Case Study Analysis Cost Of Capital At Ameritrade Finance Essay

Case Study Analysis Cost Of upper-case letter At Ameritrade Finance EssayCapital Asset de termine Model is a model that describes the relationship between gambleiness and evaluate fall outandthat is commitd in the pricing of risky securities. explanation Capital Asset Pricing Model (CAPM)The general idea behind CAPM is that arrangeors need to be compensated in two ways time look on of moneyand risk.The time shelter of money is represented by the risk-free(rf) regularisein the formula and compensates the investors for placing money in any investiture over a period of time. The early(a) 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 comp ars the bring tos of the addition to the market over a period of time and to the market premium (Rm-rf).The CAPM says that the expected authorize of a security or a portfolio equals the straddle on a ri sk-free security plus a risk premium. If this expected growth does non meet or bemuse 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 forecast the expected return of a beginning in this CAPM example if the risk-free measure is3%, the beta (risk measure) of the com jeller storage 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 term 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 man-to-man stocks is pointless, because you can duplicate the reward and risk characteristics of any security just by victimization the right mix of cash with the appropriate asset class. This is wherefore 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 comp atomic number 18s 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 cost takers who cant influence the determine 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 bound in their borrowing and lending under the risk free rate of interest.How to Calculate the Cost of Equity CAPMThe cost of beauteousness 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). Th e 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, impart not go away. As an example, a company has a beta of 0.9, the risk-free rate is 1 percentage and the expected return on the equity investment is 4 percent.InstructionsDetermine 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 find oneself 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 iwhereWe thus have an asset pricing model the CAPM.Example. figure 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 = 0? dissolving agent Same as the risk-free rate, 5%. The stock whitethorn have significant uncertainty in its return. This uncertainty is uncorrelated with the market return.What should be the expected return on a stock with = 1? process 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 ber = (0.5)(0.05)+(0.5)(0.14) = 9.5%.Multi operator CAPMIn CAPM, investors care about returns on their investments over the next shorthorizon they follow myopic investment strategies.In practice, however Investors do invest over long horizons Investment opportunities do change over time.In equilibrium, an assets premium is given by a multi- factor CAPM Limitations of CAPMBased on highly restrictive assumptions i.e. no tax, transaction costs etcSerious doubts about its testability.Market factor is not the sole factor influencing stock returns.Summary of CAPMCAPM is attractive1. It is simple and sensibleis built on modern portfolio theorydistinguishes systematic risk and non-systematic riskprovides a simple pricing model.2. It is comparatively easy to implement.CAPM is controversial1. It is difficult to testdifficult to identify the market portfoliodifficult to estimate returns and betas.2. Em pirical evidence is mixed.3. Alternative pricing models might do better.Multi-factor CAPM.Consumption CAPM (C-CAPM).APT.Other Methods for calculating cost of equityThere are 3 methods which are mainly utilize for calculating Cost of equity other than CAPMArbitrage Pricing theory3 factor methodDividend Growth MethodArbitrage Pricing TheoryAPT 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 + UWhere, R = return on any stockRe = anticipate or Normal return (depends on all of information shareholders have on the stock for next month.)U = Uncertain or jeopardizey return (this comes from information revealed in the month)U = m + Where,m = Systematic risk or market risk (it influences all assets of market) Unsystematic risk (it affects single asse t 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 literal 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 relationshipWhere b1, b2 and b3 are sensitivities associated with factor 1, factor 2 and factor 3 which can be interest rate or other legal injury factors.Noise = is event alone(p) 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 sensitiveness to each of the factors. Thus, formula modifies toWhere, rf = risk free rate is subtracted from each return to give risk premium associated from each factor.Analysis of the formulaIf we put value for b = 0, the expected risk premium will be zero. It will create a diversified portfoli o which has zero sensitivity to macroeconomic factor which offers risk free rate of interest. Portfolio offered a higher return, investors could receive 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. apportion 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 TheoryThe various steps during Arbitrage Pricing Theory can be stated asIdentify the macroeconomic factors APT doesnt indicate which factors are to be considered. But there are 6 principle factors which areYield spreadinterest rate,exc hange rate,GNPinflationportion of the market returnEstimate the risk premium of each factorEstimate the factor sensitivityNet Return = risk free interest rate + expected risk premium3 factor modelIt is a special case of APTIt considers 3 major factors called asmarket factorsize factorbook to market factor.There is also evidence that these factors are related to company profitability and therefore may be option 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, a good deal like the CAPM.It was researched by Fama and French.Dividend Growth MethodDividend Discount Model.It is useful when the growth rate of dividend is forecasted continually.The present value of stocks is given asWhere,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 valu e becomes infinite.For perpetual growth, r g.Growing perpetuity formula,Where,P0 in terms of next years expected dividend DIVg = the projected growth trendr = 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 exampleSuppose 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. past cost of equity r is given asWhen 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 formulaFor example,YearDividend (in Rs. Million)Percent change (g)20001.2320011.30(1.30 1.23) / 1.23 = 5.7%20021.36(1.36 1.30) / 1.30 = 4.6%20031.43(1.43 1.36) / 1.36 = 5.1%20041.50(1.50 1.43) / 1.43 = 4.9%Growth rate is average of all percent changes and equalsThis model serve s 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 BetaBeta 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 alike markets have similar risks.Interpretation of betaBeta = 1,it matches market portfolioBeta 1, higher risk.Beta Methods for calculation of betaIt is calculated asbeta_i = frac mathrmCov(R_i,R_m)mathrmVar(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 retu rn and the individual asset return. Then required co-variances and variances can be calculated. If coefficient of correlation P is known thenThe 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 precondition that beta is a linear risk measure, the beta of a portfolio of assets as simply the weighted average of al l the individual betas that comprise the portfolio.HANUEstimate of Risk PremiumWe dont have reliable estimate where stock market will move in future. So we are using long term historic spreadsheets for estimate large stock than small stocks because they are more closer to proper estimate of marketWe are considering all values after plump for World War because after that laws became stable in U.S.Risk premium = Rm RfU.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 %