T. Rowe Price Retirement 2010 Fund (PARAX) Simple Excess Return Model

T. Rowe Price Retirement 2010 Fund

PARAX (NASDAQ)

(%)

Models
T. Rowe Price Retirement 2010 Fund Simple Excess Return Model

# Render description block
model.render_description({
    "data": r"""
## Simple Excess Return Model

This model is used to estimate the value of companies that have **reached maturity** and earn stable excess returns with little to no chance of high growth.

**Note:** Excess return models are better suited for estimating the fair value of financial companies compared to enterprise valuation models, such as the **Discounted Free Cash Flow Model**.

> See [Valuing Financial Service Firms](https://pages.stern.nyu.edu/~adamodar/pdfiles/papers/finfirm09.pdf){target="_blank"}

### Fair Value Formulas

`Fair Value` = `Book Value of Equity` + `Present Value of Future Excess Returns`

`Present Value of Future Excess Returns` = `Next Year's Excess Return per Share` / (`Discount Rate` - `Growth In Perpetuity`)

> This model was inspired by Prof. Aswath Damodaran's spreadsheet [⬇️eqexret.xls](https://pages.stern.nyu.edu/~adamodar/pc/eqexret.xls)
""",
    "properties": {
        "width": "responsive"
    }
})

# --- Assumptions
assumptions.set({
    "timeseries": "annual",
    "data": {
        "#historicalYears": """
            3
        """,
        "#beta": """
            profile:beta
        """,
        "%riskFreeRate": """
            treasury:year10
        """,
        "%equityRiskPremium": """
            risk:totalEquityRiskPremium
        """,
        "%discountRate": """
            assumption:%riskFreeRate + assumption:#beta * assumption:%equityRiskPremium
        """,
        "%growthInPerpetuity": """
            2.5%
        """,
    },
    "titles": {
        "#historicalYears": "Historical Years",
        "#beta": "Beta",
        "%riskFreeRate": "Risk Free Rate",
        "%equityRiskPremium": "Equity Risk Premium",
        "%discountRate": "Discount Rate",
        "%growthInPerpetuity": "Growth In Perpetuity",
    },
    "properties": {
        "width": "responsive",
        "title": "Assumptions",
        "id": "component-2",
        "bindTo": None
    },
    "descriptions": {
        "#historicalYears": r"""
The number of years of historical data used to calculate averages and trends for analysis.
        """,
        "#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 is the additional return over the risk-free rate expected by investors for equity risk.
        """,
        "%discountRate": r"""
`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)
        """,
        "%growthInPerpetuity": r"""
The stable rate at which the company's book value is assumed to grow in perpetuity.
        """,
    },
    "hierarchies": [
        {
            "parent": "%discountRate",
            "children": [
                "#beta",
                "%riskFreeRate",
                "%equityRiskPremium",
            ]
        },
    ]
})

# --- Historical Calculations
data.compute({
    "user:dividendsPaidToCommonShareholders": """
        dividend:adjDividend * income:weightedAverageShsOut
    """,
    "user:#bookValue": """
        balance:totalStockholdersEquity / income:weightedAverageShsOut
    """,
    "user:%returnOnEquity": """
        income:netIncome / balance:totalStockholdersEquity:-1
    """,
    "user:%payoutRatio": """
        dividend:adjDividend / income:eps
    """,
    "user:#retainedEarnings": """
        income:eps - dividend:adjDividend
    """,
}, forecast=0, timeseries="annual")

model.render_table({
    "timeseries": "annual",
    "data": {
        "user:dividendsPaidToCommonShareholders": "Common Dividends Paid",
        "user:#bookValue": "Book Value",
        "user:%returnOnEquity": "Return on Equity",
        "user:%payoutRatio": "Payout Ratio",
        "user:#retainedEarnings": "Retained Earnings",
    },
    "start": data.get("""
        -assumption:#historicalYears
    """),
    "end": 0,
    "properties": {
        "title": "Historical Calculations",
        "order": "descending",
        "number_format": "M",
        "include_ltm": True,
        "display_averages": True,
        "width": "responsive"
    }
})

# --- ROE & Payout
assumptions.set({
    "timeseries": "annual",
    "data": {
        "%returnOnEquity": """
            function:average(start=-assumption:#historicalYears, end=0):user:%returnOnEquity
            or if this >= 100%:
            100%
        """,
        "%stablePayoutRatio": """
            1 - assumption:%growthInPerpetuity / assumption:%returnOnEquity
        """,
    },
    "titles": {
        "%returnOnEquity": "Return on Equity",
        "%stablePayoutRatio": "Stable Payout Ratio",
    },
    "properties": {
        "width": "responsive",
        "title": "ROE & Payout",
        "id": "component-4",
        "bindTo": "component-2"
    },
    "descriptions": {
        "%returnOnEquity": r"""
Return On Equity (ROE) is used to estimate the Earnings Per Share (EPS) expressed as a percentage of Book Value.
        """,
        "%stablePayoutRatio": r"""
The stable payout ratio estimates what the company can afford to pay out in dividends.

`Stable Payout Ratio` = 1 - `Growth in Perpetuity` / `Return on Equity`
        """,
    }
})

# --- Forecast Calculations
data.compute({
    "income:eps": """
        user:#bookValue:-1 * assumption:%returnOnEquity
    """,
    "dividend:adjDividend": """
        income:eps * assumption:%stablePayoutRatio
    """,
    "user:#retainedEarnings": """
        income:eps - dividend:adjDividend
    """,
    "user:#bookValue": """
        user:#bookValue:-1 + user:#retainedEarnings
    """,
    "user:#equityCostPerShare": """
        user:#bookValue:-1 * assumption:%discountRate
    """,
    "user:#excessReturn": """
        income:eps - user:#equityCostPerShare
    """,
    "user:%returnOnEquity": """
        income:eps / user:#bookValue:-1
    """,
}, forecast=5, timeseries="annual")

# --- Fair Value Calculation
data.compute_results({
    "#terminalValue": """
        user:#excessReturn:1 / (assumption:%discountRate - assumption:%growthInPerpetuity)
    """,
    "#fairValue": """
        result:#terminalValue + user:#bookValue
    """,
}, timeseries="annual")

model.render_results({
    "timeseries": "annual",
    "data": {
        "user:#excessReturn:1": {
            "label": "Next Year's Excess Return per Share",
            "type": "$"
        },
        "assumption:%discountRate": {
            "label": "Discount Rate",
            "type": "%"
        },
        "assumption:%growthInPerpetuity": {
            "label": "Growth In Perpetuity",
            "type": "%"
        },
        "user:#bookValue": {
            "label": "Book Value of Equity",
            "type": "$"
        },
        "result:#terminalValue": {
            "label": "+ Present Value of Future Excess Returns",
            "type": "$"
        },
        "result:#fairValue": {
            "label": "= Fair Value",
            "type": "$"
        },
    },
    "properties": {
        "title": "Fair Value Calculation",
        "width": "responsive",
        "hidden_keys": []
    }
})

# --- Fair Value
model.set_final_value({
    "value": data.get("""
        result:#fairValue
    """, timeseries="annual"),
    "units": "$",
    "title": "Fair Value",
    "properties": {
        "width": "full" 
    }
})

model.render_chart({
    "timeseries": "annual",
    "data": {
        "income:eps": "Eps",
        "user:#equityCostPerShare": "Equity Cost per Share",
        "user:#excessReturn": "Excess Return",
    },
    "start": -10,
    "end": 5,
    "properties": {
        "title": "Preview Excess Returns",
        "include_ltm": False,
        "set_editable": [],
        "hidden_keys": [],
        "bar_keys": [],
        "width": "full"
    }
})

# Render description block
model.render_description({
    "data": r"""
## Understanding the Calculations

Excess Return represents the additional earnings the company generates over the cost of equity. It is calculated as:

`Excess Return` = `Earnings per Share (EPS)` - `Equity Cost per Share`

We forecast EPS figures based on our assumed return on equity and the beginning book value per share, which is the equity per share at the start of the fiscal year.

`Earnings per Share (EPS)` = `Beginning Book Value` * `Return on Equity`

Equity Cost per Share is the expected return required by equity investors.

`Equity Cost per Share` = `Beginning Book Value` * `Cost of Equity`

Ending Book Value reflects the updated value of equity after accounting for retained earnings during the period:

`Ending Book Value` = `Beginning Book Value` + `Retained Earnings`

Retained Earnings is the portion of earnings not paid out as dividends and reinvested in the company. It is calculated as:

`Retained Earnings` = `Earnings per Share (EPS)` - `Dividend per Share`

Dividends are determined using the payout ratio, which represents the portion of earnings paid out.

`Dividend per Share` = `Earnings per Share (EPS)` * `Payout Ratio`
""",
    "properties": {
        "width": "responsive"
    }
})

# --- Preview Calculations
data.compute({
    "user:%payoutRatio": """
        assumption:%stablePayoutRatio
    """,
}, forecast=5, timeseries="annual")

model.render_table({
    "timeseries": "annual",
    "data": {
        "user:#bookValue:-1": "Beginning Book Value",
        "user:#bookValue": "Ending Book Value",
        "user:%returnOnEquity": "Return on Equity",
        "income:eps": "Earnings per Share (EPS)",
        "user:%payoutRatio": "Payout Ratio",
        "dividend:adjDividend": "Dividend per Share",
        "user:#retainedEarnings": "Retained Earnings",
        "assumption:%discountRate": "Cost of Equity (Discount Rate)",
        "user:#equityCostPerShare": "Equity Cost per Share",
        "user:#excessReturn": "Excess Return",
    },
    "start": 1,
    "end": 5,
    "properties": {
        "title": "Preview Calculations",
        "order": "ascending",
        "number_format": "M",
        "include_ltm": True,
        "display_averages": False,
        "width": "responsive"
    }
})

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Simple Excess Return Model

This model is used to estimate the value of companies that have reached maturity and earn stable excess returns with little to no chance of high growth.

Note: Excess return models are better suited for estimating the fair value of financial companies compared to enterprise valuation models, such as the Discounted Free Cash Flow Model.

See Valuing Financial Service Firms

Fair Value Formulas

Fair Value = Book Value of Equity + Present Value of Future Excess Returns

Present Value of Future Excess Returns = Next Year's Excess Return per Share / (Discount Rate - Growth In Perpetuity)

This model was inspired by Prof. Aswath Damodaran's spreadsheet ⬇️eqexret.xls

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 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.	%
↳ Equity Risk Premium Equity Risk Premium The market risk premium is the additional return over the risk-free rate expected by investors for equity risk.	%
Historical Years Historical Years The number of years of historical data used to calculate averages and trends for analysis.	#
Growth In Perpetuity Growth In Perpetuity The stable rate at which the company's book value is assumed to grow in perpetuity.	%
Return on Equity Return on Equity Return On Equity (ROE) is used to estimate the Earnings Per Share (EPS) expressed as a percentage of Book Value.	%
Stable Payout Ratio Stable Payout Ratio The stable payout ratio estimates what the company can afford to pay out in dividends. `Stable Payout Ratio` = 1 - `Growth in Perpetuity` / `Return on Equity`	%

Historical Calculations

Monetary values in USD amounts except #	Average	LTM Mar 07	2025	2024	2023
Common Dividends Paid
Book Value
Return on Equity
Payout Ratio
Retained Earnings

Fair Value Calculation
Next Year's Excess Return per Share
Discount Rate	7.45%
Growth In Perpetuity	2.5%
Book Value of Equity
+ Present Value of Future Excess Returns
= Fair Value

Simple Excess Return Model

Fair Value Formulas

Assumptions

Discount Rate

Beta

Risk Free Rate

Equity Risk Premium

Historical Years

Growth In Perpetuity

Return on Equity

Stable Payout Ratio

Historical Calculations

Fair Value Calculation

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

T. Rowe Price Retirement 2010 Fund Simple Excess Return Model

Simple Excess Return Model

Fair Value Formulas

Assumptions

Discount Rate

Beta

Risk Free Rate

Equity Risk Premium

Historical Years

Growth In Perpetuity

Return on Equity

Stable Payout Ratio

Historical Calculations

Fair Value Calculation

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)