Capital Asset Pricing Model – Understanding Cost of Capital

The fundamental valuation of an asset to estimate intrinsic value, using free cash flow model to estimate the value. These expected cash flows are discounted at cost of equity and debt, this lesson discusses an overview of Capital Asset Pricing Model to give you tools to understand the concepts better. This lesson discusses the risk, it’s imperative to learn about the development of Capital Asset Pricing middle Road. The series is getting rebooted under Investment Analysis and Portfolio Management Series.  William Sharpe (1964), Litner (1965) and Mossin (1966) are credited with the development of Capital Market Theory and Capital Asset Pricing Model, a critical underpinning to the portfolio theory.

Dr. Harry Markowitz is considered the father of modern portfolio theory. He published the paper Portfolio Selection in March, 1952 issue of the Journal of Finance, a gamechanger for portfolio management.  

The premise of the portfolio theory is that investors make decisions on expected return and risk: i.e., variability of the portfolio. Variance is the measure of the risk of a portfolio; the higher the risk higher the expected return. Investors will need extra compensation for an additional unit of risk. There are various measures to capture risk example Sharpe ratio, the Treynor ratio. For this course, it’s good to have a basic understanding of concepts in statistics. Variance is the square of standard deviation. The CAPM is the model that you will be using in this course to quantify the cost of equity.

Understanding Beta 

Risk can be divided into diversifiable and non-diversifiable risks. Diversifiable risk is a firm inherent risk, a risk that can de be diversified using more securities in the portfolio. Firm risk is a unique risk pertinent to business and strategy risk. Non-diversifiable risk is a global macro risk example; recession and interest rate risk cannot be diversified. Capital Asset Pricing Model uses riskless assets with a market portfolio. Riskless assets have zero variance, government securities of advanced countries example the United States of short-term duration. Market Portfolio includes tradeable assets, both financial and real assets. Examples of financial assets are stocks, and bonds, while real assets include commodities, land, art, etc. Investment Analysis and Portfolio Management covers the derivation of the model along with concepts like capital market line and security market line. An in-depth understanding of CAPM in essential for the understanding of portfolio management. Look out for the Investment Analysis and Portfolio Management for an in-depth understanding of the CAPM model and portfolio management.  

Beta measures systematic risk and can be calculated in various ways. One is by measuring the covariance with the benchmark index, another through regression analysis – regressing a company’s returns with that of the benchmark index.

Yahoo finance and other online sources share the beta of companies example, Microsoft has a beta of 0.91 calculated for five years monthly. This means that the price of the stock is likely to increase by 91 percent if NASDAQ goes up by 100 percent or fall by 91 percent if NASDAQ falls by 100 percent. 

Beta is the covariance of a security with the benchmark index. Beta is what we are interested to discuss today. Look out for an in-depth analysis on CAPM in the upcoming series on investment analysis and portfolio management. 

The S&P 500® is widely regarded as the best single gauge of large-cap U.S. equities. 

The value of beta will be given to measure cost of equity using the CAPM.

CAPM= Risk free rate + Beta (Market Risk Premium)                                                 

R_{f =} Risk free rate. Risk free asset has zero variance and zero correlation with risky assets. There are two ways of using risk free rate. Usually T bills or short term yields are used but according to Aswath Damodaran in the text book Investment Valuation its better to use treasury bonds for valuing long term projects or valuations. When calculating risk premium i.e. excess return over risk free rate, the duration of the term must be similar to that of treasury bonds. Bonds have interest, default and reinvestment risk its better to refer to Fixed Income Introduction online course on The middle Road. Many advanced countries have no default risk for their government securities, for countries with sovereign risk use the formula below. 

Risk free rate in local currency = Government or Sovereign Bond Rate –  Default Spread  

The sovereign rate is the yield of the bond.

• Beta measured against a market portfolio which includes all traded securities held in proportion to their market value.   
• We are assuming no there are no transaction costs or private information

Intrinsic valuation includes measuring present value of expected cash flows. For equity valuation, the cash flows are calculated after debt payments, expenses, reinvestment needs etc. Includes return to only equity with the discounting rate is cost of equity. For valuing firm valuation, the cash flows are prior to debt payments but after firm has invested in reinvestment for growth. Incudes return to both equity and bond holders, preferred stock holders. The discounting rate is WACC i.e. weighted average cost of capital (cost of equity and cost of debt based on their proportions). CAPM uses single factor model to calculate the value of Beta, there are other models arbitrage and multifactor models to calculate multifactor beta values. However, here we will use only single factor model. 

WACC = C_e (E/E+D) + C_d (D/E+D)

 C_{e = Cost of Equity}   C_{d  =  Cost of Debt}  

Present Value of the Firm = Present value of Equity + Market Value of Debt

The article Explaining Why Investors Hold Sovereign Bonds with Default Risk based on the NBER working paper series Sovereign Bonds since Waterloo Josefin Meyer Carmen M. Reinhart Christoph Trebesch, the author Linda Gorman shares a synopsis of the research paper. Government can issue debt in a foreign currency; the Napoleon wars led to the external bond issuance. According to the report, from 1815 to 2016, investors reaped an average inflation-adjusted return of 6.77 percent on a global portfolio of sovereign bonds in British pounds or U.S. dollars. The sample database included over 1400 bonds from countries other than the U.S. and U.K.; these bonds are classified as external sovereign bonds. The data set has 219968 monthly observations with another data set based on haircuts on the bonds due to restructuring or repudiation of bonds. Haircuts are the discount given on the par value of the bond. Research shows coupon payments accounted for 70 percent of the returns on the bonds.

Cost of Equity 

For an all equity firm, the cost of equity is used as the discounting rate. Beta is the covariance of the stock with the benchmark index.

Cost of Equity =   Risk free rate + Beta (Market Risk Premium)

Cost of Capital = Cost of equity (Proportion of equity used to fund business) + pretax cost of debt (1-tax rate) (Proportion of debt used to fund business)

Cost of Debt

Firms use loans, bonds and other forms of debt to fund expansion or meeting working capital requirements. Cost of debt for advanced companies is easier to measure but more complicated to calculate the cost of borrowing for emerging markets. To estimate cost of debt especially for emerging markets, you need to understand country default spreads. For example, country’s with Aaa ratings have no default risk i.e. the markets expect these country’s will not default on their debt. Example Singapore, Sweden

* Adjusted default spread Rwanda 8.16%, Philippines 2.82%, Serbia 5.34%

Cost of debt for emerging markets = Riskless rate + Country default spread emerging markets + Company default spread synthetic ratings

Companies default risk can be measured through credit default spreads. As the default risk increase, the cost of borrowing increases. For example, to calculate cost of debt for a company in Ghana, you will need to take the yield on the government security usually of 3 months for risk free rate. It usually better to consider government security of the borrowing duration. To know more about bonds, refer to the free online course on fixed income securities.

For country default risk and risk premiums refer to the link here posted by  Aswath Damodaran. Add default spread to the mature market premium to arrive at the total equity risk premium. Bonds value are recorded on par but the premium or discount on the par value is amortized over time. Long term debt is more than one year in duration when you are using bonds for valuing cost structure.

Tax Shield Interest payments/expense are tax deductible, so after tax cost of debt is lower than pretax cost of debt

After tax cost of debt= Pretax cost of debt (1-tax rate)