Fundamentals of Corporate Finance - Assignment Example

1. Top Choice Investments have given you '2,000,000 to invest for them. The funds can be invested in one or more projects. These projects are all indivisible. The investors require a minimum return of 25% and they are high risk takers. Details of the projects are as follows. Initial cost Expected return Risk (') ' Project A 1,200,000 22% 8% Project B 800,000 28% 10% Project C 1,200,000 30% 15% Project D 1,200,000 34% 17% Correlation coefficients between project returns are as follows. A & B 0.7 A & C 0.6 A & D 0.6 B & C 0.65 B & D 0.3 C & D 0.8 Required: (i) Evaluate how all of the '2M should be invested using portfolio theory (15 marks) Combination 1: A&B Analysis ' ' ' In. Cost Expected Return Std. dev Proportion A 1200000 22% 8% 0.6 B 800000 28% 10% 0.4 ' ' Correlation between A & B: 'ab 0.7 ' ' Portfolio return: Rp=wara + wbrb 0.244 ' ' Portfolio st. dev 'p=sqrt (wa2'a2 + wb2'b2 + 2wawb'ab'a'b) 0.081191 Portfolio theory suggests that the decision for the combination of stocks in order to maximize the return to the investors should incorporate two measures: the portfolio return of the combination, as well as the portfolio risk which is measured by the standard deviation of the portfolio. The return on this combination of portfolio is measured by getting the weighted return for each stock and adding them; as apparent in the equation where wa is the proportion of stock a to the whole portfolio investment and ra is the expected return for it. The same goes for stock b. By adding the product of the proportion and the return of these two stocks that form the combination, we get the portfolio return of 24.4% In order to get the risk of the combination of projects a and b, we use the formula for 'p=sqrt (wa2'a2 + wb2'b2 + 2wawb'ab'a'b), where we get the products of the variances of the proportions and the individual risks, adding them and adding them to the last figure which incorporates their correlation. With projects a and b's correlation of 0.7, we get a risk of .081191. Combination 2: B&C Analysis ' ' ' In. Cost Expected Return Std. dev Proportion B 800000 28% 10% 0.4 C 1200000 30% 15% 0.6 ' ' Correlation between B & C: 'bc 0.65 ' ' Portfolio return: Rp=wbrb + wcrc 0.292 ' ' Portfolio st. dev 'p=sqrt (wb2'b2 + wc2'c2 + 2wbwc'bc'b'c) 0.119917 By applying the same formula for projects b and c, we get the portfolio return of 29.2%, higher than the combination of projects a and b. The portfolio standard deviation on the other hand is 0.119917-the higher risk accompanying the higher expected return for the portfolio. Combination 3: B&D Analysis ' ' ' In. Cost Expected Return Std. dev Proportion B 800000 28% 10% 0.4 D 1200000 34% 17% 0.6 ' ' Correlation between B & D: 'bd 0.3 ' ' Portfolio return: Rp=wbrb + wdrd 0.316 ' ' Portfolio st. dev 'p=sqrt (wb2'b2 + wd2'd2 + 2wbwd'bd'b'd) 0.120216 Combinations of projects b and d have the highest return at 31.6%, with the highest risk of .120216 compared to the other two combinations. This higher return, when expected to have a drastic counterpart in the increase in risk is offset by the correlation of the two projects. This combination offers the lowest correlation at 0.3, which means that the projects' returns are not strongly correlated to the movement of the other, although the positive sign of correlation suggests the same direction of the two stocks in terms of movement. Recommendation The four projects offer seven possible combinations; however, because these projects are indivisible, the only three possible combinations left which are possible within the 2,000,000 limit are the combinations a and b, b and c, and b and d. These three combinations are assessed according to their returns and risks, measuring the returns by getting the proportion and weighted return, and then getting the risk by getting the portfolio standard deviation. Because the investors require a minimum return of 25%, combination of projects a and b is already eliminated from the choices. When both the combination of projects b and c, and projects b and d offer returns higher than 25%, the combination of projects b and d should be chosen because such portfolio provides the highest returns. High returns definitely accompany higher risks, but as it is stated in the question that the investors are high risk takers, they can opt for the combination which maximizes the value of their investment, which is the combination of projects b and d. This combination also offers the lowest correlation of all the seven combinations, which maximizes the effect of diversification. (ii) Discuss the various views and approaches to capital structure. (15 marks) Capital structure pertains to how a company finances its assets. One approach to capital structure is its default structure which utilizes an all-equity financing. This equity financing, as the company grows will not be sufficient in order to provide for some other activities such as expansion. Thus, the utilization of debt financing is necessary. The combination of debt and equity financing is another approach. The use of debt does not only provide an alternate financing for the company. In the world where there are no market distortions such as taxes, the utilization of debt would just be like the utilization of equity if we are talking about the effect of capital structure on the profitability of the company, or its return on equity. But in this world where there are taxes, debt financing provides a significant advantage to an organization. This is called the financial leverage, which increases the return on equity because of the tax shield that debt financing provides. This tax shield arises because interest payments are tax deductible. However, the combination of debt-equity as an approach to capital structure in order to provide financial leverage for the company only provides the firm benefits up to a certain point. When the company's debt reaches a certain level, its credit rating falls because of the issue of sustainability of the business supported by the company's own internal financing. Therefore, the company becomes riskier and higher costs of debts are required by creditors in order to compensate for the added risks. This offsets the benefits to the company of financial leverage. 2. (a) Top Choice's beta is 1.5. The expected return on treasury securities is 5 percent and the expected return on the market portfolio is 12 percent. Calculate the required return on the stock of this firm (15 marks) ' ' rm rf ' ' 12% 5% 1.5 ' ' ' ' Top Choice beta R=rf+'(rm-rf) 16% The capital asset pricing model as a method in determining the required rate of return on the stock of Top Choice requires the determination of the risk-free rate in the market, coupled with the market risk which determines the market premium, or the difference between the market risk and the risk-free rate, and the company's beta or the volatility of the company's stocks compared to the whole market. By using this formula, we get Top Choice's required rate of return of 16%. (b) Explain the following i. Investors' required rate of return (5 marks) When the company offers a security to the investors, it competes with other assets in terms of the risk and return that the investor could get from his or her investments. Therefore, for a certain level of risk investors demand a level of return. The maximum rate of return which will entice these investors to purchase or hold on to a security is called the investors' required rate of return. ii Systematic (5 marks) When investing in stocks and other assets in financial markets, there are risks that are inherent with the system. These risks are associated with the whole market, or a certain market segment. Because this kind of risk is related to the market itself, it cannot be minimized by choosing a lot of other stocks by diversification. That is why this kind is called as undiversifiable risk. iii Unsystematic risk (5 marks) Unsystematic risk is about the risk that is inherent when investing in a certain company-also known as company-unique risks. This unsystematic risk arises from the company's industry, operations, as well as management policies that affect the profitability of the business. Therefore, the risk that is inherent in the company is unique to it and can be minimized by diversifying investments to some other companies. Unsystematic risk is also known as diversifiable risk as it can be minimized by scattering the investments in many different companies. iv Standard deviation (5 marks) According to Brealey, Myers and Marcus in the book "Fundamentals of Corporate Finance" standard deviation is the square root of variance, where variance is the average squared variation around the average from the expected returns (2004, 276-277). Standard deviation measures the dispersion of the expected returns from the required rate of return in order to assess the risk of the investment. (c) What are the underlying assumptions of the capital asset pricing model' (15 marks) 12manage.com in its explanation of William Sharpe's model, lists down the assumptions under which the CAPM can only be valid, because its simplicity requires that there are certain things that should be left constant. These assumptions include "investors are risk-averse individuals who maximize the expected utility of their end period of wealth; investors have homogeneous expectations (beliefs) about asset returns; asset returns are distributed by the normal distribution; there exists a risk-free asset that investors may borrow or lend unlimited amounts of this asset at a constant rate; there is a definite number of assets and their quantities are fixated within one period world; all assets are perfectly divisible and priced in a perfectly competitive market; asset markets are frictionless and information is costless and simultaneously available to all investors; there are no market imperfections such as taxes, regulations, or restrictions on short selling (2008 November)." Capital asset pricing model is too simple that it requires some assumptions in order for its analysis to be valid. As mentioned earlier, when the market is assumed to be in a perfectly competitive state where information is available to everyone and people are rational investors who maximize their economic utility, CAPM is valid. Also, this assumption of a perfect competition includes the assumption that buyers are small enough to influence the price of the securities in the market; therefore there are less imperfections and distortions in the market as regards the rates that are used for the model. Also, the assumption of the investors being able to borrow and lend unlimited amounts at a risk-free rate is determined, as the borrowing and lending activities do not distort the market rates. Also, the presence of taxes is eliminated in the model, as well as other costs that are related to the transactions that would affect the rates of the market. This simple model incorporates all these assumptions, and requires that the analysis fulfill the assumptions in order for the model's results be considered valid. (d) Explain the following sources of short-term financing i Trade credit (5 marks) Trade credit is one of the most accessible sources of financing for a company. Trade credit occurs when a company makes purchases from a supplier, and the supplier gives a company a certain period before it the payment for the purchases can be made. These are also called trade payables. When a company makes a purchase and the supplier agrees that the purchase can be deferred in terms of payment instead of a cash-basis transaction, the company avails of trade credit. It does not have to release cash immediately. The terms of the sale will include the length of the period before the supplier collects the payment, and the pertinent discounts and surcharges. ii Overdraft facility (5 marks) When a company withdraws from its bank an amount greater than what it has deposited in its account, and this is made with agreement with the bank, this is called overdraft. Overdraft facility in the form of financing occurs when the withdrawn amount is greater than the deposited amount of the firm as agreed with the bank, with the difference in the amount being the firm's debt to the bank. This overdraft's agreement determines the pertinent interest rate that is applicable to the loan, the time of maturity as well as the amount which is the overdraft. iii Commercial paper (5 marks) Commercial paper is a form of financing which lasts for less than six months in its usual manner. This form of financing comes in the form of a certificate for securities with a company's promise to pay. These securities are sold in financial markets to people who trust the company issuing it. The reputation and credibility of the company serves as the catch for investors to purchase and hold on to it, that they trust the company's ability to meet its obligations to them in the form of the certificate. iv Transaction loan (5 marks) Another form of credit financing from the bank is called transaction loan. Transaction loans are loans that serve a specific transaction for a company-usually a financing source for some permanent need of a company such as short-term expansion for acquisition of inventories or retirement of trade payables. Like the bank overdraft, transaction loans come in agreement which specifies the maturity date of the loan, the amount of loan as well as the pertinent interest rates that are applicable. Transaction loans usually come in the form of promissory notes to the bank, which serve as the legal binding agreement between the two parties. Bibliography 12Manage.com (2008 November 8). Valuing stocks, securities, derivatives, and/or assets by relating risk and expected return: Explanation of Capital Asset Pricing Model of William Sharpe. Available from http://www.12manage.com/methods_capm.html. [Accessed 2 December, 2008] Brealey, R. A., Myers, S. C., & Marcus, A. J. (2004) Fundamentals of Corporate Finance. Philippines: McGraw Hill. Read More