the convenience of an investment. This effect (IRR

_{2}>> IRR

_{1}) indicates that tax deductions could have a significant impact on the convenience of renovation in Italy, and, given the limitation of this article to a single case, future analyses should investigate the effect of tax deductions on the IRRs of investments in building renovation considering a larger sample of cases. In the article, we have considered a period of 20 years, as renovations are guaranteed by material suppliers and manufacturers for this minimum. Three caveats are necessary: (1) The lifespan of the renovation investment and its energy-saving effects is probably greater than 20 years, even if the useful life of the investment is reduced to 20 years for prudence, that is, paired to its guaranteed life; (2) A period of 20 years should be critically evaluated in the case of investors and/or owners of properties with a lesser payback time horizon, as in the case of elderly owners. In such cases, any terminal value of the property sale to a time t < 20 will, ceteris paribus, also consider the additional value resulting from discounting the energy savings from the year t + 1 to the year 20; (3) The time horizon of 20 years makes the valuation subject to uncertainty due to the difficulty of estimating energy costs, capital costs, inflation, and house price trends, and therefore in such cases a sensitivity analysis of explanatory variables, such as the Monte Carlo approach, should be applied and considered relevant.

_{obs}) is higher than the estimated inflation rate (IRE

_{est}), we can observe greater energy savings. In fact, the action of reducing energy costs increasingly impacts cost reduction the greater the rate of energy inflation. If the inflation rate increases progressively over the 1.00% considered in the simulation, the energy savings would also progressively increase, by definition, if compared with the base case considered in the case study. Practically, variations are not provided for energy costs outside variations for inflation, as the intervention of energy savings in the structure shows no loss of efficiency and no need for maintenance interventions. The energy of sustainable technology applied allows an energy cost savings of €173,542 (€8677 per year). Tax benefit (Tb) analysis is performed in Table 3; Tb is calculated as a deduction of 65% from the renovation investment (€138,450), to be subtracted from the tax payment in 10 years, as the total amount of €89,993 is not discounted. Tb is calculated only for approach 2 and approach 3 and has a total amount, inflated and discounted, of €78,762. The terminal value (TV) is €138,450, that is €87,492 inflated and discounted. Our investment analysis of the building renovation does not consider the cost of maintenance because the investment is related to the improvement of the energy performance of the building by means of an insulating cover that does not require maintenance for a period of 20 years, equal to the duration of the warranty for the work by the developer. The investment does not consider other maintenance, for example, in the interior of the apartments. For these reasons, it was not considered necessary to include maintenance costs in the evaluation as costs that, in any case, would be equal for each alternative considered in the case study and therefore would be excluded, ceteris paribus.

_{0}of €138.450, which determines an FIe of €173,542; NPV

_{1}has a positive value of €35,092, and IRR

_{1}is 4.097%. The investment, approach 2, has a F

_{0}of €138,450, which determines a FIe of €173,542, and the Tb is €78,672; NPV

_{2}has a positive value of €113,854, and IRR

_{2}is 11.296%. The investment, approach 3, has an F

_{0}of €138,450, which determines an FIe of €173,542, the Tb is €78,672 and the TV is €84,492; NPV

_{3}has a positive value of €198,346, and IRR

_{3}is 12.980%.

## 5. Discussion

_{0}), energy savings (IF

_{e}), Tax benefit (Tb) and terminal value (TV). This quantification allows us to perform a relative comparison of the project with the maximum generation of financial resources, which highlights the advantage of alternative case study approach 3 over alternative approaches 1 and 2, in particular with regard to the effect of Tb. In particular, data show that the:

- (1)
- Placed at 100%, the value NPV
_{1}for alternative case study—approach 1 (€35,092), the value of NPV_{2}is 324.45% (€113,854) and the value of NPV_{3}is 565.22% (€198,356). Analysis then showed that in sustainable construction projects, Tb plays an important role in NPV values, with NPV_{3}>> NPV_{1}and placed at 100% the value NPV_{1,y}for alternative case study—approach 1 (€1755), the value of NPV_{2,y}is 324.45% (€5,693) and the value of NPV_{3,y}is 565.22% (€9917). - (2)
- Placed at 100%, the value IRR
_{1}for the case study (4.907%), the value of IRR_{2}is 230.20% (11.296%) and the value of IRR_{3}is 264.53% (12.980%). Analysis shows again the important effect of Tb in determining IRR values, with IRR_{3}>> IRR_{1}.

_{1}) and is IRR

_{1}> i; IRR

_{2}and IRR

_{3}are higher by more than 10 percentage points compared to the emissions of long-term treasury bonds from the Italian State in 2015 (BTP). In our approach, the investment payback period is about 15 years without Tb (case study—approach 1) and about eight years with Tb (case study—approach 2). The calculated return on investment is higher, and this result is in contrast with a traditional view of building investments that are frequently characterized by a low return on capital and a very long pay-back period. In essence, the return of the considered investment is much higher than alternative investments, and on this, the effect of Tb has a particular influence. If the analysis is confirmed by future research, even expanding the sample, an IRR so high could attract investments in the building sector, particularly in private housing. With regard to the quantification of tax advantages, it is interesting to note that not only can owners claim tax benefits, so too can tenants and borrowers who pay for energy improvements to the building. In particular, the right to tax benefits applies to (a) owners or bare owners; (b) holders of a real right of enjoyment (usufruct, use, housing, or surface) and (c) tenants or borrowers. Italian tax law indicates that those who spend money on renovations to reduce energy consumption are entitled to tax advantages. If in the building in question there are 16 apartments, 13 of which are inhabited by the owner and three of which are for rent, tax advantages can be claimed in all 16 cases by the owners and even by the tenants. It should be recognized, however, that, for renters, it is not possible to achieve the benefit of a higher value of the building in the event that it is sold. However, renters can claim a partial deduction of costs incurred to improve energy efficiency through taxes. The analysis has some limitations because it does not take into account the following: (1) any difference in the cost of use of capital (discount rate) for every resident in the building; (2) the presence of a constraint of age for residents to conduct investment: in fact, some elderly residents might not have a useful life of 20 years (OT) and, therefore, the assessment would be valid only if these residents gave value to legacy; (3) the determination of the time horizon (OT) and the lack of consideration of any outflows over OT; (4) the consideration (or lack of consideration) of transaction costs related to investment property (costs of transferring ownership and/or expenses related to the signing of loans for financing the property and/or charges related to the preparation of tax returns for Tb); (5) the presence of possible claims by tax agencies related to tax requirements, with related effects on the values Tb during the OT period; (6) the presence of any unexpected charges due to the application of technologies or plant new and untested for durations in OT. These claims could make the DCF application subject to variability and subjectivity that should be exposed, if possible, during the construction of the model and dissemination of the results. We have suggested the application of the discounted cash flow (DCF) method, usually applied in the valuation of building investments for commercial or industrial purposes, even in the case of building investments made by private individuals. In fact, in buildings purchased for residential purposes, the LCC approach prevails when quantifying long-term costs. In the suggested approach, which can be expanded and applied in a larger sample to achieve general conclusions, it is evident that even the cost of energy improvements to houses could be considered a financial investment, since it allows the investor to obtain economic advantages at a deferred time and generates a measurable value. This evaluation could address two additional topics: (1) Houses are one of the largest investments of Italian families, so investments in housing, even for energy improvements, are an important choice for the majority of Italian families; (2) State strategies in terms of tax reductions can generate not only an incentive but also a distorting effect on competition if reductions allow excess returns compared with market average performance; in this way, the state, in supporting construction activities, could at the same time disadvantage other activities or sectors from which capital is subtracted to make subsidized investments by the state, although useful when generating positive externalities.

## 6. Conclusions

_{2}, which considers Tb, and IRR

_{3}, which considers Tb and TV, are about 10 percentage points higher than the emissions of long-term 2015 Italian treasury bonds (BTP), assumed to be a discounted rate. The investments in increasing building quality could ensure an IRR higher than the estimated discount rate, and even higher than the long term cost of debt of a loan with a real estate warranty, which actually is, in Italy, comparable with BTP rate. The results must, however, be received with caution, as they relate only to this case study. It may therefore be useful to extend the analysis to a sample of cases in order to check the results of the article on a broader basis in terms of IRR. The model is useful even if applied by consumers in evaluating investments in building renovation, in a stand-alone perspective and even comparing them with other types of investment, given that the home investment is the main investment of Italian families. Moreover, the DCF approach presented here could define a method that can be applied to a larger sample; further research could have the aim of deepening the DCF approach and considering explicitly equity capital cost of use. Given the results of the research and its limitations, the applied DCF model can be further developed particularly to quantify the values of positive externalities financed with public spending via tax benefits to buildings owners. In the end, we have prepared an open-sample spreadsheet, even for a single-consumer’s application, and have made it freely available as an open-access software package.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Financial Outflow of the Building | Type of Outflow | Value in €—Year 0—Construction Phase | ||
---|---|---|---|---|

Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | ||

Project | F_{0} | −4550 | −4550 | −4550 |

Site preparation and authorizations | F_{0} | −6600 | −6600 | −6600 |

Construction supervision | F_{0} | −6200 | −6200 | −6200 |

Drainage and insulation | F_{0} | −14,500 | −14,500 | −14,500 |

Materials | F_{0} | −39,550 | −39,550 | −39,550 |

Installations | F_{0} | −17,650 | −17,650 | −17,650 |

Labour | F_{0} | −27,500 | −27,500 | −27,500 |

Finishes | F_{0} | −5600 | −5600 | −5600 |

Plaster and painting | F_{0} | −16,300 | −16,300 | −16,300 |

Total Investment | F_{0} | −138,450 | −138,450 | −138,450 |

Square meters m^{2} (available per housing) | 1368 | 1368 | 1368 |

Financial inflow for energy savings (FIe) | Type of Inflow | Not Discounted and Not Inflated Values | Discounted and Inflated Values | ||||
---|---|---|---|---|---|---|---|

Value in €—Year 1/20—Management Phase | Value in €—Year 1/20—Management Phase | ||||||

FIe per Year (Inflation Rate 1.0%—Discount Rate 2.5%) | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | |

FIe year 1 | FIe | 11,022 | 11,022 | 11,022 | 10,861 | 10,861 | 10,861 |

FIe year 2 | FIe | 11,022 | 11,022 | 11,022 | 10,596 | 10,596 | 10,596 |

FIe year 3 | FIe | 11,022 | 11,022 | 11,022 | 10,337 | 10,337 | 10,337 |

FIe year 4 | FIe | 11,022 | 11,022 | 11,022 | 10,085 | 10,085 | 10,085 |

FIe year 5 | FIe | 11,022 | 11,022 | 11,022 | 9839 | 9839 | 9839 |

FIe year 6 | FIe | 11,022 | 11,022 | 11,022 | 9599 | 9599 | 9599 |

FIe year 7 | FIe | 11,022 | 11,022 | 11,022 | 9365 | 9365 | 9365 |

FIe year 8 | FIe | 11,022 | 11,022 | 11,022 | 9137 | 9137 | 9137 |

FIe year 9 | FIe | 11,022 | 11,022 | 11,022 | 8914 | 8914 | 8914 |

FIe year 10 | FIe | 11,022 | 11,022 | 11,022 | 8696 | 8696 | 8696 |

FIe year 11 | FIe | 11,022 | 11,022 | 11,022 | 8484 | 8484 | 8484 |

FIe year 12 | FIe | 11,022 | 11,022 | 11,022 | 8277 | 8277 | 8277 |

FIe year 13 | FIe | 11,022 | 11,022 | 11,022 | 8076 | 8076 | 8076 |

FIe year 14 | FIe | 11,022 | 11,022 | 11,022 | 7879 | 7879 | 7879 |

FIe year 15 | FIe | 11,022 | 11,022 | 11,022 | 7686 | 7686 | 7686 |

FIe year 16 | FIe | 11,022 | 11,022 | 11,022 | 7499 | 7499 | 7499 |

FIe year 17 | FIe | 11,022 | 11,022 | 11,022 | 7316 | 7316 | 7316 |

FIe year 18 | FIe | 11,022 | 11,022 | 11,022 | 7138 | 7138 | 7138 |

FIe year 19 | FIe | 11,022 | 11,022 | 11,022 | 6963 | 6963 | 6963 |

FIe year 20 | FIe | 11,022 | 11,022 | 11,022 | 6794 | 6794 | 6794 |

Total FIe financial flow | FIe | 220,440 | 220,440 | 220,440 | 173,542 | 173,542 | 173,542 |

Financial flow per year | 11,022 | 11,022 | 11,022 | 8677 | 8677 | 8677 |

Tb Financial Inflow | Type of Inflow | Not Discounted and Not Inflated Values | Discounted and Inflated Values | ||||
---|---|---|---|---|---|---|---|

Value in €—Year 1/20—Management Phase | Value in €—Year 1/20—Management Phase | ||||||

Tb per Year (Discount Rate 2.5%) | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | |

Tb year 1 | Tb | 0 | 8999 | 8999 | 0 | 8780 | 8780 |

Tb year 2 | Tb | 0 | 8999 | 8999 | 0 | 8566 | 8566 |

Tb year 3 | Tb | 0 | 8999 | 8999 | 0 | 8357 | 8357 |

Tb year 4 | Tb | 0 | 8999 | 8999 | 0 | 8153 | 8153 |

Tb year 5 | Tb | 0 | 8999 | 8999 | 0 | 7954 | 7954 |

Tb year 6 | Tb | 0 | 8999 | 8999 | 0 | 7760 | 7760 |

Tb year 7 | Tb | 0 | 8999 | 8999 | 0 | 7571 | 7571 |

Tb year 8 | Tb | 0 | 8999 | 8999 | 0 | 7386 | 7386 |

Tb year 9 | Tb | 0 | 8999 | 8999 | 0 | 7206 | 7206 |

Tb year 10 | Tb | 0 | 8999 | 8999 | 0 | 7030 | 7030 |

Year 11 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 12 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 13 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 14 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 15 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 16 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 17 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 18 | - | 0 | 0 | 0 | 0 | 0 | 0 |

Year 19 | - | 0 | 0 | 0 | 0 | 0 | 0 |

TV year 20 | TV | 0 | 0 | 138,450 | 0 | 0 | 84,492 |

Total financial inflow | Tb + TV | 0 | 89,993 | 228,443 | 0 | 78,762 | 163,254 |

Financial inflow per year | 0 | 4500 | 11,422 | 0 | 3938 | 8163 |

Financial Flow Analysis | Type of Flow | Not Discounted and Not Inflated Values | Discounted and Inflated Values | ||||
---|---|---|---|---|---|---|---|

Value in €—Year 1/20—Management Phase | Value in €—Year 1/20—Management Phase | ||||||

Financial Flow (FF) per Year | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | Case Study—Approach 1 | Case Study—Approach 2 | Case Study—Approach 3 | |

FF year 0 | FF | −138,450 | −138,450 | −138,450 | −138,450 | −138,450 | −138,450 |

FF year 1 | FF | 11,022 | 20,021 | 20,021 | 10,861 | 19,640 | 19,640 |

FF year 2 | FF | 11,022 | 20,021 | 20,021 | 10,596 | 19,161 | 19,161 |

FF year 3 | FF | 11,022 | 20,021 | 20,021 | 10,337 | 18,694 | 18,694 |

FF year 4 | FF | 11,022 | 20,021 | 20,021 | 10,085 | 18,238 | 18,238 |

FF year 5 | FF | 11,022 | 20,021 | 20,021 | 9839 | 17,793 | 17,793 |

FF year 6 | FF | 11,022 | 20,021 | 20,021 | 9599 | 17,359 | 17,359 |

FF year 7 | FF | 11,022 | 20,021 | 20,021 | 9365 | 16,936 | 16,936 |

FF year 8 | FF | 11,022 | 20,021 | 20,021 | 9137 | 16,523 | 16,523 |

FF year 9 | FF | 11,022 | 20,021 | 20,021 | 8914 | 16,120 | 16,120 |

FF year 10 | FF | 11,022 | 20,021 | 20,021 | 8696 | 15,727 | 15,727 |

FF year 11 | FF | 11,022 | 11,022 | 11,022 | 8484 | 8484 | 8484 |

FF year 12 | FF | 11,022 | 11,022 | 11,022 | 8277 | 8277 | 8277 |

FF year 13 | FF | 11,022 | 11,022 | 11,022 | 8076 | 8076 | 8076 |

FF year 14 | FF | 11,022 | 11,022 | 11,022 | 7879 | 7879 | 7879 |

FF year 15 | FF | 11,022 | 11,022 | 11,022 | 7686 | 7686 | 7686 |

FF year 16 | FF | 11,022 | 11,022 | 11,022 | 7499 | 7499 | 7499 |

FF year 17 | FF | 11,022 | 11,022 | 11,022 | 7316 | 7316 | 7316 |

FF year 18 | FF | 11,022 | 11,022 | 11,022 | 7138 | 7138 | 7138 |

FF year 19 | FF | 11,022 | 11,022 | 11,022 | 6963 | 6963 | 6963 |

FF year 20 | FF | 11,022 | 11,022 | 149,472 | 6794 | 6794 | 91,286 |

Total Financial Flow | FF | 81,990 | 171,982 | 310,432 | 35,092 | 113,854 | 198,346 |

NPV_{1}, NPV_{2}, NPV_{3} | 35,092 | 113,854 | 198,346 | ||||

IRR_{1}, IRR_{2}, IRR_{3} | 4.907% | 11.296% | 12.980% | ||||

NPV_{y} | 1755 | 5693 | 9917 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bonazzi, G.; Iotti, M.
Evaluation of Investment in Renovation to Increase the Quality of Buildings: A Specific Discounted Cash Flow (*DCF*) Approach of Appraisal. *Sustainability* **2016**, *8*, 268.
https://doi.org/10.3390/su8030268

**AMA Style**

Bonazzi G, Iotti M.
Evaluation of Investment in Renovation to Increase the Quality of Buildings: A Specific Discounted Cash Flow (*DCF*) Approach of Appraisal. *Sustainability*. 2016; 8(3):268.
https://doi.org/10.3390/su8030268

**Chicago/Turabian Style**

Bonazzi, Giuseppe, and Mattia Iotti.
2016. "Evaluation of Investment in Renovation to Increase the Quality of Buildings: A Specific Discounted Cash Flow (*DCF*) Approach of Appraisal" *Sustainability* 8, no. 3: 268.
https://doi.org/10.3390/su8030268