BARK, Inc. (BARK) Two-Stage Excess Return Model

BARK, Inc.

BARK (NYSE)

(%)

Valuation
BARK, Inc. Two-Stage Excess Return Model

"""
    Model: Two-Stage Excess Return Model

# Render model description
model.render_description(r"""
## Two-Stage Excess Return Model

Used to estimate the value of companies based on two stages of growth. An initial period of high growth, represented by [Sum of discounted excess returns in Growth Stage], followed by a period of stable growth, represented by [Discounted excess return in terminal stage]. Excess Return models are better suited to calculate the intrinsic value of a financial company than an enterprise valuation model (such as the Discounted Free Cash Flow Model).

Read more: [GitHub Documentation](https://github.com/DiscountingCashFlows/Documentation/blob/main/models-documentation/excess-return-models.md#two-stage-excess-return-model-source-code)
""")

# Initialize assumptions
assumptions.init({
    "data": {
        "%discount_rate": None,
        "high_growth_years": 5,
        "%stable_return_on_equity": None,
        "%stable_growth_in_perpetuity": "2.5%",
        "%market_premium": data.get("risk:totalEquityRiskPremium"),
        "%risk_free_rate": data.get("treasury:year10"),
        "beta": data.get("profile:beta", default=1),
        "historical_years": 10,
    },
    "hierarchies": [{
        "parent": "%discount_rate",
        "children": ["beta", "%risk_free_rate", "%market_premium"]
    }]
})

# Set the discount rate to 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)

# Compute historical values and ratios
data.compute({
    '#index': 1,
    "dividendsPaidToCommon": "dividend:adjDividend * income:weightedAverageShsOut",
    "#bookValue": "balance:totalStockholdersEquity / income:weightedAverageShsOut",
    "%returnOnEquity": "income:netIncome / balance:totalStockholdersEquity:-1",
    "%payoutRatio": "dividend:adjDividend / income:eps",
    "#retainedEarningsPerShare": "income:eps - dividend:adjDividend",
    '%adjDividendGrowth': "function:growth:dividend:adjDividend",
})

data.set_default_range(f"{-assumptions.get('historical_years')}->0")

# Calculate average payout ratio and return on equity
average_payout_ratio = data.average("%payoutRatio", 0)
average_return_on_equity = data.average("%returnOnEquity")
assumptions.set("%stable_return_on_equity", average_return_on_equity)
assumptions.set_bounds(
    "%stable_return_on_equity", low="0%", high="100%"
)
stable_payout_ratio = 1 - assumptions.get("%stable_growth_in_perpetuity") / assumptions.get("%stable_return_on_equity")

payout_increase = (stable_payout_ratio - average_payout_ratio) / assumptions.get('high_growth_years')

# Compute forecasted values and ratios
data.compute({
    "#index": "#index:-1 + 1",
    "%payoutIncrease": f"#index * {payout_increase}",
    "%payoutRatio": f"%payoutIncrease:-1 + {average_payout_ratio}",
    "#beginningBookValue": "#bookValue:-1",
    "%returnOnEquity": assumptions.get('%stable_return_on_equity'),
    "income:eps": "#beginningBookValue * %returnOnEquity",
    "dividend:adjDividend": f"income:eps * %payoutRatio",
    "#retainedEarningsPerShare": "income:eps - dividend:adjDividend",
    "#bookValue": "#beginningBookValue + #retainedEarningsPerShare",
    "#equityCostPerShare": f"#beginningBookValue * {assumptions.get('%discount_rate')}",
    "#excessReturnPerShare": "income:eps - #equityCostPerShare",
    "%costOfEquity": assumptions.get("%discount_rate"),
    "#discountedExcessReturnPerShare": """
        function:discount:#excessReturnPerShare 
        rate:%costOfEquity
    """,
}, forecast=assumptions.get("high_growth_years"))

# Terminal year value calculation
terminal_book_value = data.get(f"#bookValue:{assumptions.get('high_growth_years')}")
terminal_eps = terminal_book_value * assumptions.get("%stable_return_on_equity")
terminal_equity_cost = terminal_book_value * assumptions.get("%discount_rate")
terminal_excess_return = terminal_book_value * (
            assumptions.get("%stable_return_on_equity") - assumptions.get("%discount_rate"))

if terminal_excess_return <= 0:
    model.warn("Excess return is negative. The Cost of Equity (Discount Rate) is higher than the Return on Equity.")

sum_of_discounted_excess_returns = data.sum(
    f"#discountedExcessReturnPerShare:1->{assumptions.get('high_growth_years')}")
terminal_value_of_excess_returns = terminal_excess_return / (
            assumptions.get("%discount_rate") - assumptions.get("%stable_growth_in_perpetuity"))
discounted_terminal_value = terminal_value_of_excess_returns / (
            1 + assumptions.get("%discount_rate")) ** assumptions.get("high_growth_years")
ltm_book_value_of_equity = data.get("#bookValue")

stock_value = ltm_book_value_of_equity + discounted_terminal_value + sum_of_discounted_excess_returns

model.set_final_value({
    "value": stock_value,
    "units": "$"
})

# Render results
model.render_results([
    [stock_value, "Estimated Value", "$"],
    [ltm_book_value_of_equity, "Book value of equity invested", "$"],
    [sum_of_discounted_excess_returns, "Sum of discounted excess returns in Growth Stage", "$"],
    [terminal_eps, "Terminal stage EPS", "$"],
    [terminal_book_value, "Terminal stage Book Value", "$"],
    [terminal_equity_cost, "Terminal stage Equity Cost", "$"],
    [discounted_terminal_value, "Discounted excess return in terminal stage", "$"],
    [terminal_value_of_excess_returns, "Excess Returns in the Terminal Stage", "$"],
    [assumptions.get("%discount_rate"), "Terminal Cost of Equity (the discount rate)", "%"],
    [terminal_excess_return, "Terminal year's excess return", "$"],
    [average_return_on_equity, "Average historical Return on Equity", "%"],
    [average_payout_ratio, "Average historical Payout Ratio", "%"],
    [stable_payout_ratio, "Payout Ratio in stable stage", "%"],
    [data.get("treasury:year10"), "Yield of the U.S. 10 Year Treasury Bond", "%"],
])

# Render chart
model.render_chart({
    "data": {
        "#bookValue": "Ending Book Value",
        "income:eps": "EPS",
        "dividend:adjDividend": "Dividend",
        "%payoutRatio": "Payout Ratio",
        "%returnOnEquity": "Return on Equity",
        "%costOfEquity": "Cost of Equity"
    },
    "start": -assumptions.get('historical_years'),
    "properties": {
        "title": "Historical and Forecasted Data",
        "set_editable": [
            "#bookValue",
            "%payoutRatio",
            "%returnOnEquity",
            "%costOfEquity"
        ],
        "hidden_keys": [
            "%payoutRatio",
            "%returnOnEquity",
            "%costOfEquity"
        ]
    }
})

# Projections Table
model.render_table({
    "data": {
        "#beginningBookValue": "Beginning Book Value",
        "#bookValue": "Ending Book Value",
        "income:eps": "EPS",
        "%returnOnEquity": "Return on Equity",
        "dividend:adjDividend": "Dividend per Share",
        "%payoutRatio": "Payout Ratio",
        "#retainedEarningsPerShare": "Retained Earnings",
        "#equityCostPerShare": "Equity Cost",
        "%costOfEquity": "Cost of Equity",
        "#excessReturnPerShare": "Excess Return",
        "#discountedExcessReturnPerShare": "Discounted Excess Return",
    },
    "start": -1,
    "properties": {
        "title": "Projected data",
        "order": "ascending"
    },
})

# Historical Table
model.render_table({
    "data": {
        "income:netIncome": "Net Income",
        "balance:totalStockholdersEquity": "Total Stockholders Equity",
        "%returnOnEquity": "Return on Equity",
        "dividendsPaidToCommon": "Dividends Paid to Common Shareholders",
        "%payoutRatio": "Payout Ratio",
        "income:weightedAverageShsOut": "Shares Outstanding",
        "income:eps": "Earnings per Share",
        "dividend:adjDividend": "Dividend per Share",
        "%adjDividendGrowth": "Dividend Growth Rate",
        "#bookValue": "Book Value",
    },
    "start": -assumptions.get('historical_years'),
    "end": 0,
    "properties": {
        "title": "Historical data",
        "number_format": "M",
        "display_averages": True
    },
})

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

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.
    """,

"high_growth_years": r"""
        ## High Growth Years

The estimated number of years during which the company is expected to experience high growth. After this period, the company will transition to a stable growth phase.
    """,

"%stable_return_on_equity": r"""
        ## Stable Return on Equity

The stable Return On Equity (ROE) estimated after the last projected period.
    """,

"%stable_growth_in_perpetuity": r"""
        ## Stable Growth in Perpetuity

The stable rate at which the company's book value is assumed to grow in perpetuity after the last projected period.
    """,

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

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

print("End of model.")

Warnings

Estimated Value

USD

Market Price USD

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

Two-Stage Excess Return Model

Interactive Assumptions

Discount Rate 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 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 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 Market Premium 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.	%
High Growth Years High Growth Years High Growth Years The estimated number of years during which the company is expected to experience high growth. After this period, the company will transition to a stable growth phase.	#
Stable Return On Equity Stable Return On Equity Stable Return on Equity The stable Return On Equity (ROE) estimated after the last projected period.	%
Stable Growth In Perpetuity Stable Growth In Perpetuity Stable Growth in Perpetuity The stable rate at which the company's book value is assumed to grow in perpetuity after the last projected period.	%
Historical Years Historical Years Historical Years The number of historical years used to calculate averages for historical data.	#

Results
Estimated Value	0.105 USD
Book value of equity invested	0.471 USD
Sum of discounted excess returns in Growth Stage	-0.138 USD
Terminal stage EPS	0.046 USD
Terminal stage Book Value	0.696 USD
Terminal stage Equity Cost	0.09 USD
Discounted excess return in terminal stage	-0.228 USD
Excess Returns in the Terminal Stage	-0.42 USD
Terminal Cost of Equity (the discount rate)	12.99%
Terminal year's excess return	-0.044 USD
Average historical Return on Equity	6.65%
Average historical Payout Ratio	0%
Payout Ratio in stable stage	62.43%
Yield of the U.S. 10 Year Treasury Bond	4.25%

Historical and Forecasted Data

Monetary values in USD

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Edit Chart Values	2026-03-31	2027-03-31	2028-03-31	2029-03-31	2030-03-31

↳ Growth Rate

Projected data

Monetary values in USD amounts except #	2025 Mar 31	LTM Mar 20	2026 Mar 31	2027 Mar 31	2028 Mar 31	2029 Mar 31	2030 Mar 31
Beginning Book Value	0.786	0.568	0.568	0.601	0.631	0.657	0.679
Ending Book Value	0.568	0.471	0.601	0.631	0.657	0.679	0.696
EPS	-0.19	-0.189	0.038	0.04	0.042	0.044	0.045
Return on Equity	-23.59%	-32.57%	6.65%	6.65%	6.65%	6.65%	6.65%
Dividend per Share			0.005	0.01	0.016	0.022	0.028
Payout Ratio	12.49%	12.49%	12.49%	24.97%	37.46%	49.94%	62.43%
Retained Earnings			0.033	0.03	0.026	0.022	0.017
Equity Cost	0.102	0.074	0.074	0.078	0.082	0.085	0.088
Cost of Equity	12.99%	12.99%	12.99%	12.99%	12.99%	12.99%	12.99%
Excess Return	-0.292	-0.262	-0.036	-0.038	-0.04	-0.042	-0.043
Discounted Excess Return			-0.032	-0.03	-0.028	-0.026	-0.023

Historical data

Monetary values in USD amounts except #	Average	LTM Mar 20	2025 Mar 31	2024 Mar 31	2023 Mar 31	2022 Mar 31	2021 Mar 31	2020 Mar 31	2019 Mar 31
Net Income	-41.5	-32.41	-32.88	-37.01	-61.52	-68.3	-31.39	-31.37	-37.08
Total Stockholders Equity	53.42	81.25	99.53	139.4	170.5	217.1	-159	-75.4	-46.01
Return on Equity	6.65%	-32.57%	-23.59%	-21.7%	-28.34%	42.96%	41.63%	68.18%	6.65%
Dividends Paid to Common Shareholders
Payout Ratio	12.49%	12.49%	12.49%	12.49%	12.49%	12.49%	12.49%	12.49%
Shares Outstanding	166.1	172.4	175.3	177.3	176.7	156.2	137.7	166.7	166.7
Earnings per Share	-0.246	-0.189	-0.19	-0.21	-0.36	-0.27	-0.31	-0.22	-0.22
Dividend per Share
Dividend Growth Rate
Book Value	0.288	0.471	0.568	0.786	0.965	1.39	-1.15	-0.452	-0.276

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BARK, Inc. Two-Stage Excess Return Model

Estimated Value

USD

Market Price USD

Two-Stage Excess Return Model

Interactive Assumptions

Discount Rate

Discount Rate

Beta

Beta

Risk Free Rate

Risk-Free Rate

Market Premium

Market Premium

High Growth Years

High Growth Years

Stable Return On Equity

Stable Return on Equity

Stable Growth In Perpetuity

Stable Growth in Perpetuity

Historical Years

Historical Years

Results

Historical and Forecasted Data

Projected data

Historical data

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)