Deutsche Rohstoff AG (DR0.DE) Discounted Free Cash Flow - Perpetuity

Deutsche Rohstoff AG

DR0.DE (XETRA)

Valuation
Deutsche Rohstoff AG Discounted Free Cash Flow - Perpetuity

"""
    Model: Discounted Free Cash Flow - Perpetuity

# Render model description
model.render_description(r"""
## Discounted Free Cash Flow Model

Discounted Free Cash Flow calculates the value of a share based on the company's estimated future Free Cash Flow figures.

See our [GitHub Model Documentation](https://github.com/DiscountingCashFlows/Documentation/blob/main/models-documentation/discounted-free-cash-flow.md#discounted-free-cash-flow-model-source-code)
""")

# Initialize assumptions
assumptions.init({
    "data": {
        "%discount_rate": None,
        "beta": data.get("profile:beta", default=1),
        "%risk_free_rate": data.get("treasury:year10"),
        "%market_premium": data.get("risk:totalEquityRiskPremium"),
        "%growth_in_perpetuity": data.get("treasury:year10"),
        "historical_years": 10,
        "projection_years": 5,
        "%revenue_growth_rate": None,
        "%operating_cash_flow_margin": None,
        "%capital_expenditure_margin": None,
    },
    "hierarchies": [{
        "parent": "%discount_rate",
        "children": ["beta", "%risk_free_rate", "%market_premium"]
    }]
})

# WACC Calculation
risk_free_rate = assumptions.get("%risk_free_rate")
beta = assumptions.get("beta")
market_premium = assumptions.get("%market_premium")
cost_of_equity = risk_free_rate + beta * market_premium
cost_of_debt = data.get("income:interestExpense") / data.get("balance:totalDebt")

tax_rate = data.get("income:incomeTaxExpense") / data.get("income:incomeBeforeTax")

if tax_rate < 0:
    tax_rate = 0

market_cap = data.get("profile:price") * data.get("income:weightedAverageShsOut")
debt_weight = data.get("balance:totalDebt") / (market_cap + data.get("balance:totalDebt"))
equity_weight = 1 - debt_weight
wacc = debt_weight * cost_of_debt * (1 - tax_rate) + equity_weight * cost_of_equity

# Set the discount rate to the WACC
assumptions.set("%discount_rate", wacc)

data.compute({
    "%operatingCashFlowMargin": "flow:operatingCashFlow / income:revenue",
    "%capitalExpenditureMargin": "flow:capitalExpenditure / income:revenue",
    "%grossMargin": "income:grossProfit / income:revenue",
    "%operatingMargin": "income:operatingIncome / income:revenue",
    "%netMargin": "income:netIncome / income:revenue",
    "discountedFreeCashFlow": "flow:freeCashFlow",
    "%revenueGrowthRate": "function:growth:income:revenue",
})

average_revenue_growth_rate = data.average(f"%revenueGrowthRate:{-assumptions.get('historical_years')}->0")
assumptions.set("%revenue_growth_rate", average_revenue_growth_rate)

average_operating_cash_flow_margin = data.average(f"%operatingCashFlowMargin:{-assumptions.get('historical_years')}->0")
assumptions.set("%operating_cash_flow_margin", average_operating_cash_flow_margin)

average_capital_expenditure_margin = data.average(f"%capitalExpenditureMargin:{-assumptions.get('historical_years')}->0")
assumptions.set("%capital_expenditure_margin", average_capital_expenditure_margin)

data.compute({
    "linearRegressionRevenue": f"""
        function:linear_regression:income:revenue 
        start:{-assumptions.get('historical_years')}
    """,
}, forecast=assumptions.get("projection_years"))

data.compute({
    "income:revenue": f"""
        function:compound:{data.get('linearRegressionRevenue:1')} 
        rate:{assumptions.get('%revenue_growth_rate')}
        offset:-1
    """,
    "%revenueGrowthRate": "function:growth:income:revenue",
    "flow:operatingCashFlow": f"income:revenue * {assumptions.get('%operating_cash_flow_margin')}",
    "computedCapitalExpenditure": f"income:revenue * {assumptions.get('%capital_expenditure_margin')}",
    "flow:freeCashFlow": "flow:operatingCashFlow + computedCapitalExpenditure",
    "flow:capitalExpenditure": "flow:freeCashFlow - flow:operatingCashFlow",
    "discountedFreeCashFlow": f"""
        function:discount:flow:freeCashFlow 
        rate:{assumptions.get('%discount_rate')}
        continuous:true
    """,
    # Informational computations
    "%operatingCashFlowMargin": "flow:operatingCashFlow / income:revenue",
    "%capitalExpenditureMargin": "flow:capitalExpenditure / income:revenue",
    "%freeCashFlowMargin": "flow:freeCashFlow / income:revenue",
    "#compoundedDiscountRate": f"""
        function:compound:1
        rate:{assumptions.get('%discount_rate')} 
        continuous:true
    """,
    "%compoundedDiscountRate": "#compoundedDiscountRate - 1",
}, forecast=assumptions.get("projection_years"))

# Calculating the Terminal Value
# TV = FCF * (1 + Growth in Perpetuity) / (Discount Rate - Growth in Perpetuity)
terminal_value = \
    data.get(f"flow:freeCashFlow:{assumptions.get('projection_years')}") * \
    (1 + assumptions.get("%growth_in_perpetuity")) / \
    (assumptions.get("%discount_rate") - assumptions.get("%growth_in_perpetuity"))

# Discount the terminal value into the present
tv_discount_rate = (1 + assumptions.get("%discount_rate")) ** assumptions.get('projection_years')
discounted_terminal_value = terminal_value / tv_discount_rate

# Get the sum between current date and projection years
discounted_free_cash_flow_sum = data.sum("discountedFreeCashFlow:1->*")

# Add all Discounted FCFs and the Discounted Terminal Value to calculate the enterprise value
enterprise_value = discounted_terminal_value + discounted_free_cash_flow_sum

# Equity value is calculated by adding cash and subtracting total debt from the enterprise value
equity_value = enterprise_value + data.get("balance:cashAndShortTermInvestments") - \
               data.get("balance:totalDebt")

stock_value = equity_value / data.get("income:weightedAverageShsOut")

model.set_final_value({
    "value": stock_value,
    "units": '$'
})

model.render_results([
    [terminal_value, "Terminal Value", "$"],
    [discounted_terminal_value, "Discounted Terminal Value", "$"],
    [discounted_free_cash_flow_sum, "Sum of Discounted Free Cash Flow", "$"],
    [enterprise_value, "Enterprise Value", "$"],
    [data.get("balance:cashAndCashEquivalents"), "Cash and Equivalents", "$"],
    [data.get("balance:totalDebt"), "Total Debt", "$"],
    [equity_value, "Equity Value", "$"],
    [data.get("income:weightedAverageShsOut"), "Shares Outstanding", "$"],
    [stock_value, "Estimated Value per Share", "$"],
    [data.get("treasury:year10"), "Yield of the U.S. 10 Year Treasury Note", "%"],
    [average_operating_cash_flow_margin, "Average Cash from Operating Activities Margin", "%"],
    [average_capital_expenditure_margin, "Average Capital Expenditure Margin", "%"],
    [cost_of_equity, "Cost of Equity", "%"],
    [equity_weight, "Equity Weight", "%"],
    [cost_of_debt, "Cost of Debt", "%"],
    [debt_weight, "Debt Weight", "%"],
    [tax_rate, "Tax Rate", "%"],
])

model.render_chart({
    "data": {
        "income:revenue": "Revenue",
        "flow:operatingCashFlow": "Operating Cash Flow",
        "flow:freeCashFlow": "Free Cash Flow",
        "flow:capitalExpenditure": "Capital Expenditure",
        "linearRegressionRevenue": "Linear Regression Revenue Line",
        "discountedFreeCashFlow": "Discounted Free Cash Flow"
    },
    "start": -assumptions.get("historical_years"),
    "end": "*",
    "properties": {
        "title": "Historical Values",
        "set_editable": [
            "income:revenue",
            "flow:operatingCashFlow",
            "flow:freeCashFlow"
        ],
        "hidden_keys": [
            "flow:capitalExpenditure",
            "linearRegressionRevenue",
            "discountedFreeCashFlow"
        ],
        "number_format": "M",
        "width": "full"
    },
})

# Forecast table
model.render_table({
    "data": {
        "income:revenue": "Revenue",
        "%revenueGrowthRate": "Revenue Growth Rate",
        "flow:operatingCashFlow": "Operating Cash Flow",
        "%operatingCashFlowMargin": "Operating Cash Flow Margin",
        "flow:capitalExpenditure": "Capital Expenditure",
        "%capitalExpenditureMargin": "Capital Expenditure Margin",
        "flow:freeCashFlow": "Free Cash Flow",
        "%freeCashFlowMargin": "Free Cash Flow Margin",
        "%compoundedDiscountRate": "Compounded Discount Rate",
        "discountedFreeCashFlow": "Discounted Free Cash Flow",
    },
    "start": -1,
    "end": "*",
    "properties": {
        "title": "Forecast Data",
        "order": "ascending",
        "include_ltm": False,
        "number_format": "M",
        "width": "full"
    },
})

# Historical table
model.render_table({
    "data": {
        "income:revenue": "Revenue",
        "%revenueGrowthRate": "Revenue Growth Rate",
        "income:costOfRevenue": "Cost of Revenue",
        "income:grossProfit": "Gross Profit",
        "%grossMargin": "Gross Margin",
        "income:operatingIncome": "Operating Income",
        "%operatingMargin": "Operating Margin",
        "income:netIncome": "Net Income",
        "%netMargin": "Net Margin",
        "flow:operatingCashFlow": "Cash from Operating Activities",
        "%operatingCashFlowMargin": "Cash from Operating Activities Margin",
        "flow:capitalExpenditure": "Capital Expenditure",
        "flow:freeCashFlow": "Free Cash Flow",
    },
    "start": -assumptions.get("historical_years"),
    "end": 0,
    "properties": {
        "title": "Historical Data",
        "display_averages": True,
        "order": "descending",
        "number_format": "M"
    },
})

assumptions.set_description({
    "%discount_rate": r"""
        ## Discount Rate
        
        `Discount Rate` = `Equity Weight` * `Cost of Equity` + `Debt Weight` * `Cost of Debt` * (1 - `Tax Rate`)
        
        Calculated using Weighted Average Cost of Capital (WACC) formula. It represents a firm’s average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt.
        
        [Read More](https://www.investopedia.com/terms/w/wacc.asp)
        
        ---
        
        ### Cost of Equity
        
        `Cost of Equity` = `Risk Free Rate` + `Beta` * `Market Premium`
        
        The cost of equity is the theoretical rate of return that an equity investment should generate. It is calculated using the CAPM formula.
        
        [Read More](https://www.investopedia.com/terms/c/costofequity.asp#mntl-sc-block_1-0-20)
        
        ---
        
        ### Cost of Debt
        
        `Cost of Debt` = `Interest Expense` / `Total Debt`
        
        The cost of debt is the effective rate that a company pays on its debt, such as bonds and loans.
        
        [Read More](https://www.investopedia.com/terms/c/costofdebt.asp)
        
        ---
        
        ### Equity & Debt Weights
        
        `Debt Weight` = `Total Debt` / (`Market Capitalization` + `Total Debt`) = 1 - `Equity Weight`
        
        The Equity Weight represents the proportion of equity-based financing (Market Capitalization), while the Debt Weight represents the proportion of debt-based financing (Total Debt).
        
        ---
        
        ### Tax Rate
        
        `Tax Rate` = `Income Tax Expense` / `Income Before Tax`
        
        The overall tax rate paid by the company on its earned income.
    """,

"beta": r"""
        ## Beta
        
        Beta measures the volatility of a stock's price in relation to the overall stock market. A higher beta indicates greater price fluctuations relative to the market.
    """,

"%risk_free_rate": r"""
        ## Risk-Free Rate
        
        The risk-free rate represents the return an investor expects from an absolutely risk-free investment over a specified time period. By default, it is set to the current yield of the U.S. 10-Year Treasury Bond.
    """,

"%market_premium": r"""
        ## Market Premium
        
        The market risk premium represents the additional return over the risk-free rate that investors expect for taking on the risks associated with equities.
    """,

"%growth_in_perpetuity": r"""
        ## Growth in Perpetuity
        
        The rate at which the company's free cash flow is assumed to grow indefinitely. By default, this rate equals the yield of the U.S. 10-Year Treasury Bond.
    """,

"historical_years": r"""
        ## Historical Years
        
        The number of years of historical data used to calculate averages and trends for analysis.
    """,

"projection_years": r"""
        ## Projection Years
        
        The number of years into the future for which the analysis projects financial performance and metrics.
    """,

"%revenue_growth_rate": r"""
        ## Revenue Growth Rate
        
        The annual growth rate applied to projected revenue, starting from the second projection year onward.
    """,

"%operating_cash_flow_margin": r"""
        ## Operating Cash Flow Margin
        
        `Projected Operating Cash Flow` = `Projected Revenue` * `Operating Cash Flow Margin`
        
        This margin represents the percentage of revenue used to estimate future Operating Cash Flow.
    """,

"%capital_expenditure_margin": r"""
        ## Capital Expenditure Margin
        
        `Projected Free Cash Flow` = `Projected Operating Cash Flow` - `Projected Revenue` * `Capital Expenditure Margin`
        
        This margin is used to estimate future capital expenditures as a percentage of revenue, which in turn is subtracted from Operating Cash Flow to calculate Free Cash Flow.
    """,
})

print(f"End of model.")

Estimated Value

EUR

Market Price EUR

* Values are not guaranteed, please do your own
research before making investment decisions.

Discounted Free Cash Flow Model

Discounted Free Cash Flow calculates the value of a share based on the company's estimated future Free Cash Flow figures.

See our GitHub Model Documentation

Interactive Assumptions

Discount Rate Discount Rate `Discount Rate` = `Equity Weight` * `Cost of Equity` + `Debt Weight` * `Cost of Debt` * (1 - `Tax Rate`) Calculated using Weighted Average Cost of Capital (WACC) formula. It represents a firm’s average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt. Read More Cost of Equity `Cost of Equity` = `Risk Free Rate` + `Beta` * `Market Premium` The cost of equity is the theoretical rate of return that an equity investment should generate. It is calculated using the CAPM formula. Read More Cost of Debt `Cost of Debt` = `Interest Expense` / `Total Debt` The cost of debt is the effective rate that a company pays on its debt, such as bonds and loans. Read More Equity & Debt Weights `Debt Weight` = `Total Debt` / (`Market Capitalization` + `Total Debt`) = 1 - `Equity Weight` The Equity Weight represents the proportion of equity-based financing (Market Capitalization), while the Debt Weight represents the proportion of debt-based financing (Total Debt). Tax Rate `Tax Rate` = `Income Tax Expense` / `Income Before Tax` The overall tax rate paid by the company on its earned income.	%
↳ Beta Beta Beta measures the volatility of a stock's price in relation to the overall stock market. A higher beta indicates greater price fluctuations relative to the market.	#
↳ Risk Free Rate Risk-Free Rate The risk-free rate represents the return an investor expects from an absolutely risk-free investment over a specified time period. By default, it is set to the current yield of the U.S. 10-Year Treasury Bond.	%
↳ Market Premium Market Premium The market risk premium represents the additional return over the risk-free rate that investors expect for taking on the risks associated with equities.	%
Growth In Perpetuity Growth in Perpetuity The rate at which the company's free cash flow is assumed to grow indefinitely. By default, this rate equals the yield of the U.S. 10-Year Treasury Bond.	%
Historical Years Historical Years The number of years of historical data used to calculate averages and trends for analysis.	#
Projection Years Projection Years The number of years into the future for which the analysis projects financial performance and metrics.	#
Revenue Growth Rate Revenue Growth Rate The annual growth rate applied to projected revenue, starting from the second projection year onward.	%
Operating Cash Flow Margin Operating Cash Flow Margin `Projected Operating Cash Flow` = `Projected Revenue` * `Operating Cash Flow Margin` This margin represents the percentage of revenue used to estimate future Operating Cash Flow.	%
Capital Expenditure Margin Capital Expenditure Margin `Projected Free Cash Flow` = `Projected Operating Cash Flow` - `Projected Revenue` * `Capital Expenditure Margin` This margin is used to estimate future capital expenditures as a percentage of revenue, which in turn is subtracted from Operating Cash Flow to calculate Free Cash Flow.	%

Results
Terminal Value	-209.6 Bil. EUR
Discounted Terminal Value	-155 Bil. EUR
Sum of Discounted Free Cash Flow	-6.3 Bil. EUR
Enterprise Value	-161.3 Bil. EUR
Cash and Equivalents	16.8 Mil. EUR
Total Debt	176.7 Mil. EUR
Equity Value	-161.4 Bil. EUR
Shares Outstanding	4.9 Mil. EUR
Estimated Value per Share	-32.97 Thou. EUR
Yield of the U.S. 10 Year Treasury Note	4.24%
Average Cash from Operating Activities Margin	62.8%
Average Capital Expenditure Margin	-182.5%
Cost of Equity	7.58%
Equity Weight	51.71%
Cost of Debt	6.04%
Debt Weight	48.29%
Tax Rate	20.84%

Historical Values

In Millions of EUR

{"sectionId": "section-chart-1", "sectionType": "chart", "title": "Historical Values", "dates": [2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029], "series": [{"label": "Revenue", "mappingKey": "income:revenue", "data": [1.9, 9.17, 53.75, 109.1, 41.2, 38.68, 73.32, 165.4, 196.7, 236.4, {"y": 221.6, "oy": 221.6, "e": true, "c": 2025, "g": -6.25, "og": -6.25}, {"y": 436.5, "oy": 436.5, "e": true, "c": 2026, "g": 96.98, "og": 96.98}, {"y": 859.8, "oy": 859.8, "e": true, "c": 2027, "g": 96.98, "og": 96.98}, {"y": 1693, "oy": 1693, "e": true, "c": 2028, "g": 96.98, "og": 96.98}, {"y": 3336, "oy": 3336, "e": true, "c": 2029, "g": 96.98, "og": 96.98}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Operating Cash Flow", "mappingKey": "flow:operatingCashFlow", "data": [1.19, 2.91, 37.85, 68.67, 34.93, 13.99, 51.82, 142.7, 139.3, 131.8, {"y": 139.2, "oy": 139.2, "e": true, "c": 2025, "g": 5.61, "og": 5.61}, {"y": 274.1, "oy": 274.1, "e": true, "c": 2026, "g": 96.98, "og": 96.98}, {"y": 540.0, "oy": 540.0, "e": true, "c": 2027, "g": 96.98, "og": 96.98}, {"y": 1063, "oy": 1063, "e": true, "c": 2028, "g": 96.98, "og": 96.98}, {"y": 2095, "oy": 2095, "e": true, "c": 2029, "g": 96.98, "og": 96.98}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Free Cash Flow", "mappingKey": "flow:freeCashFlow", "data": [-8.86, -63.18, -13.93, 2.47, -14.79, -22.85, -1.01, 53.78, -59.48, -53.52, {"y": -265.2, "oy": -265.2, "e": true, "c": 2025, "g": 395.6, "og": 395.6}, {"y": -522.5, "oy": -522.5, "e": true, "c": 2026, "g": 96.98, "og": 96.98}, {"y": -1029, "oy": -1029, "e": true, "c": 2027, "g": 96.98, "og": 96.98}, {"y": -2027, "oy": -2027, "e": true, "c": 2028, "g": 96.98, "og": 96.98}, {"y": -3993, "oy": -3993, "e": true, "c": 2029, "g": 96.98, "og": 96.98}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Capital Expenditure", "mappingKey": "flow:capitalExpenditure", "data": [-10.05, -66.1, -51.78, -66.21, -49.72, -36.84, -52.83, -88.95, -198.7, -185.3, -404.4, -796.6, -1569, -3090, -6088], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Linear Regression Revenue Line", "mappingKey": "linearRegressionRevenue", "data": [-13.03, 10.43, 33.9, 57.36, 80.82, 104.3, 127.7, 151.2, 174.7, 198.1, 221.6, 245.1, 268.5, 292.0, 315.4], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Discounted Free Cash Flow", "mappingKey": "discountedFreeCashFlow", "data": [-8.86, -63.18, -13.93, 2.47, -14.79, -22.85, -1.01, 53.78, -59.48, -53.52, -257.4, -477.3, -885.0, -1640, -3042], "dataType": ".", "numberFormat": "M", "hidden": true}], "editableDates": {"2025": 36, "2026": 37, "2027": 38, "2028": 39, "2029": 40}, "properties": {"number_format": "M", "display_table": true}, "width": "full"}

Edit Chart Values	2025	2026	2027	2028	2029

↳ Growth Rate

Forecast Data

amounts of EUR except for #	2024	2025	2026	2027	2028	2029
Revenue	236.4	221.6	436.5	859.8	1,694	3,336
Revenue Growth Rate	20.19%	-6.25%	96.98%	96.98%	96.98%	96.98%
Operating Cash Flow	131.8	139.2	274.1	540	1,064	2,095
Operating Cash Flow Margin	55.75%	62.8%	62.8%	62.8%	62.8%	62.8%
Capital Expenditure	-185.3	-404.4	-796.6	-1,569	-3,091	-6,088
Capital Expenditure Margin	-78.39%	-182.5%	-182.5%	-182.5%	-182.5%	-182.5%
Free Cash Flow	-53.52	-265.2	-522.5	-1,029	-2,027	-3,993
Free Cash Flow Margin	-22.64%	-119.7%	-119.7%	-119.7%	-119.7%	-119.7%
Compounded Discount Rate		3.06%	9.47%	16.29%	23.55%	31.24%
Discounted Free Cash Flow	-53.52	-257.4	-477.3	-885	-1,641	-3,043

Historical Data

amounts of EUR except for #	Average	LTM	2024	2023	2022	2021	2020	2019	2018	2017	2016	2015
Revenue	105.7	236.8	236.4	196.7	165.4	73.32	38.68	41.2	109.1	53.75	9.17	1.9
Revenue Growth Rate	96.98%	0.201%	20.19%	18.87%	125.6%	89.54%	-6.12%	-62.22%	102.9%	486.1%	383.4%	-91.71%
Cost of Revenue	60.42	113.8	144.6	97.65	72.28	48.43	43.07	27.53	75.84	35.53	5.14	0.653
Gross Profit	45.25	123	91.73	99	93.15	24.89	-4.38	13.67	33.21	18.21	4.03	1.24
Gross Margin	38.82%	51.93%	38.81%	50.34%	56.31%	33.95%	-11.33%	33.19%	30.46%	33.89%	43.91%	65.56%
Operating Income	23.95	80.43	82.86	82.8	79.35	32.6	-16.16	-10.54	-40.11	-23.4	-6.46	2.14
Operating Margin	8.92%	33.96%	35.06%	42.1%	47.96%	44.46%	-41.78%	-25.57%	-36.78%	-43.54%	-70.49%	112.8%
Net Income	23.46	50.22	50.22	65.18	60.77	24.79	-16.1	0.186	13.87	7.67	0.102	1.15
Net Margin	17.63%	21.2%	21.25%	33.14%	36.73%	33.82%	-41.62%	0.451%	12.72%	14.28%	1.11%	60.88%
Cash from Operating Activities	69.37	138	131.8	139.3	142.7	51.82	13.99	34.93	68.67	37.85	2.91	1.19
Cash from Operating Activities Margin	62.8%	58.26%	55.75%	70.82%	86.27%	70.68%	36.17%	84.79%	62.97%	70.42%	31.78%	62.92%
Capital Expenditure	-90.31	-186.9	-185.3	-198.7	-88.95	-52.83	-36.84	-49.72	-66.21	-51.78	-66.1	-10.05
Free Cash Flow	-20.93	-48.92	-53.52	-59.48	53.78	-1.01	-22.85	-14.79	2.47	-13.93	-63.18	-8.86