CRA International, Inc. (CRAI) Discounted Future Market Cap

CRA International, Inc.

CRAI (NASDAQ)

(%)

Valuation
CRA International, Inc. Discounted Future Market Cap

"""
    Model: Discounted Future Market Cap

# Render model description
model.render_description(r"""
## Discounted Future Market Cap

This model estimates the intrinsic value of a common share by projecting the Future Market Capitalization using the estimated PE Ratio and then discounting it to the Present using an Annual Required Rate of Return.
""")

# 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"),
        "pe_ratio": data.get("quote:close") / data.get("income:eps"),
        "%revenue_growth_rate": None,
        "%net_income_margin": None,
        "historical_years": 10,
        "projection_years": 5,
    },
    "hierarchies": [{
        "parent": "%discount_rate",
        "children": ["beta", "%risk_free_rate", "%market_premium"]
    }]
})

# Calculate cost of equity
cost_of_equity = assumptions.get("%risk_free_rate") + assumptions.get("beta") * assumptions.get("%market_premium")
assumptions.set("%discount_rate", cost_of_equity)

# Compute metrics
data.compute({
    "%grossMargin": "income:grossProfit / income:revenue",
    "%operating_margin": "income:operatingIncome / income:revenue",
    "%netMargin": "income:netIncome / income:revenue",
    "%revenueGrowthRate": "function:growth:income:revenue",
    "%netIncomeGrowthRate": "function:growth:income:netIncome",
    "%totalStockholdersEquityGrowthRate": "function:growth:balance:totalStockholdersEquity",

# Calculating NOPAT (Net Operating Profit After Taxes)
    "%taxRate": "income:incomeTaxExpense / income:incomeBeforeTax",
    "incomeTax": "income:operatingIncome * %taxRate",
    "nopat": "income:operatingIncome - incomeTax",

# Calculating Invested Capital
    "investedCapital": [
        "balance:totalNonCurrentAssets", "-", "balance:cashAndCashEquivalents", "+",
        "balance:totalCurrentAssets", "-", "balance:totalCurrentLiabilities"
    ],
    "%roic": "nopat / investedCapital",
})

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

assumptions.set("%net_income_margin", data.average(f"%netMargin"))
assumptions.set_bounds(
    "%net_income_margin", low=0, high="100%"
)

assumptions.set("%revenue_growth_rate", data.average(f"%revenueGrowthRate"))
assumptions.set_bounds(
    "%revenue_growth_rate", low=0, high="25%"
)

# Calculate a linear regression for forecasting revenues
data.compute({
    "linearRegressionRevenue": f"function:linear_regression:income:revenue start:{-assumptions.get('historical_years')}",
}, forecast=assumptions.get("projection_years"))

# Compute forecasted values and ratios
data.compute({
    "income:revenue": f"function:compound:{data.get('linearRegressionRevenue:1')} rate:{assumptions.get('%revenue_growth_rate')} offset:-1",
    "%revenueGrowthRate": "function:growth:income:revenue",
    "income:netIncome": f"income:revenue * {assumptions.get('%net_income_margin')}",
}, forecast=assumptions.get("projection_years"))

projected_revenue = data.get("revenue")
projected_net_income = data.get(f"income:netIncome:{assumptions.get('projection_years')}")

shares_outstanding = data.get("income:weightedAverageShsOut")
future_market_cap = assumptions.get("pe_ratio") * projected_net_income
discounted_future_market_cap = future_market_cap / (
            (1 + assumptions.get("%discount_rate")) ** assumptions.get("projection_years"))

stock_value = discounted_future_market_cap / shares_outstanding

# Set the final value
model.set_final_value({
    "value": stock_value,
    "units": "$"
})

# Render results
model.render_results([
    [stock_value, "Present Value", "$"],
    [projected_net_income, "Estimated net income", "$"],
    [future_market_cap, "Estimated market capitalization", "$"],
    [discounted_future_market_cap, "Market capitalization discounted to present", "$"],
    [shares_outstanding, "Shares Outstanding", "#"],
    [data.get("income:eps"), "Earnings Per Share (EPS)", "$"],
    [data.get("quote:close"), "Market Price", "$"],
    [data.get("ratio:priceEarningsRatio"), "Price to Earnings (PE) Ratio", "#"]
])

# Render chart
model.render_chart({
    "data": {
        "income:revenue": "Revenue",
        "income:netIncome": "Net Income",
        "linearRegressionRevenue": "Linear Regression Revenue"
    },
    "start": -assumptions.get("historical_years"),
    "end": "*",
    "properties": {
        "title": "Historical and forecasted data",
        "set_editable": [
            "income:revenue",
            "income:netIncome"
        ],
        "hidden_keys": ["linearRegressionRevenue"]
    }
})

# Render table for estimated future values
model.render_table({
    "data": {
        "income:revenue": "Revenue",
        "%revenueGrowthRate": "Revenue Growth Rate",
        "income:netIncome": "Net Income",
    },
    "start": -1,
    "end": "*",
    "properties": {
        "title": "Estimated Future Values",
        "order": "ascending",
        "number_format": "M"
    }
})

# Render historical values table
model.render_table({
    "data": {
        "income:revenue": "Revenue",
        "income:costOfRevenue": "Cost of Revenue",
        "income:grossProfit": "Gross Profit",
        "%grossMargin": "Gross Margin",
        "income:operatingIncome": "Operating Income",
        "%operating_margin": "Operating Margin",
        "income:netIncome": "Net Income",
        "%netMargin": "Net Margin",
    },
    "start": -assumptions.get("historical_years"),
    "end": 0,
    "properties": {
        "title": "Historical Values",
        "display_averages": True,
        "order": "descending",
        "number_format": "M"
    },
})

# Render historical growth rates table
model.render_table({
    "data": {
        "income:revenue": "Revenue",
        "%revenueGrowthRate": "Revenue Growth Rate",
        "income:netIncome": "Net Income",
        "%netMargin": "Net Margin",
        "%netIncomeGrowthRate": "Net Income Growth Rate",
        "balance:totalStockholdersEquity": "Stockholders Equity",
        "%totalStockholdersEquityGrowthRate": "Equity Growth Rate",
        "%roic": "Return on Invested Capital (ROIC)",
        "nopat": "After-tax Operating Income",
        "%taxRate": "Income Tax Rate",
        "investedCapital": "Invested Capital",
    },
    "start": -assumptions.get("historical_years"),
    "end": 0,
    "properties": {
        "title": "Historical Growth Rates",
        "display_averages": True,
        "order": "descending",
        "number_format": "M"
    },
})

# Set description 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

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.
    """,

"pe_ratio": r"""
        ## Price to Earnings (PE) Ratio

Estimated Price to Earnings (PE) Ratio at the end of the projection period.

`Future Market Cap` = `PE Ratio` * `Projected Net Income`
    """,

"%revenue_growth_rate": r"""
        ## Revenue Growth Rate

The annual revenue growth rate is applied to projected revenue starting from the second projection year onward.
    """,

"%net_income_margin": r"""
        ## Net Income Margin

Net Income expressed as a percentage of Revenue.
    """,

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

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

"projection_years": r"""
        ## Projection Years

The number of years for projecting the analysis into the future.
    """,
})

print("End of model.")

Estimated Value

USD

Market Price USD

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

Discounted Future Market Cap

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 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.	%
Pe Ratio Price to Earnings (PE) Ratio Estimated Price to Earnings (PE) Ratio at the end of the projection period. `Future Market Cap` = `PE Ratio` * `Projected Net Income`	#
Revenue Growth Rate Revenue Growth Rate The annual revenue growth rate is applied to projected revenue starting from the second projection year onward.	%
Net Income Margin Net Income Margin Net Income expressed as a percentage of Revenue.	%
Historical Years Historical Years The number of historical years used to calculate averages for historical data.	#
Projection Years Projection Years The number of years for projecting the analysis into the future.	#

Results
Present Value	133.1 USD
Estimated net income	51.92 Mil. USD
Estimated market capitalization	1.35 Bil. USD
Market capitalization discounted to present	901.8 Mil. USD
Shares Outstanding	6.78 Mil.
Earnings Per Share (EPS)	7.5 USD
Market Price	195.1 USD
Price to Earnings (PE) Ratio	25.94

Historical and forecasted data

Monetary values are in USD

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Edit Chart Values	2025	2026	2027	2028	2029

↳ Growth Rate

Estimated Future Values

amounts of USD except for #	2024	LTM	2025	2026	2027	2028	2029
Revenue	687.4	697.5	722.9	779.8	841.1	907.3	978.7
Revenue Growth Rate	10.17%	1.46%	5.16%	7.87%	7.87%	7.87%	7.87%
Net Income	46.65	50.96	38.35	41.37	44.62	48.13	51.92

Historical Values

amounts of USD except for #	Average	LTM	2024	2023	2022	2021	2020	2019	2018	2017	2016	2015
Revenue	503.8	697.5	687.4	624	590.9	565.9	508.4	451.4	417.6	370.1	324.8	303.6
Cost of Revenue	354.4	484.2	479.9	452.2	410.1	400.1	370.7	317.8	289.2	258.8	227.4	207.7
Gross Profit	149.4	213.3	207.5	171.7	180.8	165.9	137.7	133.6	128.5	111.2	97.4	95.91
Gross Margin	29.75%	30.58%	30.18%	27.52%	30.6%	29.31%	27.08%	29.6%	30.76%	30.06%	29.99%	31.59%
Operating Income	41.7	76.68	70.75	56.61	58.74	55.74	34.8	29.35	28.93	15.76	18.92	12.39
Operating Margin	7.69%	10.99%	10.29%	9.07%	9.94%	9.85%	6.84%	6.5%	6.93%	4.26%	5.83%	4.08%
Net Income	28.85	50.96	46.65	38.48	43.62	41.68	24.51	20.75	22.49	7.62	12.89	7.66
Net Margin	5.3%	7.31%	6.79%	6.17%	7.38%	7.36%	4.82%	4.6%	5.38%	2.06%	3.97%	2.52%

Historical Growth Rates

amounts of USD except for #	Average	LTM	2024	2023	2022	2021	2020	2019	2018	2017	2016	2015
Revenue	503.8	697.5	687.4	624	590.9	565.9	508.4	451.4	417.6	370.1	324.8	303.6
Revenue Growth Rate	7.87%	1.46%	10.17%	5.6%	4.41%	11.32%	12.63%	8.07%	12.85%	13.95%	6.99%	-0.918%
Net Income	28.85	50.96	46.65	38.48	43.62	41.68	24.51	20.75	22.49	7.62	12.89	7.66
Net Margin	5.3%	7.31%	6.79%	6.17%	7.38%	7.36%	4.82%	4.6%	5.38%	2.06%	3.97%	2.52%
Net Income Growth Rate	25.67%	9.24%	21.24%	-11.78%	4.66%	70.07%	18.12%	-7.76%	195%	-40.84%	68.32%	-43.86%
Stockholders Equity	208.9	227.3	212.1	212.1	211.2	205.8	209	197.8	196.5	207.2	207.9	211.1
Equity Growth Rate	0.575%	7.19%	-0.013%	0.448%	2.58%	-1.52%	5.7%	0.651%	-5.19%	-0.315%	-1.51%	-1.69%
Return on Invested Capital (ROIC)	11.11%	18.47%	16.98%	15.34%	14.41%	15.5%	8.11%	6.76%	11.81%	4.31%	6.99%	3.51%
After-tax Operating Income	29.98	54.37	49.83	41.66	43.57	42.8	25.36	22.72	22.47	8.01	12.3	6.63
Income Tax Rate	30.62%	29.09%	29.57%	26.41%	25.82%	23.21%	27.11%	22.58%	22.33%	49.22%	34.98%	46.47%
Invested Capital	257.1	294.3	293.4	271.5	302.3	276.1	312.7	336.2	190.3	185.7	176	189.1