Foundations of Finance - Essay Example

Foundations of Finance- Group Based Assignment College 17th March 2008. Introduction Decision Makingis the utmost component in the life of a business and manager. Being a Finance manager is again another great problem where both the owners and the shareholders have to be satisfied. This is a dilemma facing each financial manager. The owner wants to retain as much as possible but the shareholders demand to fully disperse the profits. Another issue to be considered is selecting the companies for giving loans. Another crucial decision making is investments. Through this report we will bring such issues to light by computing some prime financial figures of two companies, namely DGSE COMPANIES INC and PUBLIC SERVICE ENTRP GRP INC. The report analyses the risk and return of these two companies. Then the cost structure of these companies is compared. The first part of the report focuses on calculating the means and the variances of the two companies. 'Mean' provides a measure of average return to investors while the 'variance' and hence the 'standard deviation' indicate risk. The second part of this report focuses on calculating the cost of capital for DGSE COMPANIES INC to aid the appraisal of a project under scrutiny. The cost of capital is the "opportunity cost of an investment; that is, the rate of return that a company would otherwise be able to earn at the same risk level as the investment that has been selected". CAPM will be used as the model. The equity cost of capital is found by accumulating the data relating to the company's and market returns at different points in time. PART - A RISK - RETURN RELATIONSHIP RETURN: The Mean, a measure of return is calculated by the formula: 'R' indicates the monthly holding period returns 'n' signifies the number of months The calculations yield a mean value of 0.026557 for DGSE COMPANIES INC and 0.014395 for PUBLIC SERVICE ENTRP GRP INC. These figures can be interpreted as for an investor investing $1 in DGSE COMPANIES INC and $1 in PUBLIC SERVICE ENTRP GRP INC, after a month he will get an average holding period return of 2.6 cents and 1.4 cents on his investments respectively. RISK: The Variance and the closely related Standard Deviation are measures of dispersions, which indicate how the possible values are spread around the mean and are an indicator of risk. For the purpose of calculations, the following formula is used for variance: As per the calculations, the monthly variance for DGSE COMPANIES INC is 0.0401 (4.01 %) and for PUBLIC SERVICE ENTRP GRP INC is 0.0050 (0.5%). The square roots of these figures give the monthly standard deviation which equals 0.200 (20%) and 0.0707 (7%), respectively. The Variance is indicative of volatility, hence the risk. It indicates how risky the investment is. A Comparison of risk and return of the two companies will give a clear idea. Table 1. RISK - RETURN RELATIONSHIP S.No Company Name Risk (%) Variance Return (%) - Mean 1 DGSE COMPANIES INC 4.01 2.6 2 PUBLIC SERVICE ENTRP GRP INC 0.5 1.4 The famous phrase "Higher the risk, higher the return" holds well in our case. Chart 1 Source: Primary Table 2. YEAR WISE RETURN COMPARISON YEAR DGSE PUBLIC 1997 0.0932 0.0212 1998 0.0418 0.0270 1999 0.0895 -0.0058 2000 0.0449 0.0401 2001 -0.0188 0.0034 2002 -0.0849 -0.0142 2003 0.0806 0.0318 2004 0.0199 0.0202 2005 -0.0269 0.0229 2006 0.0261 0.0063 Chart 2 Source: Primary CALCULATION OF MINIMUM VARIANCE PORTFOLIO S.No Company Name Risk (%) Variance Return (%) - Mean 1 DGSE COMPANIES INC 4.01 2.6 2 PUBLIC SERVICE ENTRP GRP INC 0.5 1.4 The total portfolio return considering equal proportion of each companies share is (0.5)*2.6 + (0.5)*1.4 = 2% By Trial and error method, the minimum variance portfolio is arrived at respective proportions. The following table and chart indicate the minimum variance and the efficient frontier. S.No Proportion (A) Proportion (B) Return (A) Return (B) Portfolio return 1 0.1 0.9 2.6 1.4 1.52 2 0.2 0.8 2.6 1.4 1.64 3 0.3 0.7 2.6 1.4 1.76 4 0.4 0.6 2.6 1.4 1.88 5 0.5 0.5 2.6 1.4 2 6 0.6 0.4 2.6 1.4 2.12 7 0.7 0.3 2.6 1.4 2.24 8 0.8 0.2 2.6 1.4 2.36 9 0.9 0.1 2.6 1.4 2.48 The minimum variance for the portfolio lies at equal proportions of A and B. This is the efficient frontier beyond which the portfolio return increases and below which the portfolio return decreases. This is represented in chart as follows: Minimum Variance Portfolio Conclusion: The portfolio has a minimum risk at a return of 2%. Equal proportion of both the companies is to be invested to reach the minimum variance portfolio. PART - B COST OF CAPITAL Cost of Capital is the required return necessary to make a capital budgeting project, such as building a new factory, worthwhile. Cost of capital includes the cost of debt and the cost of equity. The cost of capital determines how a company can raise money (through a stock issue, borrowing, or a mix of the two). This is the rate of return that a firm would receive if it investedin a different vehicle withsimilar risk. - Investopedia COST OF DEBT The effective rate that a company pays on its currentdebt is the cost of Debt. This can be measured in either before-or after-tax returns; however,because interest expense is deductible, the after-tax cost is seen most often.This is one part of the company's capital structure, which also includes the cost of equity. A company will use various bonds, loans and other forms of debt, sothis measure is usefulfor giving an idea as to the overall ratebeing paid bythe companyto use debt financing. The measure can also give investors an idea as to the risk of the company compared to others, because riskier companies generally have a higher cost of debt. To get the after-tax rate, you simply multiply the before-tax rate by one minus the marginal tax rate (before-tax rate x (1-marginal tax)). If a company's only debt were a single bond in which it paid 5%, the before-tax cost of debt would simply be 5%. If, however, the company's marginal tax rate were 40%, the company's after-tax cost of debt would be only 3% (5% x (1-40%)) - Investopedia COST OF EQUITY In financial theory, Cost of Equity is the return that stockholders require for a company. The traditional formula is the dividend capitalization model: A firm's cost of equity represents the compensation that the market demands in exchange for owning the asset and bearing the risk of ownership. For example, let's say you require a rate of return of 10% on an investment inTSJSports.The stock is currently trading at $10 and will pay a dividend of $0.30. Through a combination of dividends and share appreciation you require a $1.00 return on your $10.00 investment. Therefore the stock will have to appreciate by $0.70, which,combined with the $0.30from dividends, givesyou your 10% cost of equity. The capital asset pricing model (CAPM) is another method used to determine cost of equity - Investopedia CAPITAL ASSET PRICING MODEL (CAPM) A model that describes the relationship between risk and expected returnandthat is used in the pricing of risky securities. This model is used to arrive at the cost of equity. The general idea behind CAPM is that investors need to be compensated in two ways: time value of moneyand risk. The time value of money is represented by the risk-free (rf) ratein the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking onadditional risk. This is calculated by taking a risk measure (beta)that compares the returns of the asset to the market over a period of time and to the market premium (Rm-rf). Assumptions of CAPM All investors have rational expectations. There are no arbitrage opportunities. Returns are distributed normally. Fixed quantity of assets. Perfectly efficient capital markets. Investors are solely concerned with level and uncertainty of future wealth Separation of financial and production sectors. Thus, production plans are fixed. Risk-free rates exist with limitless borrowing capacity and universal access. The Risk-free borrowing and lending rates are equal. No inflation and no change in the level of interest rate exists. Perfect information, hence all investors have the same expectations about security returns for any given time period. Shortcomings of CAPM The model assumes that asset returns are (jointly) normally distributed random variables. It is however frequently observed that returns in equity and other markets are not normally distributed. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect. The model assumes that the variance of returns is an adequate measurement of risk. This might be justified under the assumption of normally distributed returns, but for general return distributions other risk measures (like coherent risk measures) will likely reflect the investors' preferences more adequately. The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black, Michael Jensen, and Myron Scholes. Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong - indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market). The model assumes that given a certain expected return investors will prefer lower risk (lower variance) to higher risk and conversely given a certain level of risk will prefer higher returns to lower ones. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well. The model assumes that all investors have access to the same information and agree about the risk and expected return of all assets. (Homogeneous expectations assumption) The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model. The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted. The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the inobservability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll's Critique. Theories such as the Arbitrage Pricing Theory (APT) have since been formulated to circumvent this problem. Because CAPM prices a stock in terms of all stocks and bonds, it is really an arbitrage pricing model which throws no light on how a firm's beta gets determined. The model does not appear to adequately explain the variation in stock returns. Empirical studies show that low beta stocks may offer higher returns than the model would predict. Some data to this effect was presented as early as a 1969 conference in Buffalo, New York in a paper by Fischer Black , Michael Jensen , and Myron Scholes . Either that fact is itself rational (which saves the efficient markets hypothesis but makes CAPM wrong), or it is irrational (which saves CAPM, but makes EMH wrong indeed, this possibility makes volatility arbitrage a strategy for reliably beating the market). The model assumes that investors demand higher returns in exchange for higher risk. It does not allow for investors who will accept lower returns for higher risk. Casino gamblers clearly pay for risk, and it is possible that some stock traders will pay for risk as well. The model assumes that all investors agree about the risk and expected return of all assets. (Homogeneous expectations assumption) The model assumes that there are no taxes or transaction costs, although this assumption may be relaxed with more complicated versions of the model. The model assumes that asset returns are log normally distributed random variables. There is significant evidence that equity and other markets are complex, chaotic systems. As a result, large swings (3 to 6 standard deviations from the mean) occur in the market more frequently than the normal distribution assumption would expect. These swings can greatly impact an asset's value. The market portfolio consists of all assets in all markets, where each asset is weighted by its market capitalization. This assumes no preference between markets and assets for individual investors, and that investors choose assets solely as a function of their risk-return profile. It also assumes that all assets are infinitely divisible as to the amount which may be held or transacted. The market portfolio should in theory include all types of assets that are held by anyone as an investment (including works of art, real estate, human capital...) In practice, such a market portfolio is unobservable and people usually substitute a stock index as a proxy for the true market portfolio. Unfortunately, it has been shown that this substitution is not innocuous and can lead to false inferences as to the validity of the CAPM, and it has been said that due to the in observability of the true market portfolio, the CAPM might not be empirically testable. This was presented in greater depth in a paper by Richard Roll in 1977, and is generally referred to as Roll's Critique. Theories such as the Arbitrage Pricing Model (APT) have since been formulated to circumvent this problem. The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken. The security market line plots the results of the CAPM for all different risks (betas). Using the CAPM modeland the following assumptions, we can compute the expected return of a stock: if the risk-free rate is3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17% (3%+2(10%-3%)). WEIGHTED AVERAGE COST OF CAPITAL One cost of equity and cost of debt are determines, the weighted average cost of capital is determined by assigning weights. WACC, thus, expresses the overall return required to satisfy the demands of both the groups of stakeholders. The WACC takes into account the relative weights of each component of the capital structure as the name implies so. The mathematical representation of the WACC concept is as follows: The market value of equity reflects the total value of a firm's equity currently available on the market. This can be calculated by multiplying the number of shares outstanding by the closing price, and finally multiplying this by 1000; the annual report on the company's website indicated that the number of shares were actually larger than the initial figure we obtained, and therefore the latter figure is necessary in order to calculate a more accurate and larger company value1. = 67739 (number of shares outstanding) x 1000 x 21.64 (closing share price) = $1,465,871,960.00 On the other hand, 'market value of debt' provides a measurement of the weight assigned to debt, as a proportion of the total capital finance of the company. However, for this project the long-term debt will be assumed to represent the market value of debt and on December 2005 this stood at $954,924,999.23. Calculating ''and '' While computing the 'cost of the debt' we take the borrowing rate of Old National Bancorp as a sum of the 'risk-free return' as indicated by one-month Treasury Bill rate used in CAPM and a 'default premium' defined by the credit spread. The debt rating category for this is 'AA'. Consequently, the credit spread for this is 0.5% per annum. This debt rating category indicates that the company has an adequate capacity to pay interest and repay principal; however, it provides investors with less protection than higher rated bonds, and so financial distress is more likely2. In order to compute the cost of debt, we will use the following formula: = + Credit Spread Thus, = 1.50% +0.5% = 2% (per annum) Quite rightly, WACC also incorporates debt tax shields. Since shareholders are concerned with the cash flows after the corporate taxes have been paid, therefore, there arises a need to incorporate the term '' into the formula indicating that the debt returns are tax deductible. '' indicates marginal corporate tax rate which was 35% as at December 2005. After some calculations we can see that the after-tax cost of debt is 3.84% [(5.90 x (1 - 0.35)]. Calculating the cost of capital With all the unknowns identified, we can now calculate the cost of capital as the 'after-tax weighted average cost of capital'. As per the CAPM and FFM, we have two values for the cost of equity 6.46% and 7.63% respectively. Therefore, we have two different values of WACC as illustrated: Thus, as per the WACC calculations above for the project under inspection to yield a positive 'Net Present Value', it should give a return higher than 5.426% using CAPM or 6.135% using FFM. Only under such a scenario can the investors be compensated for their capital investments. Furthermore, it must be noted that the CAPM model conveyed that the cost of equity was 6.46% compared to that of 7.63% in the Fama-French model. Therefore, the difference between the two models in our case is not large. Tests have shown that the difference of 2% per year between the estimates of the cost of equity from the CAPM, and the three factor model are common3. The main problem with respect to the calculations is the fact that it still relies on the standard deviations of factor sensitivities. These are large compared to the factor coefficients themselves, and are caused mainly by the volatility of returns over time. The Fama-French model has not triumphed in making the problem regarding volatility and credibility of returns disappear, as the standard errors of more than 3.0% per year in cost of equity is typical for both the CAPM and the three factor model. Conclusion The CAPM is appealing in its elegance and logic. When you look at the math, the theory becomes most appealing. However doubts begin to arise when one examines the assumptions more closely and these doubts are as much reinforced by the empirical tests. The models focus on market rather than total risk is clearly a useful way of thinking about the riskiness of the assets in general. Thus as a conceptual model, CAPM is of fundamental importance. Although the CAPM is enticing with the precision of numbers we do not know precisely how to measure any kind of inputs required for implementing CAPM. Historical data for return and beta vary greatly depending on the time period studied and the methods used to estimate them. The estimates used in CAPM are subject to potentially large errors. Because CAPM represents the way people who want to maximize returns while minimizing risk ought to behave, assuming they can get all the necessary data, the model is definitely here to stay. CAPM is a very easy and basic model and models must be developed considering the following limitations of CAPM. Attempts will continue to improve the model and to make it more useful. BIBLIOGRAPHY: 1. Brealey, Richard A., Stewart C. Myers, Franklin Allen Corporate Finance, 8th edition. London : McGraw-Hill/Irwin, 2006. 2. Van Horne, Wachowicz, Fundamentals of Financial Management, Ninth Edition, Prentice Hall of India 3. Fama, E. F. and K. R. French "Industry costs of equity." Journal of Financial Economics (1997). 4. Fischer, Jordan, "Security analysis and portfolio management", sixth edition, Prentice Hall Edition, pp 644 to 646. 5. Fama E. and K. French (1996), 'The CAPM is Wanted, Dead or Alive', Journal of Finance 51, 1947-58. 6. Ang A. and J. Chen (2006), 'CAPM over the Long Run: 1926-2001', forthcoming in the Journal of Empirical Finance. 7. Fama, E. and French, K. (1992). The Cross-Section of Expected Stock Returns, Journal of Finance, June 1992, 427-466. 8. Black, F., Jensen, M., and Scholes, M. The Capital Asset Pricing Model: Some Empirical Tests, in M. Jensen ed., Studies in the Theory of Capital Markets. (1972). 9. http://www.investopedia.com/terms/c/costofequity.asp Read More