// +------------------------------------------------------------+
//   Model: Two-Stage Excess Return Model 								
//   © Copyright: https://discountingcashflows.com
// +------------------------------------------------------------+

Input(
	{
		_DISCOUNT_RATE: '',
		HIGH_GROWTH_YEARS: 5,
		_STABLE_RETURN_ON_EQUITY: '',
		_STABLE_GROWTH_IN_PERPETUITY: '',
		_MARKET_PREMIUM: '',
		_RISK_FREE_RATE: '',
		BETA: '',
		HISTORICAL_YEARS: 10,
	},
	[{
		parent:'_DISCOUNT_RATE',
		children:['BETA', '_RISK_FREE_RATE', '_MARKET_PREMIUM']
	}]
);

$.when(
  get_income_statement(),
  get_income_statement_ltm(),
  get_balance_sheet_statement(),
  get_balance_sheet_statement_quarterly('length:2'),
  get_profile(),
  get_dividends_annual(),
  get_treasury(),
  get_fx(),
  get_risk_premium()).done(
  function($income, $income_ltm, $balance, $balance_quarterly, $profile, $dividends, $treasury, $fx, $risk_premium){
  try{    
    var response = new Response({
      income: $income,
      income_ltm: $income_ltm,
      balance: $balance,
      balance_quarterly: $balance_quarterly,
      balance_ltm: 'balance_quarterly:0',
      profile: $profile,
      treasury: $treasury,
      dividends: $dividends,
      risk_premium: $risk_premium,
    }).toOneCurrency('income', $fx).merge('_ltm');
    response.balance[0]['date'] = 'LTM';
    
    // +---------------- ASSUMPTIONS SECTION -----------------+
    setAssumption('_MARKET_PREMIUM', response.risk_premium.totalEquityRiskPremium );
	setAssumption('_RISK_FREE_RATE', response.treasury.year10);
    setAssumption('_STABLE_GROWTH_IN_PERPETUITY', response.treasury.year10);
    if(response.profile.beta){
    	setAssumption('BETA', response.profile.beta);
    }
    else{
    	setAssumption('BETA', 1);
    }
    setAssumption('_DISCOUNT_RATE', toP(getAssumption('_RISK_FREE_RATE') + getAssumption('BETA')*getAssumption('_MARKET_PREMIUM')));
	
    var sensitivity = 0.01;
    var prefDividendsRatio = absolute((response.income[0].eps * response.income[0].weightedAverageShsOut - response.income[0].netIncome) / response.income[0].netIncome);
    var commonIncome = [];
    if( prefDividendsRatio > sensitivity ){
      commonIncome = ['eps:0', '*', 'weightedAverageShsOut:0'];
    }
    else{
      commonIncome = ['netIncome:0'];
    }
    // Setup Original Data
    var original_data = new DateValueData({
      'netIncome': new DateValueList(response.income, 'netIncome'),
      'totalStockholdersEquity': new DateValueList(response.balance, 'totalStockholdersEquity'),
      'weightedAverageShsOut': new DateValueList(response.income, 'weightedAverageShsOut'),
      'eps': new DateValueList(response.income, 'eps'),
      'adjDividend': new DateValueList(response.dividends, 'adjDividend'),
    });
    var currentDate = original_data.lastDate();
    var nextYear = currentDate + 1;
    var forecast_end_date = currentDate + getAssumption('HIGH_GROWTH_YEARS');
    
    // Compute historical values and ratios
    var historical_computed_data = original_data.setFormula({
      'commonIncome': commonIncome,
      'preferredStockDividends': ['netIncome:0', '-', 'commonIncome:0'],
      'dividendsPaidToCommon': ['adjDividend:0', '*', 'weightedAverageShsOut:0'],
      'bookValue': ['totalStockholdersEquity:0', '/', 'weightedAverageShsOut:0'],
      '_returnOnEquity': ['commonIncome:0', '/', 'totalStockholdersEquity:-1'],
      '_payoutRatio': ['adjDividend:0', '/', 'eps:0'],
      'retainedEarnings': ['eps:0', '-', 'adjDividend:0'],
      '_adjDividendGrowth': ['function:growth_rate', 'adjDividend'],
      'index': [1],
    }).compute();
    
    var averagePayoutRatio = historical_computed_data.get('_payoutRatio').sublist(nextYear - getAssumption('HISTORICAL_YEARS')).average();
    var averageReturnOnEquity = historical_computed_data.get('_returnOnEquity').sublist(nextYear - getAssumption('HISTORICAL_YEARS')).average();
	setAssumption('_STABLE_RETURN_ON_EQUITY', toP(averageReturnOnEquity));
    var stablePayoutRatio = 1 - (getAssumption('_STABLE_GROWTH_IN_PERPETUITY') / getAssumption('_STABLE_RETURN_ON_EQUITY'));
    
    // Compute forecasted values and ratios
    var forecasted_data = historical_computed_data.setFormula({
      'bookValue': ['bookValue:-1', '+', 'retainedEarnings:0'],
      'eps': ['bookValue:-1', '*', getAssumption('_STABLE_RETURN_ON_EQUITY')],
      'adjDividend': ['eps:0', '*', '_payoutRatio:0'],
      'retainedEarnings': ['eps:0', '-', 'adjDividend:0'],
      '_returnOnEquity': ['eps:0', '/', 'bookValue:-1'],
      'equityCostPerShare': ['bookValue:-1', '*', '_costOfEquity:0'],
      'excessReturnPerShare': ['eps:0', '-', 'equityCostPerShare:0'],
      'discountedExcessReturnPerShare': ['function:discount', 'excessReturnPerShare', {rate: '_costOfEquity', start_date: currentDate}],
      '_costOfEquity': [getAssumption('_DISCOUNT_RATE')],
      'index': ['index:-1', '+', 1],
      '_payoutIncrease': ['index:0', '*', (stablePayoutRatio - averagePayoutRatio)/(getAssumption('HIGH_GROWTH_YEARS'))],
      '_payoutRatio': ['_payoutIncrease:-1', '+', averagePayoutRatio],
      'beginningBookValue': ['bookValue:-1'],
    }).setEditable(_edit(), {
      start_date: nextYear,
      keys: ['bookValue', '_payoutRatio', '_returnOnEquity', '_costOfEquity'],
    }).compute({forecast_end_date: forecast_end_date});
    // +------------- END OF ASSUMPTIONS SECTION -------------+
    
    // +---------------- MODEL VALUES SECTION ----------------+
    // Terminal year value calculation
    var terminalBookValue = forecasted_data.get('bookValue').valueAtDate(forecast_end_date);
    var terminalEPS = terminalBookValue * getAssumption('_STABLE_RETURN_ON_EQUITY');
    var terminalEquityCost = terminalBookValue * getAssumption('_DISCOUNT_RATE');
    var terminalExcessReturn = terminalBookValue * (getAssumption('_STABLE_RETURN_ON_EQUITY') - getAssumption('_DISCOUNT_RATE'));
    if(terminalExcessReturn <= 0){
        warning("Excess return is negative. The Cost of Equity (Discount Rate) is higher than the Return on Equity.");
    }
    var sumOfDiscountedExcessReturns = forecasted_data.get('discountedExcessReturnPerShare').sublist(nextYear).sum();
    var terminalValueOfExcessReturns = terminalExcessReturn / (getAssumption('_DISCOUNT_RATE') - getAssumption('_STABLE_GROWTH_IN_PERPETUITY'));
    var discountedTerminalValue = (terminalValueOfExcessReturns) / Math.pow(1 + getAssumption('_DISCOUNT_RATE'), getAssumption('HIGH_GROWTH_YEARS'));
    var ltmBookValueOfEquity = historical_computed_data.get('bookValue').valueAtDate('LTM');
	
    var valuePerShare = ltmBookValueOfEquity + discountedTerminalValue + sumOfDiscountedExcessReturns;
    var currency = response.currency;
    // If we are calculating the value per share for a watch, we can stop right here.
    if(_StopIfWatch(valuePerShare, currency)){
      return;
    }
    _SetEstimatedValue(valuePerShare, currency);
    print(valuePerShare, 'Estimated Value', '#', currency);
    print(ltmBookValueOfEquity, "Book value of equity invested", '#', currency);
    print(sumOfDiscountedExcessReturns, "Sum of discounted excess returns in Growth Stage", '#', currency);
    print(terminalEPS, "Terminal stage EPS", '#', currency);
    print(terminalBookValue, "Terminal stage Book Value", '#', currency);
    print(terminalEquityCost, "Terminal stage Equity Cost", '#', currency);
    print(discountedTerminalValue, "Discounted excess return in terminal stage", '#', currency);
    print(terminalValueOfExcessReturns, "Excess Returns in the Terminal Stage", '#', currency);
    print(getAssumption('_DISCOUNT_RATE'), "Terminal Cost of Equity (the discount rate)", '%');
    print(terminalExcessReturn, "Terminal year's excess return", '#', currency);
    print(averageReturnOnEquity, "Average historical Return on Equity", '%');
    print(averagePayoutRatio, "Average historical Payout Ratio", '%');
    print(stablePayoutRatio, "Payout Ratio in stable stage", '%');
    print(response.treasury.year10/100, 'Yield of the U.S. 10 Year Treasury Bond', '%');
    // +------------- END OF MODEL VALUES SECTION ------------+
    
    // +------------------- CHARTS SECTION -------------------+
    forecasted_data.removeDate('LTM').renderChart({
      start_date: nextYear - getAssumption('HISTORICAL_YEARS'),
      keys: ['bookValue', 'eps', 'adjDividend', '_payoutRatio', '_returnOnEquity', '_costOfEquity'],
      properties: {
        title: 'Historical and Forecasted Data',
        currency: currency,
        disabled_keys: ['_payoutRatio', '_returnOnEquity', '_costOfEquity'],
        hide_growth: ['_payoutRatio', '_returnOnEquity', '_costOfEquity'],
      }
    });
	// +---------------- END OF CHARTS SECTION ---------------+ 
    
    // +------------------- TABLES SECTION -------------------+
    // Dividend Table
    forecasted_data.removeDate('LTM').renderTable({
      start_date: currentDate,
      keys: ['beginningBookValue', 'bookValue', 'eps', '_returnOnEquity', 'adjDividend', '_payoutRatio', 
             'retainedEarnings', 'equityCostPerShare', '_costOfEquity', 'excessReturnPerShare', 'discountedExcessReturnPerShare'],
      rows: ['Beginning Book Value', 'Ending Book Value', 'EPS', '{%} Return on equity', 'Dividend', '{%} Payout Ratio',
                'Retained earnings', 'Equity cost', '{%} Cost of equity', 'Excess Return', 'Discounted Excess Return'],
      properties: {
        'title': 'Projected data (Per Share)',
        'currency': currency,
      },
    });
    
    // Historical Table
    historical_computed_data.renderTable({
      start_date: nextYear - getAssumption('HISTORICAL_YEARS'),
      keys: ['netIncome', 'totalStockholdersEquity', '_returnOnEquity', 'dividendsPaidToCommon',
             '_payoutRatio', 'weightedAverageShsOut', 'eps', 'adjDividend', '_adjDividendGrowth', 'bookValue'],
      rows: ['Net income', 'Equity', '{%} Return on equity', 'Dividends paid', 
             '{%} Payout ratio', 'Shares outstanding', '{PerShare} EPS',
             '{PerShare} Dividends', '{%} Dividend Growth Rate', '{PerShare} Ending Book Value'],
      properties: {
        'title': 'Historical data',
        'currency': currency,
        'number_format': 'M',
        'display_averages': true,
        'column_order': 'descending',
      },
    });
    // +---------------- END OF TABLES SECTION ---------------+
  }
  catch (error) {
    throwError(error);
  }
});

Description(`
	<h5>Two-Stage Excess Return Model</h5>
	<p>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).</p>
	<p class='text-center'>Read more: <a href='https://github.com/DiscountingCashFlows/Documentation/blob/main/models-documentation/excess-return-models.md#two-stage-excess-return-model-source-code' target='_blank'><i class="fab fa-github"></i> GitHub Documentation</a></p>
`,
  {
    _DISCOUNT_RATE: [
      '{Equation} \\text{Discount Rate} = \\text{Equity Weight} * \\text{Cost of Equity} + \\text{Debt Weight} * \\text{Cost of Debt} * (1 - \\text{Tax Rate})',
      '{Paragraph} 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.',
      '{Link} https://www.investopedia.com/terms/w/wacc.asp',
      
      '{Title} Cost of Equity',
      '{Equation} \\text{Cost of Equity} = \\text{Risk Free Rate} + \\text{Beta} * \\text{Market Premium}',
      '{Paragraph} The cost of equity is the theoretical rate of return that an equity investment should generate. It is calculated using the CAPM formula.',
      '{Link} https://www.investopedia.com/terms/c/costofequity.asp#mntl-sc-block_1-0-20',
      
      '{Title} Cost of Debt',
      '{Equation} \\text{Cost of Debt} = \\frac{\\text{Interest Expense}}{\\text{Total Debt}}',
      '{Paragraph} The cost of debt is the effective rate that a company pays on its debt, such as bonds and loans.',
      '{Link} https://www.investopedia.com/terms/c/costofdebt.asp',
      
      '{Title} Equity & Debt Weights',
      '{Equation} \\text{Debt Weight} = \\frac{\\text{Total Debt}}{\\text{Market Capitalization} + \\text{Total Debt}} = 1 - \\text{Equity Weight}',
      '{Paragraph} 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).',
      
      '{Title} Tax Rate',
      '{Equation} \\text{Tax Rate} = \\frac{\\text{Income Tax Expense}}{\\text{Income Before Tax}}',
      '{Paragraph} The overall tax rate paid by the company on its earned income.',
    ],
    _GROWTH_IN_PERPETUITY: 'The rate at which the company\'s free cash flow is assumed to grow in perpetuity. By default, this is equal to the yield of the U.S. 10 Year Treasury Bond.',
    _OPERATING_CASH_FLOW_MARGIN: [
      '{Equation} \\text{Projected Operating Cash Flow} = \\text{Projected Revenue} * \\text{Operating Cash Flow Margin}',
      'The margin used to project future Operating Cash Flow as a % from future Revenue.',
    ],
    _CAPITAL_EXPENDITURE_MARGIN: [
      '{Equation} \\text{Projected Free Cash Flow} = \\text{Projected Operating Cash Flow} - \\text{Projected Revenue} * \\text{Capital Expedinture Margin}',
      'The margin used to project future Capital Expedinture as a % from future Revenue, which is then used to calculate the Free Cash Flow.',
    ],	
    HISTORICAL_YEARS: 'Number of historical years used to calculate historical averages.',
    REVENUE_REGRESSION_SLOPE: `Future revenues are projected using a linear regression curve of past revenues.
      Set the slope:
      '>1' for a steeper revenue regression curve
      '0' for flat
      '<0' for inverse slope`,
    _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 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.',
    BETA: 'Beta is a value that measures the price fluctuations (volatility) of a stock with respect to fluctuations in the overall stock market.',
  });

Ticker	Company	Exchange	Currency
-	-	-	-

Ticker	Company
-	-

Login
Sign Up

GrafTech International Ltd. (EAF) NYSE

Currency in USD

Volume:

Day's Range:

EAF Selected Model: Two-Stage Excess Return Model

Name	Model	Model Type
	No model selected	-

*Notifications are added from the Watchlist&Notifications page.

Disclaimer: The data contained in this website is not necessarily real-time nor accurate. All derived (stocks, indexes, futures), cryptocurrencies, and Forex prices are not provided by exchanges but rather by our third party API www.financialmodellingprep.com, and so prices may not be accurate and may differ from the actual market price, meaning prices are indicative and not appropriate for trading purposes. Therefore, Discounting Cash Flows Group doesn't bear any responsibility for any trading losses you might incur as a result of using this data. Discounting Cash Flows Group or anyone involved with Discounting Cash Flows Group will not accept any liability for loss or damage as a result of reliance on the information including data, quotes, charts and buy/sell signals contained within this website. Please be fully informed regarding the risks and costs associated with trading the financial markets, it is one of the riskiest investment forms possible.