# Cost of Debt and Capital Asset Pricing Model Tapas K. Chakraborty A.C.W.A.

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Cost of Debt and Capital Asset Pricing Model Tapas K. Chakraborty A.C.W.A

Cost of Debt Debt is the cheapest form of financing as compared to other forms such as retained earnings, preferred stock, and common stock. Companies try to use as much debt as possible because it costs less. Debt of a firm includes bonds, debentures, and other debt securities. The lenders of debt finance are entitled to fixed rate of interest payment and redemption of debt at the end of the maturity period. Debt financing can be both long-term; required for expansion, purchasing assets, and increasing facilities, and short-term; to support day-to-day operational functions of the firm. Cost of debt refers to the effective rate that a company pays to the lenders on the existing debt. It can be measured before or after tax. But, since interest payment is tax deductible expenditure, after tax cost of debt is more reflective of effective rate, and is more comparable. It is an important construct of the cost of capital structure of the firm, the other being cost of equity. It is also a constituent of weighted average cost of capital (WACC). Cost of debt is based on the company’s cost of bond, which is a long-term debt. The rate of newly issued bond is the most appropriate to value cost of debt. A firm with no publicly traded bond can take cost of debt of other firms, with publicly traded bond to value the cost of its own debt. Cost of debt is also a yardstick to measure the riskiness of a company. More the cost of debt, more risky the company is. A potential investor can take investment decision by looking at the cost of debt of accompany.

Cost of Debt Calculated According to Barron’s Accounting Dictionary Cost of Debt = Interest Times (1 minus marginal tax rate). Symbolically, Cost of debt = i (1-t) i = rate of interest, t = corporate tax rate. Jones industries has a debt of \$600000 for 10 years, Annual interest payment is \$100000 i = 16.67% [(100000/600000)*100 = 16.67% (Historical interest rate)] t = 35% (US Federal Corporate Income tax rate. (Brigham. and Ehrardt., 2005) Cost of debt = 16.67(1 -.35) = 10.84%

Capital Assets Pricing Model Developed by Treynor, Sharpe, Linter, and Mossin, CAPM is a financial model, by which expected return on stock of a firm can be determined. The model takes into consideration the relationship between risk and return, in addition to the traditionally accepted time value of money. Time value of money is represented by risk free return (Rf). Compensation for taking risk is calculated by taking a risk measure called ‘beta’ (β). Beta compares the return of the asset to the market (Rm) and to the market premium (Rm-Rf). The expected return of a stock is compared with the required return. If the CAPM determined expected return is at least equal to or more than the required return, it may be advised to invest in the stock, else no. According to CAPM, expected return (Re) = Rf + β(Rm – Rf), where Re = expected return, Rm = expected market return, Rf = risk free rate of securities, like treasury bond or savings account.

Market Rate of Return Market return refers to the return of overall market portfolio that envelopes all assets traded in the market, weighted according their proportionate value. Market means equity market, like S&P, NASDAQ etc. Market rate of return or compounded annual growth rate (CAGR) =( P 1 /P 0 ) 1/n, where P 1 =current price of stock, P 0 =bas price of stock, n=number of years. The risk of a portfolio is the sum of risk of individual assets. (Brealey., and Myers., 1988) Behaviour of Return Over Time 0 Return Time Rm Rr Re The above diagram shows return curves, Re for less risky asset or portfolio, Rr for more risky asset or portfolio, and Rm for market portfolio.

Risk-Free Return Risk-free return refers to the minimum return an investor expects from an investment that has zero risk. This means a potential investor will accept risk only if return is higher than the aforesaid minimum return. In reality there is no such thing as risk free asset, which the model can base upon. But empirical evidences show that 2/3 rd. of the companies use long- term treasury bond rate as risk free rate. (Brunes, Eades, Harris, and Higgins,1998). Acceptance of long-term treasury bond rate as risk free return stems from the fact that, both stock and treasury bonds are long-term investments, and as such inflationary adjustments would be embodied in the return. Moreover treasury bills are more volatile than bonds.

Beta (β) Beta or beta coefficient is the measure of systematic risk of a security or a portfolio in comparison with the market. Thus beta is the response of the company’s stock to the market swing or trend. (Chandra, P., 2001). Mathematically, β = Covariance (x,y)/Variance x. Where x is the movements of stock price of the company, y is movement of the market index. A positive beta indicates the stock moves in the same direction as the market moves, and a negative beta indicates the reverse direction. β = 1 means the stock is equally volatile as the market, β > 1 means the stock is more volatile than the market, and β < 1 means the stock is less volatile than the market. For long-term treasury bond β = 0, that is no risk.

Beta Coefficients for Some Actual Companies Stock (Ticker Symbol)Beta: Thomson FinancialBeta: Yahoo! Finance Amazon.com (AMZN)1.822.87 Cisco Systems (CSCO)1.802.14 Merrill Lynch (MER)1.52 Dell Computer (Dell)1.411.71 General Electric (GE)1.251.06 Microsoft Crop. (MSFT)1.111.77 Energen Corp. (EGN)0.440.23 Empire District Electric (EDE) 0.420.00 Coca-Cola (KO)0.340.37 Procter & Gamble (PG)0.280.00 Heinz (HNZ)0.110.27 Sources: http://www.thomsonfn.com and http://finance.yahoo.com.http://www.thomsonfn.comhttp://finance.yahoo.com

Expected Return on Jones’ Stock Using CAPM Risk free return on treasury bond (Rf) 3% Return on overall market (Rm) 12% Beta(β) = 1.39 Re (expected return) = Rf + β(rm-Rf) = 3% + 1.39 (12%-3%) = 3.13% Beta greater than one means stock of Jones moves in the same direction as the market, but is more volatile than the market.

Summary  Cost of debt refers to the effective rate that is paid by the company to the lenders of the debt.  Higher the cost of debt, riskier is the company, and vice versa.  It is prudent to determine after tax cost of debt than before tax.  CAPM is a financial model that measures expected return of a stock.  CAPM considers both time value of money and compensation for risk taken.  Time value of money is measured by risk free rate of return.  Risk is measured by a term called beta-coefficient or (β), which is calculated from the covariance of the movement of company’s stock prices with the movement of market index.  The Treasury Bond rate is taken to be risk-free rate.

 Brealey R., and Myers.S., Principles of Corporate Finance, p. 143,[4 th. ed., New York, MacGraw hill]  Brunes, R.E., Eades, K.M., Harris, R.S., and Higgins, R.C., Best Practice in estimating Cost Of Capital  Chandra., P., Financial Management: Theory and Practice, p. 280,[ MacGraw Hill]  Fama, E.F., and Frenc,. K.R., (1992), The Cross Section of Expected Stock Returns, Journal of Finance, 47, 427- 465.  Fama, E.F., and French, K.R., (1993), Common Risk Factors in the returns of stocks and bonds, Journal of Finance, 33, 3-56 Reference

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