Apple (AAPL) Discounted Free Cash Flow - Perpetuity

Apple Inc.

AAPL (NASDAQ)

(%)

Valuation
Apple 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",
})

assumptions.set("%revenue_growth_rate",
                data.average(f"%revenueGrowthRate:{-assumptions.get('historical_years')}->0"))
assumptions.set("%operating_cash_flow_margin",
                data.average(f"%operatingCashFlowMargin:{-assumptions.get('historical_years')}->0"))
assumptions.set("%capital_expenditure_margin",
                data.average(f"%capitalExpenditureMargin:{-assumptions.get('historical_years')}->0"))

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
    """,
    "%operatingCashFlowMargin": "flow:operatingCashFlow / income:revenue",
    "%capitalExpenditureMargin": "flow:capitalExpenditure / income:revenue",
    "%freeCashFlowMargin": "flow:freeCashFlow / income:revenue",
}, 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, "Discounted Free Cash Flow Sum", "$"],
    [enterprise_value, "Enterprise Value", "$"],
    [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", "%"],
    [assumptions.get("%operating_cash_flow_margin"), "Cash from Operating Activities Margin", "%"],
    [assumptions.get("%capital_expenditure_margin"), "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",
        "discountedFreeCashFlow": "Discounted Free Cash Flow",
    },
    "start": -1,
    "end": "*",
    "properties": {
        "title": "Forecast Data",
        "column_order": "ascending",
        "except_ltm": True,
        "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,
        "column_order": "descending",
        "number_format": "M"
    },
})

assumptions.set_description({
    "%discount_rate": r"""
        ## Discount Rate
        
        $
        \text{Discount Rate} 
          = \text{Equity Weight} \times \text{Cost of Equity}
            + \text{Debt Weight} \times \text{Cost of Debt} \times (1 - \text{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
        
        $
        \text{Cost of Equity}
          = \text{Risk Free Rate} + \text{Beta} \times \text{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
        
        $
        \text{Cost of Debt}
          = \frac{\text{Interest Expense}}{\text{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
        
        $
        \text{Debt Weight}
          = \frac{\text{Total Debt}}{\text{Market Capitalization} + \text{Total Debt}}
          = 1 - \text{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
        
        $
        \text{Tax Rate}
          = \frac{\text{Income Tax Expense}}{\text{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
        
        $
        \text{Projected Operating Cash Flow}
          = \text{Projected Revenue} \times \text{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
        
        $
        \text{Projected Free Cash Flow}
          = \text{Projected Operating Cash Flow}
            - \text{Projected Revenue} \times \text{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 206.77 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 $ \text{Discount Rate} = \text{Equity Weight} \times \text{Cost of Equity} + \text{Debt Weight} \times \text{Cost of Debt} \times (1 - \text{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 $ \text{Cost of Equity} = \text{Risk Free Rate} + \text{Beta} \times \text{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 $ \text{Cost of Debt} = \frac{\text{Interest Expense}}{\text{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 $ \text{Debt Weight} = \frac{\text{Total Debt}}{\text{Market Capitalization} + \text{Total Debt}} = 1 - \text{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 $ \text{Tax Rate} = \frac{\text{Income Tax Expense}}{\text{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 $ \text{Projected Operating Cash Flow} = \text{Projected Revenue} \times \text{Operating Cash Flow Margin} $ This margin represents the percentage of revenue used to estimate future Operating Cash Flow.	%
Capital Expenditure Margin #Capital Expenditure Margin $ \text{Projected Free Cash Flow} = \text{Projected Operating Cash Flow} - \text{Projected Revenue} \times \text{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	3,005 Bil. USD
Discounted Terminal Value	1,904 Bil. USD
Discounted Free Cash Flow Sum	510.4 Bil. USD
Enterprise Value	2,415 Bil. USD
Equity Value	2,372 Bil. USD
Shares Outstanding	15.08 Bil. USD
Estimated Value per Share	157.2 USD
Yield of the U.S. 10 Year Treasury Note	4.4%
Cash from Operating Activities Margin	29.51%
Capital Expenditure Margin	-3.82%
Cost of Equity	9.85%
Equity Weight	96.99%
Cost of Debt
Debt Weight	3.01%
Tax Rate	23.54%

Historical Values

{"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": [233715, 215639, 229234, 265595, 260174, 274515, 365817, 394328, 383285, 391035, {"y": 425663, "oy": 425663, "e": true, "c": 2025, "g": 8.86, "og": 8.86}, {"y": 459422, "oy": 459422, "e": true, "c": 2026, "g": 7.93, "og": 7.93}, {"y": 495859, "oy": 495859, "e": true, "c": 2027, "g": 7.93, "og": 7.93}, {"y": 535185, "oy": 535185, "e": true, "c": 2028, "g": 7.93, "og": 7.93}, {"y": 577631, "oy": 577631, "e": true, "c": 2029, "g": 7.93, "og": 7.93}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Operating Cash Flow", "mappingKey": "flow:operatingCashFlow", "data": [81266, 66231, 64225, 77434, 69391, 80674, 104038, 122151, 110543, 118254, {"y": 125613, "oy": 125613, "e": true, "c": 2025, "g": 6.22, "og": 6.22}, {"y": 135575, "oy": 135575, "e": true, "c": 2026, "g": 7.93, "og": 7.93}, {"y": 146328, "oy": 146328, "e": true, "c": 2027, "g": 7.93, "og": 7.93}, {"y": 157933, "oy": 157933, "e": true, "c": 2028, "g": 7.93, "og": 7.93}, {"y": 170458, "oy": 170458, "e": true, "c": 2029, "g": 7.93, "og": 7.93}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Free Cash Flow", "mappingKey": "flow:freeCashFlow", "data": [69778, 52683, 51430, 64121, 58896, 73365, 92953, 111443, 99584, 108807, {"y": 109348, "oy": 109348, "e": true, "c": 2025, "g": 0.498, "og": 0.498}, {"y": 118021, "oy": 118021, "e": true, "c": 2026, "g": 7.93, "og": 7.93}, {"y": 127381, "oy": 127381, "e": true, "c": 2027, "g": 7.93, "og": 7.93}, {"y": 137483, "oy": 137483, "e": true, "c": 2028, "g": 7.93, "og": 7.93}, {"y": 148387, "oy": 148387, "e": true, "c": 2029, "g": 7.93, "og": 7.93}], "dataType": ".", "numberFormat": "M", "hidden": false}, {"label": "Capital Expenditure", "mappingKey": "flow:capitalExpenditure", "data": [-11488, -13548, -12795, -13313, -10495, -7309, -11085, -10708, -10959, -9447, -16264, -17554, -18946, -20449, -22071], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Linear Regression Revenue Line", "mappingKey": "linearRegressionRevenue", "data": [199609, 222215, 244820, 267425, 290031, 312636, 335241, 357847, 380452, 403057, 425663, 448268, 470873, 493478, 516084], "dataType": ".", "numberFormat": "M", "hidden": true}, {"label": "Discounted Free Cash Flow", "mappingKey": "discountedFreeCashFlow", "data": [69778, 52683, 51430, 64121, 58896, 73365, 92953, 111443, 99584, 108807, 105165, 103606, 102071, 100532, 99042], "dataType": ".", "numberFormat": "M", "hidden": true}], "displayTable": true, "editableDates": {"2025": 41, "2026": 42, "2027": 43, "2028": 44, "2029": 45}, "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	391,035	425,663	459,422	495,859	535,186	577,631
Revenue Growth Rate	2.02%	7.56%	7.93%	7.93%	7.93%	7.93%
Operating Cash Flow	118,254	125,613	135,576	146,328	157,933	170,459
Operating Cash Flow Margin	30.24%	29.51%	29.51%	29.51%	29.51%	29.51%
Capital Expenditure	-9,447	-16,265	-17,555	-18,947	-20,449	-22,071
Capital Expenditure Margin	-2.42%	-3.82%	-3.82%	-3.82%	-3.82%	-3.82%
Free Cash Flow	108,807	109,349	118,021	127,381	137,484	148,388
Free Cash Flow Margin	27.83%	25.69%	25.69%	25.69%	25.69%	25.69%
Discounted Free Cash Flow	108,807	105,166	103,607	102,071	100,533	99,043

Historical Data

amounts of USD except for #	Average	LTM	2024	2023	2022	2021	2020	2019	2018	2017	2016	2015
Revenue	309,918	395,760	391,035	383,285	394,328	365,817	274,515	260,174	265,595	229,234	215,639	233,715
Revenue Growth Rate	7.93%	1.21%	2.02%	-2.8%	7.79%	33.26%	5.51%	-2.04%	15.86%	6.3%	-7.73%	27.86%
Cost of Revenue	180,026	211,657	210,352	214,137	223,546	212,981	169,559	161,782	163,756	141,048	131,376	140,089
Gross Profit	129,892	184,103	180,683	169,148	170,782	152,836	104,956	98,392	101,839	88,186	84,263	93,626
Gross Margin	41.27%	46.52%	46.21%	44.13%	43.31%	41.78%	38.23%	37.82%	38.34%	38.47%	39.08%	40.06%
Operating Income	89,803	125,675	123,216	114,301	119,437	108,949	66,288	63,930	70,898	61,344	62,567	71,230
Operating Margin	28.62%	31.76%	31.51%	29.82%	30.29%	29.78%	24.15%	24.57%	26.69%	26.76%	29.01%	30.48%
Net Income	72,818	96,150	93,736	96,995	99,803	94,680	57,411	55,256	59,531	48,351	45,687	53,394
Net Margin	23.13%	24.3%	23.97%	25.31%	25.31%	25.88%	20.91%	21.24%	22.41%	21.09%	21.19%	22.85%
Cash from Operating Activities	91,136	108,294	118,254	110,543	122,151	104,038	80,674	69,391	77,434	64,225	66,231	81,266
Cash from Operating Activities Margin	29.51%	27.36%	30.24%	28.84%	30.98%	28.44%	29.39%	26.67%	29.15%	28.02%	30.71%	34.77%
Capital Expenditure	-11,013	-9,995	-9,447	-10,959	-10,708	-11,085	-7,309	-10,495	-13,313	-12,795	-13,548	-11,488
Free Cash Flow	80,124	98,299	108,807	99,584	111,443	92,953	73,365	58,896	64,121	51,430	52,683	69,778