The reason for this assignment is to compare three asset pricing models, namely the APT, CAPM, and the dividend discount method, and to find out the best method among the three. Also, the assignment explains the differences between the costs of equity capital of various companies. The assignment explains the application of the three asset pricing models to the modern world and their advantages and limitations in valuation of asset prices or investment portfolios.

The arbitrage pricing theory is the best method for estimating the required return rate for BP plc since the CAPM method cannot always consider the difference in assets’ returns using the betas. The dividend growth model on the other hand only puts into consideration the dividend per share of stock and the expected growth (Kevin, 2006). The APT is used to estimate the assets’ expected returns. APT unlike CAPM and the dividend growth model does not take into consideration that investors use mean-variance analysis in the investment decisions.

The ease of use of the dividend growth model is that it assumes that dividends are expected to grow at a fixed rate and hence makes it easy to calculate the required return rate based on the share of stock and the expected future dividends of the stock. The CAPM method is easy since it identifies the tangent portfolio from sound theoretical assumptions. The APT method on the other hand requires that the returns in stock be linearly related to one factor.

All three models are accurate in the calculation of the cost of equity capital; the only difference is the expected returns that an investor will get from using the different models. The assumptions for the CAPM method of investors being risk averse, markets are perfect and frictionless i.e. no taxes on sales or purchases and those investors can borrow or lend money at the risk free rate. CAPM assumptions are unrealistic since it is hard to reach a security free from risks and the borrowing and lending rates equality is incorrect. CAPM under such circumstances may not explain investors’ behavior.

According to APT, the capital markets are frictionless and perfectly competitive, and returns of a risky asset can be described by a factor model. There is a large number of securities at the disposal of the investors, and they always prefer more wealth. Finally, there are no arbitrating opportunities. These assumptions are limited by the fact that it requires the investors to perceive the risk sources, and that they reasonably estimate the factor sensitivities, which is not possible in reality. The dividend growth model implies that the stock valuation is based on the current dividend, growth of the dividend, and the required return rate. The assumptions of the dividend growth model are unrealistic in the sense that the model is a constant growth model and it is not appropriate for stocks with lower dividend yields and higher dividend growth. Another unrealistic assumption is that it is delicate to the accuracy of the inputs and investors may over rely on it as a valuation tool instead of viewing it as an estimator in its purist sense.

Based on my analysis and findings I would highly recommend the board of directors of BP plc to adopt the APT pricing model since it was developed to overcome the weaknesses of the CAPM model. In the Apt model, a number of factors may measure the systematic risk of an asset under APT unlike beta which is the most important single factor in CAPM. APT is also advantageous compared to the dividend discount model that uses a fixed rate and single dividend to value stock unlike the APT, which is more complex than the CAPM and is focused on the entire investment portfolio (Cochrane, 2001).

The cost of equity is given by the formula E(rj) =Rf+ b(Rm -Rf) where b is the beta of the security, Rf if the risk free return rate and Rm is the return on the market portfolio. Based on the above formula, the cost of equity for the Nike corporation is given by E(rj)=0.40+0.90(6.50-0.40)=5.89%. The cost of equity for Sony Corporation is represented by the formula E(rj)=0.40+1.60(9.50-0.40)=14.96%. The cost of equity for McDonald’s Corporation using the CAPM method is E(rj)=0.40+0.40(8.50-0.40)=3.64%. Sony Corporation has a high cost of equity at 14.96% compared to Nike at 5.89% and McDonald’s at 3.64%. It shows that the expected return rate by the shareholders of the company from their investment is also greater. The company has a potential for higher returns from the high beta values that are riskier. The higher discount rate shows the present value placed on the future cash flows of the company. A company’s share valuation is influenced by beta.

The factors that influence company’s beta are financial leverage that indicates higher beta, the size of the company. Thus, a large company has a smaller beta, the earnings variability, whereby the greater the variability of earnings over time is, the higher the beta is likely to be. In the corporate growth, a strong alignment has a higher beta; while in industrial affiliations betas vary significantly across industries.

The module 3 case assignment has enabled me to understand the three models used to calculate the cost of equity capital and their differences in assumptions and application. The expected returns on investment by the company’s shareholders are heavily influenced by the company’s beta and the discount rate.

The application of the dividend discount model is valuable for stock in the exchange market. Using the dividend growth model to calculate the cost of equity for BP plc the following formula is used: Rj=D1÷(Po+g), where D1 is the share dividend for the stock, Po is the price of the stock in the market, and g is the average growth rate in dividends. Di is calculated by the formula D1=Do (1+g), where Do is the share dividend, and g is the average growth rate in dividends. Do is $4.19, g=5% and Po=$50.D1=$4.19(1+0.05) =$4.3995.Rj=4.3995÷ ($50+0.05) =13.8%.

The Arbitrage Pricing theory (APT) is a model in which returns in stock should be linearly related to one factor. APT is based on the same intuition as the CAPM, but it is much more general (Shim & Siegel, 2000). In the APT, CAPM, and the dividend growth model the prices of stock reflect all future market expected returns. All three methods are used to calculate the cost of capital and can be used interchangeably. This model can be applied in the valuation of stocks of firms that pay annual constant dividend, zero dividend, annual dividend which has a constant increasing growth rate, and annual dividend that has a constant decreasing growth rate.

The CAPM method uses the following procedure: Rj=Rf +β(Rm-Rf), where Rf is the risk-free return rate, β is the beta of the security, and Rm is the return of market portfolio. Using General Motors with a beta of 1.69 as a publicly traded company, the cost of equity will be Rj=0.01+1.69(0.05-0.01) =0.077×100=7.7%. It is the cost of equity or the expected return rate by the company shareholders.

The evaluation of this assignment shows the ways in which the cost of capital is derived using the APT, CAPM, and the dividend growth model. Also, the module shows the returns to be expected by the investors of stocks. The relationship of the various asset pricing concepts and their differences has also been shown. Different companies have different expected rates of returns depending on the asset pricing model used. Therefore, it is necessary for potential investors to apply the best method to analyze the asset prices of a particular company.