BMO Pyrford Intl Stock Fd - Class A (BPIAX) Discounted Cash Flow to Firm - Perpetual Growth

BMO Pyrford Intl Stock Fd - Class A

BPIAX (NASDAQ)

(%)

Models
BMO Pyrford Intl Stock Fd - Class A 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 33: max() arg is an empty sequence

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

Discounted Cash Flow to Firm (Perpetual Growth)

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)

Market is Open

After-Hours Quote

Market is Open

After-Hours Quote

BMO Pyrford Intl Stock Fd - Class A Discounted Cash Flow to Firm - Perpetual Growth

Discounted Cash Flow to Firm (Perpetual Growth)

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)