The Cost of Common Equity
The cost of common equity is an imperfect calculation, an estimation based upon valuing the firms risk relative to the market.
Learning Objective

Utilize various formulas to calculate the cost of common equity from different perspectives
Key Points
 Debt is a firm calculation of the cost of capital, where the lender applies an premium (interest rate) to the riskfree rate based upon the organization's existing assets (collateral) and the size of the loan.
 The cost of common equity is quite a bit less clear, as it is an estimation of the organization's susceptibility to risk.
 The capital asset pricing model (CAPM) is the traditional way to approach estimating an organization's required return rate for an investor, requiring a risk estimation.
 An expansion on the CAPM approach is the FamaFrench threefactor model, which adds company size and booktomarket ratio to this calculation.
 The dividend discount model is another method, where each expected future dividend payment is discounted to present day dollars to provide a valuation of the security.
Term

pricetobook ratio
Or markettobook ratio, this ratio compares the market valuation of an organization to the book value of the organization.
Full Text
As a funding source, debt and equity are priced quite differently. While debt relies heavily on default premiums being applied to a riskfree bond rate of interest (the premium usually dependent on the size of the debt compared to the size of the firm), equity isn't quite as welldefined. As a result, the cost of common equity is often inferred through assessing and comparing it to similar risk profiles, and trying to decipher the firm's relative sensitivity to systematic (market) risk.
The Capital Asset Pricing Model
One common tool used in assessing the cost of common equity is the capital asset pricing model (CAPM), which can be described via the following formula:
What this formula is saying is essentially that the cost of equity is equal to the risk free rate of return plus a premium for the expected risk of investing in the organization's equity. The variable are defined as follows:
 E_{s}  expected return for a security
 R_{f}  expected riskfree return rate
 β_{s}  sensitivity to market risk
 R_{m}  historical return of the stock market
 (R_{m} – R_{f})  risk premium of market assets over risk free assets
Other Tools to Value Equity
The cost of common equity is essentially the same thing as estimating the expected (or required) return to investors in the stock market. The idea is simply that the higher risk an organization is, the higher the corresponding return should be. As a result, there are countless stock price evaluation strategies and tactics one could use to estimate the cost of common equity from various perspectives. Two of these include the dividend discount model and the FamaFrench threefactor model.
Dividend Discount Model
In short, this theory states that a given stock is worth the sum of its future dividend payments, discounted to their present value. This is therefore a model of deriving the present value of future dividend payments, calculated as follows (assuming no end date):
In this calculation, P is the stock price while D is the dividend, g is the (constant) growth rate, and r is the constant cost of equity and t is time.
There are a few problems with this method, most notably that a steady and perpetual growth rate that is less than the cost of capital may not be reasonable. Similarly, this model is quite vulnerable to the growth rate. Also, not all stocks pay dividends.
FamaFrench ThreeFactor Model
Another valuation model was derived by Eugene Fama and Kenneth French with the intention to include company size and pricetobook ratio with overall market risk. You'll recognize the first half of this equation as the simple CAPM calculation, while the second half includes SMB (small minus big market capitalization) and HML (high minus low booktomarket ratio) multiplied by coefficients (from linear regression). While this all sounds a bit complicated, the basic premise is to offset the risk calculation with a stronger valuation for a firm's assets and scale:
Conclusion
All and all, the valuation of common equity is always an estimation. As understanding the risk of a given organization within the stock market is intrinsically speculative, equity tends to be quite a bit more costly than debt. After all, when an organization goes bankrupt it is the debtors who are reimbursed first, preferred stock next, and common stock last. This is the riskiest position of an investment.
Key Term Reference
 Assets
 Appears in these related concepts: Secured vs. Unsecured Funding, Defining LongLived Assets, and Defining the Marketing Objectives
 Common stock
 Appears in these related concepts: Claim to Income, Market Reporting, and Accounting for Preferred Stock
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Tax Considerations, and Accounting for Interest Earned and Principal at Maturity
 Preferred Stock
 Appears in these related concepts: Preferred Stock Rules and Rights, Voting Right, and Equity Finance
 Risk free rate
 Appears in these related concepts: Expected Risk and Risk Premium, Risk Adjusting the Discount Rate, and The Cost of Debt
 Securities
 Appears in these related concepts: Reporting, Using the Yield Curve to Estimate Interest Rates in the Future, and The Capital Asset Pricing Model
 Stock
 Appears in these related concepts: Ownership Nature of Stock, Advantages of Private Financing, and Financial Instruments
 asset
 Appears in these related concepts: Goodwill Impairment, Shifts in the Money Demand Curve, and Balance Sheets
 bond
 Appears in these related concepts: Factors Affecting the Price of a Bond, Current Maturities of LongTerm Debt, and Preferred Stock
 capital
 Appears in these related concepts: Differences Between Required Return and the Cost of Capital, The Acropolis, and Other Factors of Production
 cost of capital
 Appears in these related concepts: Advantages of the Payback Method, Calculating the IRR, and Cost of Capital Considerations
 debt
 Appears in these related concepts: Deficit Spending, the Public Debt, and Policy Making, Collection from Delinquent Payables, and Debt Utilization Ratios
 debtor
 Appears in these related concepts: Credit Operations, Activities to Manage Receivables, and Defining Finance
 default
 Appears in these related concepts: Notes Payable, Corporate Bonds, and Credit Ratings
 discount
 Appears in these related concepts: The Discount Rate, Par Value at Maturity, and Present Value, Multiple Flows
 dividend
 Appears in these related concepts: Defining Dividends, Investor Preferences, and Division and Factors
 equity
 Appears in these related concepts: Motivating and Compensating Salespeople, Civil Law and Criminal Law, and The Psychology of Employee Satisfaction
 expected return
 Appears in these related concepts: Expected Return, Types of Financial Decisions: Investment and Financing, and Arbitrage Pricing Theory
 growth rate
 Appears in these related concepts: The Valuation of Stocks, Calculating Perpetuities, and Discounted Dividend vs. Corporate Valuation
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 investor
 Appears in these related concepts: Formation of the Corporation, Agency, and The United States Banking System
 market risk
 Appears in these related concepts: Measuring Risk, Defining the Security Market Line, and Types of Risk
 premium
 Appears in these related concepts: The Term Structure, Redeeming Before Maturity, and Health Insurance
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Calculating Values for Different Durations of Compounding Periods, and Present Value and the Time Value of Money
 ratio
 Appears in these related concepts: Schedules of Reinforcement, The Importance of Productivity, and Basic Descriptive Statistics
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
 risk
 Appears in these related concepts: The ExportImport Bank of the United States, Approaches to Assessing Risk, and Risks Involved in Capital Budgeting
 risk premium
 Appears in these related concepts: Understanding Future Stock Value, Measuring and Managing Risk, and The Value of Diversification
 riskfree rate
 Appears in this related concept: Defining the Cost of Capital
 securities
 Appears in these related concepts: Secondary Market Organizations, Types of Market Organizations, and Seasoned Equity Offering
 security
 Appears in these related concepts: Advantages of Public Financing, Pricing a Security, and Underwriter
 strategy
 Appears in these related concepts: Operations Management, The Impact of Business Owners on Success and Failure Rates, and Considering the Environment
 valuation
 Appears in these related concepts: Evaluating Financial Statements, Valuation of Intangible Assets, and Basic Components of Asset Valuation
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
Sources
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