Verizon Communications Inc. (VZ) Discounted Free Cash Flow - Perpetuity

Verizon Communications Inc.

VZ (NYSE)

(%)

Valuation
Verizon Communications Inc. 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

USD

Market Price USD

* 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	5,678 Bil. USD
Discounted Terminal Value	4,547 Bil. USD
Sum of Discounted Free Cash Flow	73.79 Bil. USD
Enterprise Value	4,620 Bil. USD
Cash and Equivalents	2.26 Bil. USD
Total Debt	167.7 Bil. USD
Equity Value	4,455 Bil. USD
Shares Outstanding	4.22 Bil. USD
Estimated Value per Share	1.05 Thou. USD
Yield of the U.S. 10 Year Treasury Note	4.24%
Average Cash from Operating Activities Margin	26.54%
Average Capital Expenditure Margin	-14.59%
Cost of Equity	5.88%
Equity Weight	52.14%
Cost of Debt	3.96%
Debt Weight	47.86%
Tax Rate	22.1%

Historical Values

In Millions of USD

{"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": [131620, 125980, 126034, 130863, 131868, 128292, 133613, 136835, 133974, 134788, {"y": 136158, "oy": 136158, "e": true, "c": 2025, "g": 1.02, "og": 1.02}, {"y": 136983, "oy": 136983, "e": true, "c": 2026, "g": 0.606, "og": 0.606}, {"y": 137813, "oy": 137813, "e": true, "c": 2027, "g": 0.606, "og": 0.606}, {"y": 138648, "oy": 138648, "e": true, "c": 2028, "g": 0.606, "og": 0.606}, {"y": 139488, "oy": 139488, "e": true, "c": 2029, "g": 0.606, "og": 0.606}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Operating Cash Flow", "mappingKey": "flow:operatingCashFlow", "data": [39027, 21689, 24318, 34339, 35746, 41768, 39539, 37141, 37475, 36912, {"y": 36136, "oy": 36136, "e": true, "c": 2025, "g": -2.1, "og": -2.1}, {"y": 36355, "oy": 36355, "e": true, "c": 2026, "g": 0.606, "og": 0.606}, {"y": 36575, "oy": 36575, "e": true, "c": 2027, "g": 0.606, "og": 0.606}, {"y": 36797, "oy": 36797, "e": true, "c": 2028, "g": 0.606, "og": 0.606}, {"y": 37020, "oy": 37020, "e": true, "c": 2029, "g": 0.606, "og": 0.606}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Free Cash Flow", "mappingKey": "flow:freeCashFlow", "data": [21252, 4096, 6488, 16252, 16909, 21450, 19253, 10401, 18708, 18922, {"y": 16270, "oy": 16270, "e": true, "c": 2025, "g": -14.01, "og": -14.01}, {"y": 16369, "oy": 16369, "e": true, "c": 2026, "g": 0.606, "og": 0.606}, {"y": 16468, "oy": 16468, "e": true, "c": 2027, "g": 0.606, "og": 0.606}, {"y": 16568, "oy": 16568, "e": true, "c": 2028, "g": 0.606, "og": 0.606}, {"y": 16668, "oy": 16668, "e": true, "c": 2029, "g": 0.606, "og": 0.606}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Capital Expenditure", "mappingKey": "flow:capitalExpenditure", "data": [-17775, -17593, -17830, -18087, -18837, -20318, -20286, -26740, -18767, -17990, -19865, -19985, -20107, -20228, -20351], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Linear Regression Revenue Line", "mappingKey": "linearRegressionRevenue", "data": [127482, 128350, 129217, 130085, 130952, 131820, 132688, 133555, 134423, 135290, 136158, 137025, 137893, 138761, 139628], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Discounted Free Cash Flow", "mappingKey": "discountedFreeCashFlow", "data": [21252, 4096, 6488, 16252, 16909, 21450, 19253, 10401, 18708, 18922, 15914, 15314, 14737, 14180, 13645], "dataType": ".", "numberFormat": "M", "hidden": true}], "editableDates": {"2025": 41, "2026": 42, "2027": 43, "2028": 44, "2029": 45}, "properties": {"number_format": "M", "display_table": true}, "width": "full"}

Edit Chart Values	2025	2026	2027	2028	2029

↳ Growth Rate

Forecast Data

amounts of USD except for #	2024	2025	2026	2027	2028	2029
Revenue	134,788	136,158	136,983	137,814	138,649	139,489
Revenue Growth Rate	0.608%	1.02%	0.606%	0.606%	0.606%	0.606%
Operating Cash Flow	36,912	36,136	36,355	36,576	36,797	37,020
Operating Cash Flow Margin	27.39%	26.54%	26.54%	26.54%	26.54%	26.54%
Capital Expenditure	-17,990	-19,866	-19,986	-20,107	-20,229	-20,351
Capital Expenditure Margin	-13.35%	-14.59%	-14.59%	-14.59%	-14.59%	-14.59%
Free Cash Flow	18,922	16,271	16,370	16,469	16,569	16,669
Free Cash Flow Margin	14.04%	11.95%	11.95%	11.95%	11.95%	11.95%
Compounded Discount Rate		2.24%	6.89%	11.75%	16.84%	22.15%
Discounted Free Cash Flow	18,922	15,914	15,314	14,737	14,180	13,646

Historical Data

amounts of USD except for #	Average	LTM	2024	2023	2022	2021	2020	2019	2018	2017	2016	2015
Revenue	131,742	135,292	134,788	133,974	136,835	133,613	128,292	131,868	130,863	126,034	125,980	131,620
Revenue Growth Rate	0.606%	0.374%	0.608%	-2.09%	2.41%	4.15%	-2.71%	0.768%	3.83%	0.043%	-4.29%	3.57%
Cost of Revenue	54,405	54,281	54,097	54,887	59,133	56,301	51,201	54,726	55,508	53,063	52,701	52,557
Gross Profit	77,337	81,011	80,691	79,087	77,702	77,312	77,091	77,142	75,355	72,971	73,279	79,063
Gross Margin	58.7%	59.88%	59.87%	59.03%	56.79%	57.86%	60.09%	58.5%	57.58%	57.9%	58.17%	60.07%
Operating Income	28,619	29,143	28,686	22,877	30,467	32,448	28,798	30,378	22,278	27,425	29,249	33,060
Operating Margin	21.73%	21.54%	21.28%	17.08%	22.27%	24.29%	22.45%	23.04%	17.02%	21.76%	23.22%	25.12%
Net Income	18,539	17,783	17,506	11,614	21,256	22,065	17,801	19,265	15,528	30,101	13,127	17,879
Net Margin	14.1%	13.14%	12.99%	8.67%	15.53%	16.51%	13.88%	14.61%	11.87%	23.88%	10.42%	13.58%
Cash from Operating Activities	35,051	37,610	36,912	37,475	37,141	39,539	41,768	35,746	34,339	24,318	21,689	39,027
Cash from Operating Activities Margin	26.54%	27.8%	27.39%	27.97%	27.14%	29.59%	32.56%	27.11%	26.24%	19.29%	17.22%	29.65%
Capital Expenditure	-19,241	-17,432	-17,990	-18,767	-26,740	-20,286	-20,318	-18,837	-18,087	-17,830	-17,593	-17,775
Free Cash Flow	15,810	20,178	18,922	18,708	10,401	19,253	21,450	16,909	16,252	6,488	4,096	21,252