The Goldman Sachs Group, Inc. (GS) Simple Dividend Discount Model

The Goldman Sachs Group, Inc.

GS (NYSE)

(%)

Valuation
The Goldman Sachs Group, Inc. Simple Dividend Discount Model

"""
    Model: Simple Dividend Discount Model

# Render model description
model.render_description(r"""
## Simple Dividend Discount Model

This model estimates the value of companies that have reached maturity and pay stable dividends as a significant percentage of their Free Cash Flow to Equity, with little to no high growth prospects.

See our [GitHub Documentation](https://github.com/DiscountingCashFlows/Documentation/blob/main/models-documentation/dividend-discount-models.md#simple-dividend-discount-model-source-code)
""")

# Initialize assumptions
assumptions.init({
    "data": {
        "%discount_rate": None,
        "expected_dividend": None,
        "%growth_in_perpetuity": "2.5%",
        "beta": data.get("profile:beta", default=1),
        "%risk_free_rate": data.get("treasury:year10"),
        "%market_premium": data.get("risk:totalEquityRiskPremium"),
        "historical_years": None,
        "forecast_years": 5,
    },
    "hierarchies": [{
        "parent": "%discount_rate",
        "children": ["beta", "%risk_free_rate", "%market_premium"]
    }]
})

# Calculate the discount rate as the cost of equity
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

assumptions.set("%discount_rate", cost_of_equity)

# Count all dividend payments excluding None and zero values
dividend_count = data.count("dividend:adjDividend:*", properties={"except_values": [None, 0]})

if dividend_count <= 0:
    raise ValueError("The company does not currently pay dividends!")

elif dividend_count > 10:
    assumptions.set("historical_years", 10)

else:
    # Set the historical years to the number of available dividend payments
    assumptions.set("historical_years", dividend_count)

# Compute the average annual dividend growth rate
data.compute({
    "%dividendGrowth": "function:growth:dividend:adjDividend"
}, forecast=0)

# Define the averaging period for historical dividend growth
averaging_period = f"-{assumptions.get('historical_years')}->0"
average_growth_rate = data.average(f"%dividendGrowth:{averaging_period}")

# Calculate next year's expected dividend by compounding the LTM dividend
# at the average growth rate over the remaining fiscal period (using continuous compounding)
ltm_dividend = data.get("dividend:adjDividend")
if ltm_dividend is not None:
    if average_growth_rate is not None:
        data.compute({
            "dividend:adjDividend": f"""
                function:compound:{ltm_dividend}
                rate:{average_growth_rate}
                continuous:true
            """
        }, forecast=1)
        expected_dividend = data.get(f"dividend:adjDividend:1")
        assumptions.set("expected_dividend", expected_dividend)
    else:
        # Fallback to the ltm_dividend, if the average dividend
        # growth rate could not be computed
        assumptions.set("expected_dividend", ltm_dividend)
else:
    model.error("Zero dividend encountered")

# Calculate the intrinsic stock value using the Dividend Discount Model formula
stock_value = assumptions.get("expected_dividend") / (
    assumptions.get("%discount_rate") - assumptions.get("%growth_in_perpetuity"))

# Set the calculated stock value as the model's final output
model.set_final_value({
    "value": stock_value,
    "units": '$'
})

# Compute additional historical metrics for analysis
data.compute({
    "dividendsPaidToCommon": "dividend:adjDividend * income:weightedAverageShsOut",
    "%returnOnEquity": "income:netIncome / balance:totalStockholdersEquity:-1",
    "%payoutRatio": "dividend:adjDividend / income:eps",
    "%dividendYield": "dividend:adjDividend / quote:close",
    "%adjDividendGrowth": "function:growth:dividend:adjDividend",
})

# Compute projected dividends and dividend growth for the forecast period
data.compute({
    "dividend:adjDividend": f"""
        function:compound:{assumptions.get('expected_dividend')} 
        rate:{assumptions.get('%growth_in_perpetuity')}
        continuous:true
    """,
    "%adjDividendGrowth": "function:growth:dividend:adjDividend",
}, forecast=assumptions.get("forecast_years"))

# Render key results
model.render_results([
    [data.get("dividend:adjDividend:0"), "LTM Dividend", "$"],
    [average_growth_rate, "Average Dividend Growth Rate", "%"],
    [assumptions.get("expected_dividend"), "Next Year's Expected Dividend", "$"],
    [assumptions.get("%discount_rate"), 'Cost of Equity', '%'],
    [assumptions.get("%growth_in_perpetuity"), 'Expected Growth Rate', '%'],
])

# Render a chart showing historical and projected dividends
model.render_chart({
    "data": {
        "dividend:adjDividend": "Dividends",
    },
    "start": -assumptions.get("historical_years"),
    "end": "*",
    "properties": {
        "title": 'Historical and Projected Dividends',
        "include_ltm": True
    }
})

# Render a table for future dividend estimations
model.render_table({
    "data": {
        "dividend:adjDividend": "Dividend per Share",
        "%adjDividendGrowth": "Dividend Growth Rate",
    },
    "start": -1,
    "end": "*",
    "properties": {
        "title": "Future Estimations",
        "order": "ascending",
    },
})

# Render a table of historical financial values and dividend metrics
model.render_table({
    "data": {
        "income:netIncome": "Net Income",
        "balance:totalStockholdersEquity": "Equity",
        "%returnOnEquity": "Return on Equity",
        "dividendsPaidToCommon": "Common Dividends",
        "%payoutRatio": "Payout Ratio",
        "income:weightedAverageShsOut": "Shares Outstanding",
        "quote:close": "Reference Market Price",
        "income:eps": "EPS",
        "dividend:adjDividend": "Dividend per Share",
        "%adjDividendGrowth": "Dividend Growth Rate",
        "%dividendYield": "Dividend Yield",
    },
    "start": -assumptions.get("historical_years"),
    "end": 0,
    "properties": {
        "title": "Historical Values",
        "order": "descending",
        "display_averages": True,
        "number_format": "M"
    },
})

# Set descriptions for assumptions
assumptions.set_description({
    "%discount_rate": r"""
        ## Discount Rate

`Discount Rate` = `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)
    """,

"beta": r"""
        ## Beta

Beta is a value that measures the price fluctuations (volatility) of a stock with respect to fluctuations in the overall stock market.
    """,

"%risk_free_rate": r"""
        ## Risk-Free Rate

The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. By default, it is equal to the current yield of the U.S. 10-Year Treasury Bond.
    """,

"%market_premium": r"""
        ## Market Premium

The market risk premium represents the excess returns over the risk-free rate that investors expect for taking on the incremental risks connected to the equities market.
    """,

"expected_dividend": r"""
        ## Expected Dividend

The estimated annual dividend per share for the next year.
    """,

"%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 is equal to the yield of the U.S. 10-Year Treasury Bond.
    """,

"historical_years": r"""
        ## Historical Years

The number of historical years used to calculate averages for historical data.
    """,

"forecast_years": r"""
        ## Forecast Years
        
        The number of years into the future for which the analysis projects financial performance and metrics.
    """,
})

print("End of model.")

Estimated Value

USD

Market Price USD

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

Simple Dividend Discount Model

This model estimates the value of companies that have reached maturity and pay stable dividends as a significant percentage of their Free Cash Flow to Equity, with little to no high growth prospects.

See our GitHub Documentation

Interactive Assumptions

Discount Rate Discount Rate `Discount Rate` = `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	%
↳ Beta Beta Beta is a value that measures the price fluctuations (volatility) of a stock with respect to fluctuations in the overall stock market.	#
↳ Risk Free Rate Risk-Free Rate The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. By default, it is equal to the current yield of the U.S. 10-Year Treasury Bond.	%
↳ Market Premium Market Premium The market risk premium represents the excess returns over the risk-free rate that investors expect for taking on the incremental risks connected to the equities market.	%
Expected Dividend Expected Dividend The estimated annual dividend per share for the next year.	#
Growth In Perpetuity Growth in Perpetuity The rate at which the company's free cash flow is assumed to grow indefinitely. By default, this is equal to the yield of the U.S. 10-Year Treasury Bond.	%
Historical Years Historical Years The number of historical years used to calculate averages for historical data.	#
Forecast Years Forecast Years The number of years into the future for which the analysis projects financial performance and metrics.	#

Results
LTM Dividend	14 USD
Average Dividend Growth Rate	17.34%
Next Year's Expected Dividend	16.54 USD
Cost of Equity	10.02%
Expected Growth Rate	2.5%

Historical and Projected Dividends

Monetary values are in USD

Future Estimations

amounts of USD except for #	2025	LTM	2026	2027	2028	2029	2030
Dividend per Share	14	14	16.54	17.39	17.83	18.28	18.73
Dividend Growth Rate	21.74%	0%	18.11%	5.2%	2.51%	2.5%	2.5%

Historical Values

amounts of USD except for #	Average	LTM	2025	2024	2023	2022	2021	2020	2019	2018	2017	2016
Net Income	11,243	16,670		14,276	8,516	11,261	21,635	9,459	8,466	10,459	4,286	7,398
Equity	103,553	124,000		121,996	116,905	117,189	109,926	95,932	90,265	90,185	82,243	86,893
Return on Equity	10.92%			12.21%	7.27%	10.24%	22.55%	10.48%	9.39%	12.72%	4.93%	8.53%
Common Dividends	2,395	4,334		3,773	3,578	3,169	2,278	1,782	1,542	1,214	1,165	1,111
Payout Ratio	24.07%	28.05%		27.9%	45.55%	29.44%	10.77%	19.99%	19.53%	12.34%	31.8%	15.29%
Shares Outstanding	362.3	309.6		328.1	340.8	352.1	350.5	356.4	371.6	385.4	401.6	427.4
Reference Market Price	423.8	889.6	889.6	580.1	386.4	348.1	397.5	263.7	231.6	175.0	255.5	244.9
EPS	30.3	49.91		41.22	23.05	30.57	60.35	25.01	21.25	25.53	9.12	17
Dividend per Share	7.57	14	14	11.5	10.5	9.0	6.5	5.0	4.15	3.15	2.9	2.6
Dividend Growth Rate	17.34%	0%	21.74%	9.52%	16.67%	38.46%	30%	20.48%	31.75%	8.62%	11.54%	1.96%
Dividend Yield	1.8%	1.57%	1.57%	1.98%	2.72%	2.59%	1.64%	1.9%	1.79%	1.8%	1.14%	1.06%