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The company is renowned for its commitment to innovation and excellence. Operating across aircraft propulsion, aircraft equipment, and defense segments, Safran delivers cutting-edge solutions that cater to the evolving needs of the aviation and defense industries worldwide. With a strong focus on research and development, the company continuously pushes the boundaries of technology, striving to enhance the performance, efficiency, and sustainability of its products while fostering collaborative industry partnerships to drive progress in these domains.<ref name=":0" />
The company is renowned for its commitment to innovation and excellence. Operating across aircraft propulsion, aircraft equipment, and defense segments, Safran delivers cutting-edge solutions that cater to the evolving needs of the aviation and defense industries worldwide. With a strong focus on research and development, the company continuously pushes the boundaries of technology, striving to enhance the performance, efficiency, and sustainability of its products while fostering collaborative industry partnerships to drive progress in these domains.<ref name=":0" />
Assuming that Safran implements certain growth strategies and other relevant assumptions, the expected return of an investment in the company over the next five years is approximately 5.21%. This translates to an annual return of around 1.04%. In practical terms, a £100,000 investment in Safran is projected to grow to approximately £105,210 in five years' time.


== Operations ==
== Operations ==
Line 224: Line 222:


=== Open rotor ===
=== Open rotor ===
[[File:Open rotor.png|left|thumb|250x250px]]
Safran's commitment to research and development is exemplified by its groundbreaking work on the Open Rotor, an innovative aircraft engine design. The Open Rotor project, featuring two counter-rotating propellers and no thrust reversers, represents a transformative approach to enhance fuel efficiency and reduce carbon emissions in the aviation sector. By pushing the boundaries of technology and collaborating with industry partners, Safran has demonstrated the feasibility of the Open Rotor concept through successful testing and research, positioning itself at the forefront of sustainable aviation solutions.<ref>https://www.safran-group.com/fr/actualite/quel-avenir-lopen-rotor-2019-03-28</ref>
Safran's dedication to the Open Rotor project underscores its vision for the future of aviation, striving to meet the industry's environmental challenges head-on. As the company continues to explore and develop this revolutionary engine architecture, Safran's R&D efforts highlight its commitment to driving innovation and shaping a greener, more sustainable aviation landscape for generations to come.


=== Hydrogen engine ===
=== Hydrogen engine ===
[[File:Hydrogen.png|left|thumb]]
CFM International, in collaboration with Airbus, is at the forefront of pioneering hydrogen combustion technology in the aviation industry. The joint effort aims to ground and flight test a hydrogen-fueled direct combustion engine, with the ultimate goal of developing a zero-emission aircraft for commercial service by 2035. By modifying the GE PassportTM turbofan engine to run on hydrogen and using an A380 flying testbed equipped with liquid hydrogen tanks, the partnership showcases a commitment to environmental sustainability and making significant strides towards achieving net-zero carbon emissions in aviation.<ref>https://www.safran-group.com/pressroom/cfm-and-airbus-pioneer-hydrogen-combustion-technology-2022-02-22</ref>
The groundbreaking collaboration between CFM International and Airbus represents a crucial step in ushering in a new era of hydrogen-powered flight. With both companies' expertise and resources combined, they form an ideal team to successfully demonstrate hydrogen propulsion capabilities, reaffirming the aviation industry's dedication to environmentally friendly solutions. This ambitious project not only aligns with Airbus' commitment to net-zero carbon emissions but also highlights the industry's collective efforts to accelerate the development and adoption of hydrogen technology for a greener and more sustainable aviation future.
== ESG Performance and Sustainability Analysis ==
Sustainalytics conducts sustainability assessments for listed companies, evaluating their environmental, social, and governance performance. The assigned rating is derived from an ESG risk assessment, where the lowest score signifies the best extra-financial performance.
{| class="wikitable"
|+ ESG Risk Assessment (Environment, Social, and Governance)<ref>https://fr.finance.yahoo.com/quote/SAF.PA/sustainability/</ref>
|-
! Total ESG Risk Score
| '''23''' (Medium risk)
|-
! Environmental Risk Score
| 6.9
|-
! Social Risk Score
| 10.2
|-
! Governance Risk Score
| 5.8
|}
In the "Aerospace & Defense" sector, Safran has achieved an impressive rank, securing the 3rd position out of 89 companies. Notably, among companies with a market capitalization between $51 and $103 billion, Safran holds the 1st rank. This progress signifies an improvement from 2019, when Safran was ranked 6th out of 82 companies in the same sector.<ref>https://www.safran-group.com/news/constantly-improving-esg-extra-financial-ratings-2021-06-03</ref>


== Market ==
== Market ==
Line 407: Line 376:
== Financials ==
== Financials ==


=== Historic ===
=== Income Statement (In €) ===
 
==== Most recent year ====
In fiscal year 2022, Safran reported a significant increase in revenue, reaching €19.52 billion, which represents a remarkable growth of approximately 29% compared to the previous year's revenue of €15.13 billion. However, despite the revenue surge, the company also incurred a net loss of €2.46 billion during the same period.
 
==== Previous Four Years ====
Over the past four years, Safran's revenue has fluctuated, starting at $25.1 billion in 2019 and reaching $19.52 billion in 2022. During this period, the net income varied significantly, from $2.45 billion to a loss of $2.46 billion. These fluctuations reflect the challenges and changes in the aerospace industry.
 
==== Financial Performance Analysis ====
Safran has experienced a downturn in its financial performance over the last few years, and several factors may have contributed to this decline.
[[File:Safran metrics.png|center|thumb|500x500px|Safran Financial Performance Summary (2019-2022)]]
The first significant cause contributing to Safran's recent poor results is the Covid-19 pandemic, which led to a drastic shutdown in air traffic. As international travel and aviation activities were severely restricted, demand for aircraft engines and related products declined substantially, affecting Safran's revenue and profitability.
 
Another factor impacting Safran's financials is the increase in costs, particularly in raw materials. The rising costs of essential inputs for their manufacturing processes put pressure on their profit margins, making it challenging to maintain previous levels of profitability.
 
Additionally, currency fluctuations between the euro and the US dollar have played a role in the company's adverse results. Safran operates in a global market and conducts business in multiple currencies. Fluctuations in exchange rates can lead to uncertain revenues and costs, making financial planning and forecasting more challenging.
 
It's worth noting that these challenges are not unique to Safran alone, as the aerospace industry, like many others, has been significantly affected by the global economic disruptions caused by the pandemic.
 
== Risks ==
 
=== Market Risk ===
Demand Fluctuations: Changes in demand for commercial aircraft, defense equipment, and services due to economic conditions, geopolitical tensions, and technological advancements.
 
Cyclical Nature: Variations in sales and profits as the aerospace and defense industry experiences ups and downs in the economic cycle.
 
=== Regulatory and Political Risk ===
Export Control Regulations: Compliance with export controls and potential restrictions on selling certain technologies and equipment to specific countries.
 
Political Instability: Geopolitical tensions, conflicts, or changes in government policies in regions where Safran operates affecting business operations.
 
Environmental Regulations: Compliance with environmental regulations that may lead to additional costs for Safran and its operations.
 
=== Operational Risk ===
Supply Chain Disruptions: Risks associated with the complexity of Safran's supply chain for aerospace and defense products, leading to potential disruptions or delays.
 
Project Execution: Challenges in executing large-scale projects that could result in cost overruns and delays.
 
Safety Incidents: Risks associated with any safety-related incidents involving Safran's products or services, potentially leading to reputational damage and legal liabilities.
 
=== Technological and Competitive Risk ===
Rapid Technological Changes: The need to adapt to new technologies and maintain a competitive edge in the fast-paced aerospace and defense industry.
 
Intense Competition: Facing competition from both established and emerging companies in the aerospace and defense industry.
 
Cybersecurity Risk: Vulnerability to cyberattacks and data breaches due to the increasing reliance on digital technologies in aerospace and defense.
 
== Valuation ==
===What's the Current Value of Safran?===
As of 26th July 2023, the stock of Safran closed at 144.82€ per share, demonstrating a steady recovery from the impact of the Covid-19 pandemic. The current stock price is approaching its historical peak value of 148.45€, which was recorded in November 2019, indicating positive momentum in the market.
{| class="wikitable"
|+
! colspan="4" |Safran Current Valuation - July 2023
|-
|Share Price (@30/07)
|[€]
|
|'''144.82'''
|-
|Shares Outstanding
|[#M]
|
|426.5
|-
|Equity Value
|[€B]
|
|61.77
|-
|Add:
Net Debt at Dec. 31, 2022
|[€M]
|
|14
|-
|'''Enterprise Value'''
|[€B]
|
|'''61.78'''
|}
 
In our analysis of Safran's valuation, we employed three distinct methods:
#'''Discounted Cashflow''': With a discount rate of 8.7% and a long-term growth rate of 1.7%, the Perpetuity approach values Safran shares at '''152.32€''', while the EBITDA approach results in a valuation of '''140.35€'''. Given Safran's current stock price of '''144.82€''', it appears '''undervalued''' relative to the discounted cash flow (DCF) model valuation.
#'''Trading Comps''': The negative income and EBITDA figures made it impractical to apply the P/E or EV/EBITDA ratios in this case. This straightforward analysis makes it evident that the company is considered '''overvalued''' when utilizing the PB ratio. The current market value per share is 144.82€, whereas our analysis, based on the PB ratio, estimates it to be '''101.87€.'''
#'''Dividend Discount Model''': In 2019, Safran encountered challenges that led to the inability to pay dividends. However, the company has demonstrated a consistent track record of paying fair dividends in the preceding years. To assess Safran's valuation, we utilized the Gordon Growth Model (GGM) by projecting the past dividend growth rate to estimate the 2023 dividend. The GGM valuation resulted in a per-share value of '''19.67€'''. Assuming market efficiency, i.e. the current share price is correct, the adequate cost of equity of Safran would be  '''2.64%'''.
 
=== What's the expected return of an Investment in the Company? ===
Based on our DCF model and the current market value, the Stockhub users estimate that the expected return of an investment in Safran over the next five years is approximately '''5.21%'''. In practical terms, this means that a £1,000 investment in Safran is projected to grow to £1,052.10 in five years' time.
 
Assuming that a suitable return level over five years is 10% per year and  achieves its expected return level (of 5.21%), then an investment in the company is considered to be an '''<nowiki/>'unsuitable'''' one.
 
== Monte Carlo Simulations ==
 
=== Data ===
Introducing our cutting-edge Monte Carlo simulation for Safran's stock price analysis! By harnessing the power of this advanced computational method, we aim to provide you with invaluable insights into the potential behavior of Safran's stocks over time.
[[File:Sfran stock.png|none|thumb|500x500px|Historical price of Safran's equity]]
Our Monte Carlo simulation involves running thousands of random simulations based on a variety of input variables, including historical price data, volatility, and other essential market factors. Through this approach, we generate a comprehensive probability distribution of possible outcomes, enabling you to assess the potential risk and returns associated with investing in Safran.
[[File:Log distr.png|none|thumb|400x400px|Logarithmic distribution of past prices]]
 
=== Simulations ===
With our simulation, you can make data-driven decisions and gain a deeper understanding of the uncertainty surrounding the stock's performance. Embrace the future of equity research and explore the vast range of possibilities to optimize your investment strategies effectively.
[[File:MC simu.png|none|thumb|500x500px|Price paths of Safran's stock 50 days in the future for 100 simulations]]
Through our Monte Carlo simulations, we have the ability to visualize numerous paths for 100 simulations, offering a glimpse into the potential outcomes. However, to gain a deeper and more comprehensive understanding of the results, we recommend running a larger number of simulations. By doing so, we can effectively construct probability distributions that highlight the likelihood of Safran's stock price being at certain levels. This will provide a more accurate and insightful analysis, enabling you to make informed decisions with confidence.
[[File:SImu dis.png|none|thumb|500x500px|Final stock price distribution in 50 days for 1,000,000 simulations]]
From this analysis, it becomes evident that the current valuation on the 28th of July 2023, at 147.98€, appears to be somewhat inflated when we examine the Gaussian curve. The distribution of prices is skewed towards the left side of the curve, indicating a higher concentration of lower price points.
 
Please note that we utilized the article "''Monte Carlo Simulations for Stock Price Predictions [Python]''" authored by ''Elias Melul'' as a reference to develop our Python code for running the simulations. You can find the complete Python code in the appendix section.<ref>https://medium.com/analytics-vidhya/monte-carlo-simulations-for-predicting-stock-prices-python-a64f53585662</ref>
 
== Appendix ==
 
=== Financial statements ===
 
==== Income Statement (In €) ====
{| class="wikitable"
{| class="wikitable"
|+
|+
Line 585: Line 442:
|962,000
|962,000
|-
|-
|'''Net Income Common Stockholders'''
|Net Income Common Stockholders
| -4,393,000
| -4,393,000
| -2,459,000
| -2,459,000
Line 746: Line 603:
|9,692
|9,692
|}
|}
==== Balance Sheet (In €) ====
{| class="wikitable"
|+
!Year end date
!12/31/2022
!12/31/2021
!12/31/2020
!12/31/2019
|-
|'''Total Assets'''
|46,828,000
|41,716,000
|39,531,000
|42,808,000
|-
|'''Total  Liabilities Net Minority Interest'''
|35,962,000
|28,446,000
|26,781,000
|30,060,000
|-
|'''Total Equity Gross Minority  Interest'''
|10,866,000
|13,270,000
|12,750,000
|12,748,000
|-
|Total  Capitalization
|15,610,000
|17,750,000
|16,363,000
|15,507,000
|-
|Common Stock Equity
|10,411,000
|12,841,000
|12,349,000
|12,371,000
|-
|Capital  Lease Obligations
|587,000
|609,000
|608,000
|729,000
|-
|Net Tangible Assets
| -2,679,000
| -609,000
| -1,387,000
| -2,307,000
|-
|Working  Capital
| -2,479,000
|755,000
| -838,000
| -2,804,000
|-
|Invested Capital
|16,781,000
|19,373,000
|18,758,000
|18,926,000
|-
|Tangible  Book Value
| -2,679,000
| -609,000
| -1,387,000
| -2,307,000
|-
|Total Debt
|6,957,000
|7,141,000
|7,017,000
|7,284,000
|-
|Net  Debt
| -
|1,285,000
|2,662,000
|3,923,000
|-
|Share Issued
|427,246
|427,242
|427,236
|427,234
|-
|Ordinary  Shares Number
|424,559
|426,786
|426,917
|424,684
|-
|Treasury Shares Number
|2,687
|456.165
|319.284
|2,550
|}
==== Cash Flow (In €) ====
{| class="wikitable"
|+
!Year end date
!TTM
!12/31/2022
!12/31/2021
!12/31/2020
!12/31/2019
|-
|Operating Cash Flow
|3,478,000
|3,545,000
|2,436,000
|1,866,000
|3,145,000
|-
|Investing  Cash Flow
| -870,000
| -1,288,000
| -738,000
| -799,000
| -1,105,000
|-
|Financing Cash Flow
| -368,000
| -815,000
| -268,000
|68,000
| -1,740,000
|-
|End  Cash Position
|6,167,000
|6,687,000
|5,247,000
|3,747,000
|2,632,000
|-
|Changes in Cash
|2,240,000
|1,442,000
|1,430,000
|1,135,000
|300,000
|-
|Effect  of Exchange Rate Changes
|41,000
|2,000
|70,000
| -20,000
|2,000
|-
|Beginning Cash Position
|3,927,000
|5,247,000
|3,747,000
|2,632,000
|2,330,000
|-
|Other  Cash Adjustment Outside Change in Cash
| -4,000
| -4,000
| -
| -
| -
|-
|Capital Expenditure
| -834,000
| -879,000
| -756,000
| -793,000
| -1,162,000
|-
|Issuance  of Capital Stock
|0
|0
|1,000
| -
| -
|-
|Issuance of Debt
|509,000
|510,000
|2,146,000
|1,595,000
|24,000
|-
|Repayment  of Debt
| -613,000
| -671,000
| -1,367,000
| -778,000
| -875,000
|-
|Repurchase of Capital Stock
|0
| -270,000
| -73,000
| -
| -
|-
|Free  Cash Flow
|2,644,000
|2,666,000
|1,680,000
|1,073,000
|1,983,000
|}
=== '''Discounted Cashflow model (DCF)''' ===
==== Key inputs ====
{| class="wikitable"
!Description
!Value
!Commentary
|-
|Discount rate (%)
| 8.2%
|The application of the weighted average cost of capital (WACC) formula was used to compute the discount rate for future cash flows.
|-
|Long term growth rate (%)
|1.7%
|We used the growth rate of you Dividend Discount Model.
|-
|Corporate Tax Rate (%)
|25%
|According to the new French legislation, the Corporate Tax Rate should be at 25%
as from 1 January 2022.<ref>https://www.economie.gouv.fr/files/files/Actus2018/dp_plf2019.pdf</ref>
|}
For this model, we use the WACC model to compute the discount rate for the future cash flows.
{| class="wikitable"
!Cost of equity
|8.68%
|-
!Cost of debt
|5.00%
|-
!Tax rate
|25.00%
|-
!Debt
|6,957
|-
!Equity (Current market cap)
|65,010
|-
!D/(D+E)
|10%
|-
!E/(D+E)
|90%
|-
!WACC
|'''8.20%'''
|}
==== Safran Unlevered Free Cash Flows ====
{| class="wikitable"
|-
!Period (t)
!2019A
!2020A
!2021A
!2022A
!2023P
!2024P
!2025P
!2026P
!2027P
|-
| colspan="10" |
|-
!EBITDA
|5830
|2962
|2825
|3,498
|3,673
|3,857
|4,049
|4,252
|4,464
|-
!EBIT
|4,695
|1,706
|1,489
|1,958
|1,950
|1,928
|1,892
|1,838
|1,763
|-
!Tax rate
|26.30%
|27.50%
|34.40%
|31.4%
|25.0%
|25.0%
|25.0%
|25.0%
|25.0%
|-
| colspan="10" |
|-
!EBIT (1-t)
|3,460
|1,237
|977
|1,343
|1,462
|1,446
|1,419
|1,378
|1,322
|-
!D&A
|1135
|1256
|1336
|1,540
|1,723
|1,928
|2,157
|2,414
|2,701
|-
!NWC
|2,804
|838
|(755)
|2,479
|2,256
|2,053
|1,868
|1,700
|1,547
|-
!Capital expenditures
|(1,162)
|(793)
|(756)
|(879)
|(919)
|(960)
|(1,003)
|(1,048)
|(1,095)
|-
!Unlevered free cash flows  (UFCF)
|6,237
|2,538
|802
|4,483
|4,523
|4,467
|4,441
|4,444
|4,475
|-
| colspan="10" |
|-
!Discount rate (r)
|
|
|
|
|8.7%
|8.7%
|8.7%
|8.7%
|8.7%
|-
!PV of UFCFs
|
|
|
|
|4,180
|3,816
|3,506
|3,242
|3,018
|-
| colspan="10" |
|-
!Stage 1: Sum of present values
|'''17,762'''
|
|
|
|
|
|
|
|
|}
==== Terminal value - growth in perpetuity approach ====
{| class="wikitable"
!Long term growth rate
|1.7%
|-
!2022 FCF x (1+g)
|4,551
|-
!Terminal value in 2022
|69,979
|-
!Stage 2: PV of TV
|47,187
|-
|
|
|-
!Enterprise value (stage 1 + 2)
|'''64,949'''
|}
==== Terminal value - EBITDA multiple approach ====
{| class="wikitable"
!EBITDA  multiple
|14.0x
|-
!Terminal  value in 2022
|62,413
|-
!Stage  2: PV of TV
|42,085
|-
|
|
|-
!Enterprise  value (stage 1 + 2)
|'''59,847'''
|}
==== Net debt ====
{| class="wikitable"
|Data as of:
|29/07/2023
|-
!Net debt
|'''(14)'''
|}
==== Equity valuations ====
{| class="wikitable"
|
!Perpetuity approach
!EBITDA approach
|-
!Equity  value
|'''152.32 €'''
|'''140.35 €'''
|}
==== Sensitivity analysis ====
{| class="wikitable"
| colspan="2" rowspan="2" |
! colspan="5" |Constant Growth rate
|-
|''0.7%''
|''1.2%''
|'''''1.7%'''''
|''2.2%''
|''2.7%''
|-
! rowspan="7" |WACC
|''7.0%''
|162.61  €
|173.56  €
|186.49  €
|202.31  €
|221.70  €
|-
|''7.4%''
|152.93  €
|162.42  €
|173.51  €
|186.89  €
|203.02  €
|-
|''7.8%''
|144.35  €
|152.64  €
|162.22  €
|173.66  €
|187.26  €
|-
|'''''8.2%'''''
|136.68  €
|143.97  €
|'''152.32 €'''
|162.20  €
|173.80  €
|-
|''8.6%''
|129.79  €
|136.24  €
|143.58  €
|152.17  €
|162.16  €
|-
|''9.0%''
|123.56  €
|129.30  €
|135.78  €
|143.32  €
|151.99  €
|-
|''9.4%''
|117.90  €
|123.04  €
|128.80  €
|135.45  €
|143.04  €
|}
=== Trading Comparables (Comps) ===
As mentioned earlier, the negative income and EBITDA figures make it impractical to use the P/E or EV/EBITDA ratios in this case. Different valuation approaches and more comprehensive analyses are needed to accurately assess the company's financial health and potential.
For that matter we decided to use the Price-to-Book (PB) ratio, we collected the PB ratio for similar companies operting in the aerospace and defense sector. Rolls-Royce having a negative PB ratio, we left it out of our analysis.
{| class="wikitable"
!Company Name
!PB ratio
|-
|Airbus SE (EPA: AIR)
|7.32
|-
|Thales  Group (EPA: HO)
|3.86
|-
|<s>Rolls-Royce  Holdings plc (LSE: RR.)</s>
|<s>-2.75</s>
|-
|General Electric Company (NYSE:  GE)
|3.8
|-
!Average
|4.99
|-
!Median
|'''3.86'''
|}
We can then deduce the price per share using the median PB ratio.
{| class="wikitable"
! colspan="6" |Calculating the price based on PB ratio
|-
|Price
|Shares  Outstanding
|Book value
|Total assets
|Intangible  assets
|Total  liabilities
|-
|'''101.87 €'''
|426,500,000
|11,256,000,000.00 €
|46,828,000,000.00 €
|8,096,000,000.00 €
|27,476,000,000.00 €
|}
Based on this straightforward analysis, it becomes evident that the company is deemed overvalued, given its current market value per share of 144.82€ in contrast to the value of 101.87€ calculated through our analysis. However, if we solely rely on the Airbus PB (Price-to-Book) ratio, the estimated price per share would be 193.19 €, indicating an even higher level of overvaluation in this instance.
This demonstrates the limited usefulness of the Comps analysis in accurately determining the company's true value and highlights the need for incorporating multiple valuation metrics and methodologies to gain a more comprehensive understanding of its market worth.
=== Dividend Discount Model (DDM) ===
==== Equity valuation ====
In the following table, we present the key values used in a DDM (Dividend Discount Model) analysis, including the CAPM model, risk-free rate of return, beta, market rate of return, and the corresponding cost of equity.
{| class="wikitable"
!CAPM model
|Values
|-
|Risk-free rate of return (Euro  short-term rate (€STR))
|3.41%
|-
|Beta  (5Y Monthly, levered)
|1.35
|-
|Market rate of return (European  Stocks Portfolio)
|7.31%
|-
|Cost of equity
|8.7%
|}
The graphical representation below illustrates the dividend history of Safran over the past years, showcasing the annual dividends paid, including the notable occurrence of zero dividends in the year 2019.
[[File:Dividends.png|left|thumb|600x600px]]
{| class="wikitable"
!Year
!2011
!2012
!2013
!2014
!2015
!2016
!2017
!2018
!2019
!2020
!2021
!2022
|-
!Dividend per share
|0.62
|0.96
|1.12
|1.20
|1.38
|1.52
|1.60
|1.82
|0.00
|0.43
|0.50
|1.35
|}
To evaluate Safran's valuation, we applied the Gordon Growth Model (GGM), projecting the historical dividend growth rate from 2011 to 2018 to estimate the current growth rate starting from 2022. By doing so, we can make an estimation of the 2023 dividend.
{| class="wikitable"
!Period
|/
!2011-
2012
!2012-2013
!2013-2014
!2014-2015
!2015-2016
!2016-2017
!2017-2018
|-
!Dividend Growth Rate
|/
|0.55
|0.17
|0.07
|0.15
|0.10
|0.05
|0.14
|-
!Average  Growth Rate
|0.18
| colspan="7" rowspan="3" |
|-
!CAGR
|0.14
|-
!Constant  growth rate
|'''0.017'''
|}
The DDM value of '''19.67 €''' suggests that, according to the model's assumptions, the stock is overvalued relative to its intrinsic worth. On the other hand, the market value of 144.82 € reflects the collective perception of investors in the open market, which may be influenced by a variety of short-term and long-term factors.
{| class="wikitable"
!Value  per Share (DDM)
| '''                  19.67 €'''
|-
!Market value per share
|                144.82 €
|}
We also performed a sensitivity analysis.
{| class="wikitable"
|
! colspan="8" |Constant Growth rate
|-
! rowspan="8" |Cost of equity
|
|''1.1%''
|''1.3%''
|''1.5%''
|''1.7%''
|''1.9%''
|''2.1%''
|''2.3%''
|-
|''6.5%''
|25.37  €
|26.40  €
|27.51  €
|28.72  €
|30.04  €
|31.47  €
|33.04  €
|-
|''7.5%''
|21.39  €
|22.13  €
|22.91  €
|23.75  €
|24.65  €
|25.62  €
|26.66  €
|-
|''8.5%''
|18.49  €
|19.05  €
|19.63  €
|20.25  €
|20.91  €
|21.60  €
|22.35  €
|-
|''8.7%''
|18.01  €
|18.53  €
|19.08  €
|'''19.67 €'''
|20.29  €
|20.95  €
|21.65  €
|-
|''8.9%''
|17.54  €
|18.04  €
|18.57  €
|19.12  €
|19.71  €
|20.33  €
|20.99  €
|-
|''9.9%''
|15.54  €
|15.94  €
|16.35  €
|16.78  €
|17.24  €
|17.72  €
|18.22  €
|-
|''10.9%''
|13.96  €
|14.27  €
|14.61  €
|14.96  €
|15.32  €
|15.70  €
|16.10  €
|}
==== Inverse problem ====
In this section, our objective is to calculate the necessary growth rate of Safran's stock to achieve its market value, assuming market efficiency. To achieve this, we will simply reverse the GGM formula to derive the cost of equity.
{| class="wikitable"
|
|Inverse problem
|-
!Market value per share
|144.82 €
|-
!Expected  dividend per share
|1.37 €
|-
!Dividend  growth rate
|1.70%
|-
!Cost of equity
|'''2.64%'''
|}
The cost of equity of 2.64% for Safran represents the expected return or required rate of return that investors demand for holding the company's stock. A low cost of equity, such as 2.64%, indicates that investors perceive Safran as a relatively safe and stable investment.
=== Monte Carlo Simulations for Stock Price Predictions - Python Code ===
<syntaxhighlight lang="python">
"""
Created on Thu Jul 27 18:31:35 2023
@author: Jérémy Archier
"""
import csv
import matplotlib.pyplot as plt
import numpy as np
from datetime import datetime, timedelta
from scipy.stats import norm
# Step 1: Load data from the CSV file
csv_file_path = "SAF.PA.csv"
dates = []
opens = []
with open(csv_file_path, newline="") as csvfile:
    csv_reader = csv.DictReader(csvfile)
    for row in csv_reader:
        # Check if the 'Open' value is 'null' or empty or 0
        if row['Open'].strip() == '' or row['Open'].lower() == 'null' or float(row['Open']) == 0:
            # Skip the data point if there is no valid 'Open' value
            continue
        # Convert the 'Open' value to a float
        open_value = float(row['Open'])
        # Convert the 'Date' value to a datetime object
        date_value = datetime.strptime(row['Date'], '%Y-%m-%d')
        # Append the 'Date' and 'Open' values to their respective lists
        dates.append(date_value)
        opens.append(open_value)
# Step 2: Compute the logarithmic returns of the stock
log_returns = np.log(np.array(opens[1:]) / np.array(opens[:-1]))
# Plot the previous prices
plt.figure(figsize=(10, 5))
plt.plot(dates, opens, linestyle='-', color='b')
plt.xlabel('Date')
plt.ylabel('Open Value')
plt.title('Open Value as a Function of Dates')
plt.xticks(rotation=45)
plt.grid(True)
plt.tight_layout()
plt.show()
# Plot the log returns
plt.figure(figsize=(6, 5))
plt.hist(log_returns, bins=30, edgecolor='k')
plt.xlabel("Logarithmic Returns")
plt.ylabel("Frequency")
plt.title("Distribution of Logarithmic Returns")
plt.grid(True)
plt.tight_layout()
plt.show()
# Step 3: Compute the Drift
u = log_returns.mean()
var = log_returns.var()
drift = u - (0.5 * var)
# Step 4: Compute the Variance and Daily Returns
stdev = log_returns.std()
days = 50
trials = 1000000  # Reduce the number of trials to 100 for faster computation
Z = norm.ppf(np.random.rand(days, trials))  # days, trials
daily_returns = np.exp(drift + stdev * Z)
# Step 5: Calculating the stock price for every trial
price_paths = np.zeros_like(daily_returns)
price_paths[0] = opens[-1]
for t in range(1, days):
    price_paths[t] = price_paths[t - 1] * daily_returns[t]
# Step 6: Calculate the probability of reaching the target price
target_price = 150.0  # Replace this with the desired target price
# Count how many times the stock price reaches or exceeds the target price in each trial
success_count = np.sum(price_paths[-1, :] >= target_price)
# Calculate the probability as the ratio of successful trials to total trials
probability = success_count / trials
# Print the probability
print(f"The probability of the stock reaching or exceeding {target_price} is: {probability:.2%}")
# Step 7: Plot the histogram of final stock prices
final_prices = price_paths[-1, :]
plt.figure(figsize=(10, 6))
plt.hist(final_prices, bins=30, edgecolor='k', density=True)
plt.axvline(x=target_price, color='r', linestyle='dashed', linewidth=2, label=f'Target Price ({target_price})')
plt.xlabel('Stock Price')
plt.ylabel('Probability Density')
plt.title('Probability Distribution of Final Stock Prices')
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()
# Step 8: Plot the price paths for each trial
plt.figure(figsize=(10, 6))
for trial in range(trials):
    trial_dates = [dates[-1] + timedelta(days=i) for i in range(days)]
    plt.plot(trial_dates, price_paths[:, trial], linewidth=0.5)
plt.xlabel('Date')
plt.ylabel('Stock Price')
plt.title('Monte Carlo Simulation of Stock Price')
plt.tight_layout()
plt.grid(True)
plt.show()
</syntaxhighlight>


== References ==
== References ==
__INDEX__
__INDEX__
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