Case Study Analysis Cost Of Capital At Ameritrade Finance Essay

Case Study Analysis Cost Of Capital At Ameritrade Finance Essay Capital Asset Pricing Model is a model that describes the relationship between risk and expected return  and  that is used in the pricing of risky securities. Description: Capital Asset Pricing Model (CAPM) The general idea behind CAPM is that investors need to be compensated in two ways: time value of money  and risk. The time value of money is represented by the risk-free(rf) rate  in 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 on  additional 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). 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 model  and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is  3%, 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%)). CAPM has a lot of important consequences. For one thing it turns finding the efficient frontier into a doable task, because you only have to calculate the co-variances of every pair of classes, instead of every pair of everything. Another consequence is that CAPM implies that investing in individual stocks is pointless, because you can duplicate the reward and risk characteristics of any security just by using the right mix of cash with the appropriate asset class. This is why followers of MPT avoid stocks, and instead build portfolios out of low cost index funds. Cap-M looks at risk and rates of return and compares them to the overall stock market. If you use CAPM you have to assume that most investors want to avoid risk, (risk averse), and those who do take risks, expect to be rewarded. It also assumes that investors are price takers who cant influence the price of assets or markets. With CAPM you assume that there are no transactional costs or taxation and assets and securities are divisible into small little packets. CAPM assumes that investors are not limited in their borrowing and lending under the risk free rate of interest. How to Calculate the Cost of Equity CAPM The cost of equity is the amount of compensation an investor requires to invest in an equity investment. The cost of equity is estimable is several ways, including the capital asset pricing model (CAPM). The formula for calculating the cost of equity using CAPM is the risk-free rate plus beta times the market risk premium. Beta compares the risk of the asset to the market, so it is a risk that, even with diversification, will not go away. As an example, a company has a beta of 0.9, the risk-free rate is 1 percent and the expected return on the equity investment is 4 percent. Instructions Determine the market risk premium. The market risk premium equals the expected return minus the risk-free rate. The risk-free rate of return is usually the United States three-month Treasury bill rate. In our example, 4 percent minus 1 percent equals 3 percent. Multiply the market risk premium by beta. In our example, 3 percent times 0.9 equals 0.027. Add the risk-free rate to the number calculated in Step 2 to determine the cost of equity. In our example, 0.027 plus 0.01 equals a cost of equity of 0.037 or 3.7 percent. . Combining the risk-free asset and the market portfolio gives the portfolio frontier. The risk of an individual asset is characterized by its co-variability with the market portfolio. The part of the risk that is correlated with the market portfolio, the systematic risk, cannot be diversified away. Bearing systematic risk needs to be rewarded. The part of an assets risk that is not correlated with the market portfolio, the non-systematic risk, can be diversified away by holding a frontier portfolio. Bearing non-systematic risk need not be rewarded. For any asset i: where We thus have an asset pricing model the CAPM. Example. Suppose that CAPM holds. The expected market return is 14% and T-bill rate is 5%. What should be the expected return on a stock with ÃŽÂ ² = 0? Answer: Same as the risk-free rate, 5%. à ¢Ã¢â€š ¬Ã‚ ¢ The stock may have significant uncertainty in its return. à ¢Ã¢â€š ¬Ã‚ ¢ This uncertainty is uncorrelated with the market return. What should be the expected return on a stock with ÃŽÂ ² = 1? Answer: The same as the market return, 14%. What should be the expected return on a portfolio made up of 50% T-bills and 50% market portfolio? Answer: the expected return should be  ¯r = (0.5)(0.05)+(0.5)(0.14) = 9.5%. Multifactor CAPM In CAPM, investors care about returns on their investments over the next short horizon they follow myopic investment strategies. In practice, however: à ¢Ã¢â€š ¬Ã‚ ¢ Investors do invest over long horizons à ¢Ã¢â€š ¬Ã‚ ¢ Investment opportunities do change over time. In equilibrium, an assets premium is given by a multi-factor CAPM : Limitations of CAPM Based on highly restrictive assumptions i.e. no tax, transaction costs etc Serious doubts about its testability. Market factor is not the sole factor influencing stock returns. Summary of CAPM CAPM is attractive: 1. It is simple and sensible: is built on modern portfolio theory distinguishes systematic risk and non-systematic risk provides a simple pricing model. 2. It is relatively easy to implement. CAPM is controversial: 1. It is difficult to test: difficult to identify the market portfolio difficult to estimate returns and betas. 2. Empirical evidence is mixed. 3. Alternative pricing models might do better. Multi-factor CAPM. Consumption CAPM (C-CAPM). APT. Other Methods for calculating cost of equity There are 3 methods which are mainly used for calculating Cost of equity other than CAPM Arbitrage Pricing theory 3 factor method Dividend Growth Method Arbitrage Pricing Theory APT assumes that returns on securities are generated by number of industry-wide and market-wide factors. Correlation between a pair of securities occurs when these securities are affected by the SAME factor or factors. Return on any stock traded in a financial market consists of two parts. R = Re + U Where, R = return on any stock Re = Expected or Normal return (depends on all of information shareholders have on the stock for next month.) U = Uncertain or Risky return (this comes from information revealed in the month) U = m +  Ã‚ ¥Ã¢â€š ¬Ã‚   Where, m = Systematic risk or market risk (it influences all assets of market)  Ã‚ ¥Ã¢â€š ¬Ã‚  Ã¢â€š ¬Ã‚  Ã¢â€š ¬Ã‚ ½ Unsystematic risk (it affects single asset or small group interrelated of assets, it is specific to company) The capital asset pricing theory begins with an analysis of how investors construct efficient portfolios. But in real life scenarios, it isnt necessary that every time portfolios will be efficient. It is developed by Stephen Ross. Moreover, the return is assumed to obey the following simple relationship: Where b1, b2 and b3 are sensitivities associated with factor 1, factor 2 and factor 3 which can be interest rate or other price factors. Noise =  Ã‚ ¥ is event unique to the company. APT states that the expected risk premium on a stock should depend on the expected risk premium associated with each factor and the stocks sensitivity to each of the factors. Thus, formula modifies to: Where, rf = risk free rate is subtracted from each return to give risk premium associated from each factor. Analysis of the formula: If we put value for b = 0, the expected risk premium will be zero. It will create a diversified portfolio which has zero sensitivity to macroeconomic factor which offers risk free rate of interest. Portfolio offered a higher return, investors could make a risk-free (or arbitrage) profit by borrowing to buy the portfolio. If it offered a lower return, you could make an arbitrage profit by running the strategy in reverse; in other words, you would sell the portfolio and invest the proceeds in U.S. Treasury bills. Consider portfolio A and B are sensitive to factor 1, A is twice sensitive to factor1 as then portfolio Therefore, if you divided your money equally between U.S. Treasury bills and portfolio A, combined portfolio would have exactly the same sensitivity to factor 1 as portfolio B and would offer the same risk premium. Steps of Arbitrage Pricing Theory The various steps during Arbitrage Pricing Theory can be stated as: Identify the macroeconomic factors: APT doesnt indicate which factors are to be considered. But there are 6 principle factors which are: Yield spread interest rate, exchange rate, GNP inflation portion of the market return Estimate the risk premium of each factor Estimate the factor sensitivity Net Return = risk free interest rate + expected risk premium 3 factor model It is a special case of APT It considers 3 major factors called as market factor size factor book to market factor. There is also evidence that these factors are related to company profitability and therefore may be picking up risk factors that are left out of the simple CAPM. The practical application of this model is to estimate the betas for the three factors and then use them to predict where returns should fall, much like the CAPM. It was researched by Fama and French. Dividend Growth Method Dividend Discount Model. It is useful when the growth rate of dividend is forecasted constantly. The present value of stocks is given as Where, r = discount rate, g = rate of growth, DIV = annual cash payment, This formula can be used when growth rate g When growth rate = rate of return, the present value becomes infinite. For perpetual growth, r > g. Growing perpetuity formula, Where,P0 in terms of next years expected dividend DIV g = the projected growth trend r = expected rate of return on other securities of comparable risk. We can estimate cost of equity from this formula by re-arranging. Lets understand by an example: Suppose that your company is expected to pay a dividend of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year and the market expects that to continue. The current price is $25. Then cost of equity r is given as: When the growth rate isnt constant but varies from year to year, then average can be calculated. Growth rate for current year is calculated using the formula: For example, Year Dividend (in Rs. Million) Percent change (g) 2000 1.23 2001 1.30 (1.30 1.23) / 1.23 = 5.7% 2002 1.36 (1.36 1.30) / 1.30 = 4.6% 2003 1.43 (1.43 1.36) / 1.36 = 5.1% 2004 1.50 (1.50 1.43) / 1.43 = 4.9% Growth rate is average of all percent changes and equals This model serves the major advantage of being easy to understand and use but has a major drawback total dependence on dividend and it cannot be used where company isnt paying any dividend. Also, it doesnot consider any risk and is highly sensitive to the change in growth rate. Estimating Beta Beta is an important term in Capital Asset Pricing Method. Beta is the non-diversified risk of holding a single stock. But it turns out that companies in similar markets have similar risks. Interpretation of beta Beta = 1,it matches market portfolio Beta > 1, higher risk. Beta Methods for calculation of beta It is calculated as: beta_{i} = frac {mathrm{Cov}(R_i,R_m)}{mathrm{Var}(R_m)} Where, Ri = rate of return of asset and Rm is rate of return of market. Thus, beta is dependent on regression analysis. Beta is found by statistical analysis of individual, daily share price returns, in comparison with the markets daily returns over precisely the same period. We need to gather a lengthy time-series of observations for the market return and the individual asset return. Then required co-variances and variances can be calculated. If coefficient of correlation P is known then The alternative method of calculating beta is (by rearranging terms from CAPM equation): In practice, an additional constant alpha is also added in the above equation which tells how much better (or worse) the funds did than what the CAPM predicted. Alpha is a risk-adjusted measure of the so-called active return on an investment. Here, E(Ri) Rf is estimated return on asset portfolios and E(Rm) Rf is estimated return on market index. In order to check that there are no serious violations of the linear regression model assumptions. The slope of the fitted line from the linear least-squares calculation is the estimated Beta. The vertical intercept of this curve is called as the alpha. For a portfolio of assets, we have the relation: Given that beta is a linear risk measure, the beta of a portfolio of assets as simply the weighted average of all the individual betas that comprise the portfolio. HANU Estimate of Risk Premium We dont have reliable estimate where stock market will move in future. So we are using long term historical spreadsheets for estimate large stock than small stocks because they are more closer to proper estimate of market We are considering all values after Second World War because after that laws became stable in U.S. Risk premium = Rm Rf U.S. government securities rate = 6.69% (20 years bond, Exhibit 3) Average annual return for Large company stocks = 14 % (Exhibit 3) So Risk premium for Ameritrade = 14 % 6.69 % =7.31 %

Large Schools vs. Small Schools: Which perform better?

Small schools perform better than large schools in more than one aspect. A study finds that small rural communities with a school have significantly higher housing values, more new housing, smaller income variability, fewer households receiving public assistance, lower poverty and child poverty rates, more workers in professional and managerial jobs, and more workers employed within the community. (1) The existence of schools even in small rural areas proves many benefits, but there is a larger question posed, would it be more beneficial to have a small school or a large one? This paper aims to find which category offers more to the quality of students. It may be true that large schools may have grander facilities like television and radio stations but there is more than behind the curtain of facilities. An extensive body of research demonstrates numerous positive benefits of small schools and small learning communities, especially for those students who are at greatest risk of educational failure. Indeed, in a synthesis of research on small schools, Raywid (1997/1998, p. 35) concludes, â€Å"there is enough evidence now of such positive effects—and of the devastating effects of large size on substantial numbers of youngsters—that it seems morally questionable not to act on it.† (2) This is more or less the same stand that this paper takes. In a small school there would be more benefits. As you will see throughout the paper, there have been studies that point out the benefits of a small school over that of a large one.   There is almost 40 years of existing research and literature on small schools which indicates that students in small schools have higher attendance and graduation rates (1), fewer drop-outs, equal or better levels of academic achievement (2), higher levels of extra-curricular participation (3) and parent involvement, and fewer incidences of discipline and violence (4). (3) Wasley, et al (2000, pg 4) says small schools increase student attendance across all types of small schools: schools-within-schools (SWS), freestanding small schools, and multi-school small schools. Lakhman (1999), on the other hand found that between 1988 and 1998, DeWitt Clinton high school developed 10 small schools. During that time, they reduced their dropout rate by 8.5% and increased their on-time graduation rate by almost 50%. Thus, proving that small schools have the ability to improve attendance and graduation rate. Moreover, researchers observe that the effects of smallness on achievement are indirect, being mediated through other small-school features as quality of the social environment and students' sense of attachment to the school. Mitchell (2000) reminds us that in the studies conducted by Howley and others, school size had such a powerful positive effect on the achievement of poor students that it even trumped the beneficial effects of class size (Cotton, 2001). This can also be credited to the fact that in a small school, they can focus more on the need of each student. Sometimes, students does not need a large school with lots of reference books but a school that encourages a lot of help, from peers and teachers. There are several studies whose findings reveal that students at all grade levels learn more in small schools than in large schools. Several researchers have also examined middle-grades schools with interdisciplinary teams and found that students in this type of small learning community outperform similar students in schools without such organizational arrangements (Mertens and Flowers, 2003; Mertens, Flowers, and Mulhall, 2001; George and Lounsbury, 2000; Lee and Smith, 2000; Felner et al., 1997; Lee and Smith, 1993). (2) In addition from improved attendance, higher graduation rates and improved academic achievement in small schools, another factor that is considered is the students’ level of participation.   Take for example Mitchell’s (2000) observation where in a school of 2,000 students, only the most talented will be recruited for the basketball team or the drama club. The result is that a small number of gifted students dominate the sports and activity rosters, while the vast majority are relegated to spectator status. In small schools, sports teams, musical groups and clubs depend on broader participation. The number of extracurricular opportunities does increase with school size. But a twentyfold increase in population produces only a fivefold increase in opportunities. That is, as the school expands, an increasingly smaller percentage of students are needed to fill the available slots. In short, more students produce less participation. Most students will not be required to participate because there will be others who would. In a small school every student will have the opportunity to hone and improve their talents and interests. Researchers point out that, in small schools, everyone is needed to populate teams, offices, and clubs; thus, even shy and less able students are encouraged to participate and made to feel they belong. In addition to the factors mentioned, another advantage of a small school over a large one involves more personalized approach where levels of parent involvement and parent satisfaction are greater in small school environments than in large ones. Communication between parents and teachers tends to be more substantive given the fact that the teachers often know the students better in the smaller learning environment (Cotton, 2001). This is a positive reinforcement of discipline for the students.   In a smaller learning environment, the students’ activities can be monitored and can be reported to parents, whether a violation or a perceived improvement. Among the advantages mentioned, the fewer incidence of violence is perhaps the most important. â€Å"There is less violence in small schools, less vandalism, a heightened sense of belonging, and better attendance,† the KnowledgeWorks report states. (4)   Another research also showed that â€Å"In urban schools with less than 300 students, 3.9% of the schools reported serious violent incidents compared with 32.9% of schools over 1,000 students (Gregory, 2000).† Small schools are better positioned to detect and help hurting students, and to address disruptive behavior before it escalates into tragic violence and abuse. When teachers know virtually all students in a school community by name, it fosters a culture of belonging, accountability, and support. The Association for Supervision and Curriculum Development (2000) studies show that small learning environments are characterized by fewer incidents of violence and disruptive behavior, less school graffiti, lower crime levels, and less serious student misconduct. The association attribute this to what they term as â€Å"human-scale schooling† which reduces isolation and increasing the sense of belongingness. Indeed, a closer community will bring more familiarity and less hostility. Hence, with all the aspects considered in the paper, it can be deduced that in a school of smaller quantity, we can focus more on the students’ quality. From this standpoint, the performance of a small school is better. Even policy makers have noted these benefits leading to   the development of some new rules. These includes: Florida Small School Law which recognizes the benefits of small schools and prohibits, as of July 2003, the construction of large schools. As of that date, new elementary schools will be limited to 500 students, middle schools to 700, and high schools to 900. Another is the Vermont Funding for Small Schools which in 1997, Vermont adopted a new system of funding education under Vermont Act 60 – The Equal Educational Opportunity Act (EEOA). Unlike most states, Vermont choose to provide additional funding to cover the higher costs of the state's smallest school districts. An extra $1 million per year was allocated to districts with fewer than 100 students. (5) This paper believes as far as, the future can depend on small school more than large ones, and to borrow Daniel Kinnaman’s title, the future will be filled up by small schools (with) big benefits.

The Iranian Revolution - 732 Words

Longevity and positive outcomes are what determine whether a revolution is successful or not. This is not the case for Iran. Since the revolution, Iran has been economically, politically, and socially unstable. With an economy dependent on oil, a natural source whose production is unpredictable, stability is simply unattainable. With the same leader for a long period of time, not much can change politically. Oppositions and revolts can happen and disrupt the social lives of Iranian citizens. Although the Iranian Revolution was politically successful by maintaining an Islamic Republic, the revolution was unsuccessful because of the severe economic failure it was in the long term and the social unrest it still has today. The revolution of 1979 marked the beginning of Iran’s economic decay and even further economic instability. Before the revolution, Iran had one of the Middle East’s most advanced economies. Petroleum exports, which make up about 85 percent of government revenues, have decreased over the years after the revolution (Trading Economics). In fact, petroleum exports declined to 1.5 million barrels per day in 2012 from 2.5 million barrels per day in 2011 (Trading Economics). The Iranian government’s dependence on oil revenues has resulted in persistent financial instability. Because of this financial instability, Iran’s inflation rate was greatly affected. The inflation rate is the rate of change of prices calculated on a monthly or annual basis. In January 2014,Show MoreRelatedIranian Revolution1648 Words   |  7 Pagesbreeding ground for some kind of political upheaval or another. In recent times, back in 1979, there was a major revolution which was, in some ways, similar to the revolution we are seeing today. The people were angry and they were tired of being controlled by the government that was in power. 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Supporters of the revolution were very mixed in their goals for a new Iran. The Islamic Extremist lead by Ayatollah Khomeini wanted to install an Islamic regime inside of Iran that would follow Islamic law. Religious clerics viewed the Shah as not being a positive leader for Iran and wanted him overthrown and the country left as is. Iranians such as the middle class and students wanted to install an Islamic

The Wage Gap in America Essay - 1077 Words

The Wage Gap in America The wage gap is a serious problem that has consequences for women in America, our two parent families and our single mom households. The government tries to reduce the wage gap between men and women’s earnings and tries to make sure that women’s talents are properly used and rewarded. A lot has been done to relive the wage gap in the past fifty years, but it still is not enough. Women can do things on their own to help close the wage gap. They can get a non-traditional job or they can join a union. Women need to find out a company’s policy and discuss their salaries. The wage gap is a problem American women need to address, not wait on the government to fix it for us. The wage gap can be defined as the†¦show more content†¦Many employers may not realize their pay scale favors white men. Women are less likely to receive additional compensation such as bonuses, stock options, and profit sharing. Equal pay makes good business sense. It promotes a workforce that feels valued, which helps the bottom line. Fair pay polices will attract the best workers. The national committee on pay equality has a ten step guide that is developed to assist employers to recognize and reward the skills of working women. Women can decrease the wage gap by joining a union. Union members and the workers represented by unions have been paid higher wages than non-union members. Union membership and representation has been proposed as one way to raise women’s wages and decrease the wage gap between men and women. Most union members are in the public sector and include firefighters, police officers and teachers. Union pay advantage for women is 30.9 percent. 43.6 percent of the union members are women. Consider a career in a non-traditional field could help women close the wage gap. When making decisions about what to do when we grow up, most women tend to steer away from jobs they associate with men’s work. Jobs dominated by men typically pay higher wages and offer good benefits. Many non traditional jobs such as technical jobs, skilled trade occupations, and electrician provide on the job training. This means you are getting paid while training unlike manyShow MoreRelatedWage Gap in America1572 Words   |  7 PagesWage Gap in America On a broader aspect, it says men and women are equal. Though at a bottom level, women are still struggling to occupy the same status as men in the outer world. Stratification between the two genders is seen everywhere including the household or the workplace. Even today, women still earns less as compared to men involved in the same profession. Like a male physician makes $140,000, while a female in the same profession makes $88,000. Statisticians at the US census bureau lookedRead MoreGender Wage Gap in America1565 Words   |  7 PagesThe Gender Wage Gap in America The gender wage gap has been around since women began having jobs and careers. 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