Austerlitz Acquisition Corporation I (AUS) Discounted Cash Flow to Firm - Perpetual Growth

Austerlitz Acquisition Corporation I

AUS (NYSE)

(%)

Models
Austerlitz Acquisition Corporation I Discounted Cash Flow to Firm - Perpetual Growth

# Render description block
model.render_description({
    "data": r"""
## Discounted Cash Flow to Firm (Perpetual Growth)

This model estimates the fair value of a share by discounting projected **Free Cash Flow to the Firm (FCFF)**, also known as Unlevered Free Cash Flow.

The terminal value assumes cashflow grows at a constant **Growth in Perpetuity** rate forever:

`Terminal Enterprise Value` = `FCFF_(final forecast year)` × (1 + `Growth in Perpetuity`) / (`Discount Rate` - `Growth in Perpetuity`)

The terminal value and projected FCFF are discounted to present value using **WACC**.
Equity value is obtained by adjusting enterprise value for net debt:

`Equity Value` =
`Cumulative Present Value of FCFF` +
`Present Value of Terminal EV` +
`Cash and Short Term Investments` −
`Total Debt`

`Fair Value per Share` = `Equity Value` ÷ `Shares Outstanding`

> This model was inspired by Prof. Aswath Damodaran's spreadsheet [⬇️fcff2st.xls](https://pages.stern.nyu.edu/~adamodar/pc/fcff2st.xls)

> Learn more: Prof. Aswath Damodaran's [Guide to Discounted Cash Flow Valuation](https://pages.stern.nyu.edu/~adamodar/pdfiles/eqnotes/dcfallOld.pdf)
""",
    "properties": {
        "width": "responsive"
    }
})

# --- Discount Rate (WACC)
assumptions.set({
    "timeseries": "annual",
    "data": {
        "#historicalYears": """
            3
        """,
        "#beta": """
            profile:beta
        """,
        "%riskFreeRate": """
            treasury:year10
        """,
        "%equityRiskPremium": """
            risk:totalEquityRiskPremium
        """,
        "%taxRate": """
            income:incomeTaxExpense / income:incomeBeforeTax 
            or if this <= 0:
            risk:corporateTaxRate
        """,
    },
    "titles": {
        "#historicalYears": "Historical Years",
        "#beta": "Beta",
        "%riskFreeRate": "Risk Free Rate",
        "%equityRiskPremium": "Equity Risk Premium",
        "%taxRate": "Tax Rate",
    },
    "properties": {
        "width": "responsive",
        "title": "Discount Rate (WACC)",
        "id": "component-1",
        "bindTo": None
    },
    "descriptions": {
        "#historicalYears": r"""
Number of trailing fiscal years used to compute historical averages/trends that feed the model’s default forecast assumptions (e.g., margins and growth).
        """,
        "#beta": r"""
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.
        """,
        "%riskFreeRate": r"""
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.
        """,
        "%equityRiskPremium": r"""
The market risk premium represents the additional return over the risk-free rate that investors expect for taking on the risks associated with equities.
        """,
        "%taxRate": r"""
`Tax Rate` = `Income Tax Expense` / `Income Before Tax`

This is the company’s **effective tax rate**, reflecting the average rate of tax actually paid on its pre-tax earnings (including all statutory, deferred, and non-recurring items).

This rate is used to adjust the after-tax cost of debt, since interest expense is tax-deductible.

## Discount Rate

`Discount Rate` =  
`Debt Weight` × `Cost of Debt` × (1 − `Tax Rate`)  
+ `Equity Weight` × `Cost of Equity`
        """,
    }
})

# --- WACC Calculation
data.compute_results({
    "%costOfEquity": """
        assumption:%riskFreeRate +  assumption:#beta *  assumption:%equityRiskPremium
    """,
    "%costOfDebt": """
        income:interestExpense /  balance:totalDebt
    """,
    "%debtWeight": """
        balance:totalDebt / (profile:mktCap +  balance:totalDebt)
    """,
    "%equityWeight": """
        1 -  result:%debtWeight
    """,
    "%1TaxRate": """
        1 - assumption:%taxRate
    """,
    "%wacc": """
        result:%debtWeight *  result:%costOfDebt * (1 - assumption:%taxRate) +  result:%equityWeight* result:%costOfEquity
    """,
}, timeseries="annual")

model.render_results({
    "timeseries": "annual",
    "data": {
        "assumption:#beta": {
            "label": "Beta",
            "type": ""
        },
        "assumption:%equityRiskPremium": {
            "label": "* Equity Risk Premium",
            "type": "%"
        },
        "assumption:%riskFreeRate": {
            "label": "+ Risk Free Rate",
            "type": "%"
        },
        "result:%costOfEquity": {
            "label": "= Cost of Equity",
            "type": "%"
        },
        "result:%equityWeight": {
            "label": "* Equity Weight",
            "type": "%"
        },
        "result:%costOfDebt": {
            "label": "+ Cost of Debt",
            "type": "%"
        },
        "result:%debtWeight": {
            "label": "* Debt Weight",
            "type": "%"
        },
        "result:%1TaxRate": {
            "label": "* (1 - Tax Rate)",
            "type": "%"
        },
        "result:%wacc": {
            "label": "= WACC (Discount Rate)",
            "type": "%"
        },
    },
    "properties": {
        "title": "WACC Calculation",
        "width": "responsive",
        "hidden_keys": []
    }
})

# --- Discount Rate (WACC)
assumptions.set({
    "timeseries": "annual",
    "data": {
        "%discountRate": """
            result:%wacc
        """,
    },
    "titles": {
        "%discountRate": "Discount Rate",
    },
    "properties": {
        "width": "full",
        "title": "Discount Rate (WACC)",
        "id": "component-3",
        "bindTo": "component-1"
    },
    "descriptions": {
        "%discountRate": r"""
`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.
        """,
    },
    "hierarchies": [
        {
            "parent": "%discountRate",
            "children": [
                "#beta",
                "%riskFreeRate",
                "%equityRiskPremium",
                "%taxRate",
            ]
        },
    ]
})

# --- Historical Averages
data.compute({
    "user:%revenueGrowthRate": """
        ( income:revenue / income:revenue:-1 ) - 1
    """,
    "user:ebit": """
        income:ebitda - income:depreciationAndAmortization
    """,
    "user:%ebitMargin": """
        user:ebit / income:revenue
    """,
    "user:%incomeTaxRate": """
        income:incomeTaxExpense / income:incomeBeforeTax 
        or if this <= 0:
        risk:corporateTaxRate
    """,
    "user:%dAMargin": """
        income:depreciationAndAmortization / income:revenue
    """,
    "user:%capexMargin": """
        flow:capitalExpenditure / income:revenue
    """,
    "user:%changeInWcMargin": """
        flow:changeInWorkingCapital / income:revenue
    """,
    "user:freeCashflowToFirmFcff": """
        user:ebit * (1 - user:%incomeTaxRate)
        + flow:capitalExpenditure 
        + income:depreciationAndAmortization 
        + flow:changeInWorkingCapital
    """,
    "user:%fcffMargin": """
        user:freeCashflowToFirmFcff / income:revenue
    """,
}, forecast=0, timeseries="annual")

model.render_table({
    "timeseries": "annual",
    "data": {
        "income:revenue": "Revenue",
        "user:%revenueGrowthRate": "Revenue Growth Rate",
        "user:ebit": "Earnings Before Interest and Taxes (EBIT)",
        "user:%ebitMargin": "EBIT Margin",
        "income:incomeTaxExpense": "Income Tax Expense",
        "user:%incomeTaxRate": "Income Tax Rate",
        "income:depreciationAndAmortization": "Depreciation and Amortization (D&A)",
        "user:%dAMargin": "D&A Margin",
        "flow:capitalExpenditure": "Capital Expenditure (CapEx)",
        "user:%capexMargin": "CapEx Margin",
        "flow:changeInWorkingCapital": "Change in Working Capital",
        "user:%changeInWcMargin": "Change in WC Margin",
        "user:freeCashflowToFirmFcff": "Free Cashflow to Firm (FCFF)",
        "user:%fcffMargin": "FCFF Margin",
    },
    "start": data.get("""
        -assumption:#historicalYears
    """),
    "end": 0,
    "properties": {
        "title": "Historical Averages",
        "order": "descending",
        "number_format": "M",
        "include_ltm": True,
        "display_averages": True,
        "width": "responsive"
    }
})

# --- Forecast Assumptions
assumptions.set({
    "timeseries": "annual",
    "data": {
        "#highGrowthYears": """
            5
        """,
        "%growthInPerpetuity": """
            2.5%
        """,
        "%revenueGrowthRate": """
             function:average(start=-assumption:#historicalYears, end=0):user:%revenueGrowthRate
        """,
        "%ebitMargin": """
             function:average(start=-assumption:#historicalYears, end=0):user:%ebitMargin
        """,
        "%changeInWorkingCapitalMargin": """
            function:average(start=-assumption:#historicalYears, end=0):user:%changeInWcMargin
        """,
        "%depreciationAndAmortizationMargin": """
             function:average(start=-assumption:#historicalYears, end=0):user:%dAMargin
        """,
        "%capitalExpenditureMargin": """
            function:average(start=-assumption:#historicalYears, end=0):user:%capexMargin
        """,
    },
    "titles": {
        "#highGrowthYears": "High Growth Years",
        "%growthInPerpetuity": "Growth in Perpetuity",
        "%revenueGrowthRate": "Revenue Growth Rate",
        "%ebitMargin": "EBIT Margin",
        "%changeInWorkingCapitalMargin": "Change in Working Capital Margin",
        "%depreciationAndAmortizationMargin": "Depreciation and Amortization Margin",
        "%capitalExpenditureMargin": "Capital Expenditure Margin",
    },
    "properties": {
        "width": "responsive",
        "title": "Forecast Assumptions",
        "id": "component-5",
        "bindTo": None
    },
    "descriptions": {
        "#highGrowthYears": r"""
Number of years with explicit projections before the model shifts to the terminal (perpetuity) period.
        """,
        "%growthInPerpetuity": r"""
Long-run constant growth rate used to calculate terminal value after the forecast period.
        """,
        "%revenueGrowthRate": r"""
Annual % increase in revenue during the forecast period.
        """,
        "%ebitMargin": r"""
EBIT as a % of revenue; reflects operating profitability and business mix.
        """,
        "%changeInWorkingCapitalMargin": r"""
Annual change in net working capital as a % of revenue; captures cash tied up (or released) in receivables, inventory, and payables.

- A negative value represents cash tied up in operations (reduces FCFF).
- A positive value represents a release of working capital (increases FCFF).
        """,
        "%depreciationAndAmortizationMargin": r"""
D&A as a % of revenue; a non-cash expense added back in cash flow, often linked to the asset base.
        """,
        "%capitalExpenditureMargin": r"""
CapEx as a % of revenue; cash reinvestment required to maintain and grow operations.
        """,
    }
})

# --- Forecasting
data.compute({
    "income:revenue": """
        income:revenue:-1 * (1+ assumption:%revenueGrowthRate)
    """,
    "user:ebit": """
        assumption:%ebitMargin * income:revenue
    """,
    "user:freeCashflowToFirmFcff": """
        user:ebit * (1 - assumption:%taxRate)
        + income:revenue * (
        assumption:%depreciationAndAmortizationMargin 
        + assumption:%capitalExpenditureMargin
        + assumption:%changeInWorkingCapitalMargin
        )
    """,
    "user:discountedFreeCashFlow": """
        user:freeCashflowToFirmFcff / (1 + assumption:%discountRate) ** time:index * (time:index > 0)
    """,
}, forecast=data.get("""
    assumption:#highGrowthYears
"""), timeseries="annual")

model.render_chart({
    "timeseries": "annual",
    "data": {
        "income:revenue": "Revenue",
        "user:ebit": "EBIT",
        "user:freeCashflowToFirmFcff": "Free Cashflow to Firm",
    },
    "start": -10,
    "end": data.get("""
        assumption:#highGrowthYears
    """),
    "properties": {
        "title": "Forecasting",
        "include_ltm": False,
        "set_editable": ["income:revenue", "user:freeCashflowToFirmFcff"],
        "hidden_keys": [],
        "bar_keys": [],
        "width": "full"
    }
})

# --- Fair Value Calculation
data.compute_results({
    "terminalValue": """
        user:freeCashflowToFirmFcff:assumption:#highGrowthYears * (1 + assumption:%growthInPerpetuity ) / ( assumption:%discountRate - assumption:%growthInPerpetuity) 
    """,
    "%totalTerminalValueDiscountRate": """
        (1 + assumption:%discountRate) ** assumption:#highGrowthYears - 1
    """,
    "discountedTerminalValue": """
        result:terminalValue / (1 + result:%totalTerminalValueDiscountRate)
    """,
    "sumOfDiscountedFreeCashFlow": """
         function:sum(start=1, end=assumption:#highGrowthYears):user:discountedFreeCashFlow
    """,
    "equityValue": """
        result:discountedTerminalValue + result:sumOfDiscountedFreeCashFlow + balance:cashAndShortTermInvestments - balance:totalDebt
    """,
    "#valuePerShare": """
        result:equityValue / income:weightedAverageShsOut
    """,
}, timeseries="annual")

model.render_results({
    "timeseries": "annual",
    "data": {
        "user:freeCashflowToFirmFcff:assumption:#highGrowthYears": {
            "label": "Exit Free Cashflow to Firm (FCFF)",
            "type": "$"
        },
        "result:terminalValue": {
            "label": "Terminal Enterprise Value (EV)",
            "type": "$"
        },
        "result:%totalTerminalValueDiscountRate": {
            "label": "Terminal Value Discount Factor",
            "type": "%"
        },
        "result:discountedTerminalValue": {
            "label": "Present Value of Terminal EV",
            "type": "$"
        },
        "result:sumOfDiscountedFreeCashFlow": {
            "label": "+ Cumulative Present Value of FCFF",
            "type": "$"
        },
        "balance:cashAndShortTermInvestments": {
            "label": "+ Cash and Short Term Investments",
            "type": "$"
        },
        "balance:totalDebt": {
            "label": "- Total Debt",
            "type": "$"
        },
        "result:equityValue": {
            "label": "= Equity Value",
            "type": "$"
        },
        "income:weightedAverageShsOut": {
            "label": "/ Shares Outstanding",
            "type": ""
        },
        "result:#valuePerShare": {
            "label": "= Fair Value per Share",
            "type": "$"
        },
    },
    "properties": {
        "title": "Fair Value Calculation",
        "width": "responsive",
        "hidden_keys": []
    }
})

# --- Fair Value per Share
model.set_final_value({
    "value": data.get("""
        result:#valuePerShare
    """, timeseries="annual"),
    "units": "$",
    "title": "Fair Value per Share",
    "properties": {
        "width": "responsive" 
    }
})

# --- Forecasted Data
data.compute({
    "user:%revenueGrowthRate": """
        ( income:revenue / income:revenue:-1 ) - 1
    """,
    "user:%freeCashFlowMargin": """
        user:freeCashflowToFirmFcff / income:revenue
    """,
}, forecast=data.get("""
    assumption:#highGrowthYears
"""), timeseries="annual")

model.render_table({
    "timeseries": "annual",
    "data": {
        "income:revenue": "Revenue",
        "user:%revenueGrowthRate": "Revenue Growth Rate",
        "user:freeCashflowToFirmFcff": "Free Cashflow to Firm (FCFF)",
        "user:%freeCashFlowMargin": "FCFF Margin",
        "user:discountedFreeCashFlow": "Present Value of FCFF",
    },
    "start": 1,
    "end": data.get("""
        assumption:#highGrowthYears
    """),
    "properties": {
        "title": "Forecasted Data",
        "order": "ascending",
        "number_format": "M",
        "include_ltm": False,
        "display_averages": False,
        "width": "responsive"
    }
})

Error at line 495: None is not a valid number in property 'value'.

Discounted Cash Flow to Firm (Perpetual Growth)

This model estimates the fair value of a share by discounting projected Free Cash Flow to the Firm (FCFF), also known as Unlevered Free Cash Flow.

The terminal value assumes cashflow grows at a constant Growth in Perpetuity rate forever:

Terminal Enterprise Value = FCFF_(final forecast year) × (1 + Growth in Perpetuity) / (Discount Rate - Growth in Perpetuity)

The terminal value and projected FCFF are discounted to present value using WACC. Equity value is obtained by adjusting enterprise value for net debt:

Equity Value = Cumulative Present Value of FCFF + Present Value of Terminal EV + Cash and Short Term Investments − Total Debt

Fair Value per Share = Equity Value ÷ Shares Outstanding

This model was inspired by Prof. Aswath Damodaran's spreadsheet ⬇️fcff2st.xls

Learn more: Prof. Aswath Damodaran's Guide to Discounted Cash Flow Valuation

Discount Rate (WACC)

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.	%
↳ Equity Risk Premium Equity Risk 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.	%
↳ Tax Rate Tax Rate `Tax Rate` = `Income Tax Expense` / `Income Before Tax` This is the company’s effective tax rate, reflecting the average rate of tax actually paid on its pre-tax earnings (including all statutory, deferred, and non-recurring items). This rate is used to adjust the after-tax cost of debt, since interest expense is tax-deductible. Discount Rate `Discount Rate` = `Debt Weight` × `Cost of Debt` × (1 − `Tax Rate`) + `Equity Weight` × `Cost of Equity`	%
Historical Years Historical Years Number of trailing fiscal years used to compute historical averages/trends that feed the model’s default forecast assumptions (e.g., margins and growth).	#

WACC Calculation
Beta	0
* Equity Risk Premium	4.46%
+ Risk Free Rate	4.15%
= Cost of Equity	4.15%
* Equity Weight
+ Cost of Debt
* Debt Weight
* (1 - Tax Rate)	75%
= WACC (Discount Rate)

Historical Averages

Monetary values in USD amounts except #	Average	LTM Mar 07	2021 Dec 31
Revenue		0	0
Revenue Growth Rate
Earnings Before Interest and Taxes (EBIT)	-337.7	-673.7	-1.72
EBIT Margin
Income Tax Expense	-22.59	-29.17	-16
Income Tax Rate	25%	25%	25%
Depreciation and Amortization (D&A)	22.62	29.24	16
D&A Margin
Capital Expenditure (CapEx)		0	0
CapEx Margin
Change in Working Capital	-3.02	-7.55	1.51
Change in WC Margin
Free Cashflow to Firm (FCFF)	-233.7	-483.6	16.22
FCFF Margin

Forecast Assumptions

High Growth Years High Growth Years Number of years with explicit projections before the model shifts to the terminal (perpetuity) period.	#
Growth in Perpetuity Growth in Perpetuity Long-run constant growth rate used to calculate terminal value after the forecast period.	%
Revenue Growth Rate Revenue Growth Rate Annual % increase in revenue during the forecast period.	%
EBIT Margin EBIT Margin EBIT as a % of revenue; reflects operating profitability and business mix.	%
Change in Working Capital Margin Change in Working Capital Margin Annual change in net working capital as a % of revenue; captures cash tied up (or released) in receivables, inventory, and payables. A negative value represents cash tied up in operations (reduces FCFF). A positive value represents a release of working capital (increases FCFF).	%
Depreciation and Amortization Margin Depreciation and Amortization Margin D&A as a % of revenue; a non-cash expense added back in cash flow, often linked to the asset base.	%
Capital Expenditure Margin Capital Expenditure Margin CapEx as a % of revenue; cash reinvestment required to maintain and grow operations.	%

Forecasting

Monetary values in USD

Fair Value Calculation
Exit Free Cashflow to Firm (FCFF)
Terminal Enterprise Value (EV)
Terminal Value Discount Factor
Present Value of Terminal EV
+ Cumulative Present Value of FCFF	0 USD
+ Cash and Short Term Investments	1.5 Mil. USD
- Total Debt	0 USD
= Equity Value
/ Shares Outstanding	98.57 Mil.
= Fair Value per Share

Market is Open

After-Hours Quote

Market is Open

After-Hours Quote

Austerlitz Acquisition Corporation I Discounted Cash Flow to Firm - Perpetual Growth

Discounted Cash Flow to Firm (Perpetual Growth)

Discount Rate (WACC)

Discount Rate

Cost of Equity

Cost of Debt

Equity & Debt Weights

Tax Rate

Beta

Risk Free Rate

Equity Risk Premium

Tax Rate

Discount Rate

Historical Years

WACC Calculation

Historical Averages

Forecast Assumptions

High Growth Years

Growth in Perpetuity

Revenue Growth Rate

EBIT Margin

Change in Working Capital Margin

Depreciation and Amortization Margin

Capital Expenditure Margin

Forecasting

Fair Value Calculation

Discounted Cash Flow to Firm - Perpetual Growth

Earnings Power Value

Simple Dividend Discount Model

Simple Excess Return Model

Two-Stage Dividend Discount Model

Two-Stage Excess Return Model

Discounted Cash Flow to Firm - Exit Multiple

Discounted Future Market Cap

Peter Lynch Fair Value

Altman Z-Score

Beneish M-Score

Capital Asset Pricing Model (CAPM)

Margin Analysis

Piotroski F-Score

Return on Invested Capital (ROIC)

Shiller PE (CAPE) Ratio

Weighted Average Cost of Capital (WACC)