The cost of equity is given by Rj=Rf +β (Rm-Rf), where Rf is the risk free rate of return, β is the Beta of the security and Rm is the return on market portfolio. Therefore, the cost of equity for BP plc is given by Rj =0,01+2,18×(0,05-0,01) =0,0972×100=9,72%. This cost of equity is higher than I expected. The firm should have a slightly higher cost of capital than the average firm due to the expected rate of return. The betas for Royal Dutch Petroleum Company and Exxon Mobil Company are 1,28 and 0,86 respectively. The cost of equity for Royal Dutch commonly known as Shell are as follows: Rj=0,01+1,28×(0,05-0,01) =0,06×100=6% and the cost of equity for Exxon Mobil is Rj=0,01+0,86×(0,05-0,01) =0,044×100=4,4%. The cost of capital for the two firms is lower compared to the BP plc Corporation. It is surprising that some firms have a lower cost of capital than the average firm and also than the BP plc Company.

When 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;
- 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.

The arbitrage pricing theory is used to calculate the cost of capital the formula;

E (R1) = a+ βiXi +Ei

- Where a is the expected level of return of a stock when all factors are held constant,
- Xi is the value of factor 1 that affects the return on I and;
- βi measures the sensitivity of returns on a stock.
- Ei is the random error time.

This is a factor that is unique to the firm that affects the returns of a company, for example: legal action against the company or the departure of a Chief Executive Officer. The APT method of calculating the cost of capital requires that the returns in stock are linearly related to one factor (Shim & Siegel, 2000).

The module 3 SLP has enabled me to understand how to calculate the cost of capital using three different methods. The module has also showed that some firms have a lower cost of equity compared to that of the average firm. I have mastered the use of the formulas required to calculate the cost of capital and the importance of the cost of debt for a business venture and for its expected returns. The CAPM method uses the following procedure i.e.

Rj=Rf +β(Rm-Rf)

- Where Rf is the risk free rate of return,
- β is the Beta of the security and;
- Rm is the return on 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%.

The relationship between asset beta and equity beta is that asset beta takes into account only business risks while the equity beta takes into account of both the business and financial risks (Bernstein & Damodaran, 1998). Asset beta is very important, because you can compare companies and not have comparison affected by capital structure choices. The equity beta takes into account the company’s capital structure. The relationship of both concepts to the debt to equity ratios is that if the company is loaded on debt, then it tends to be more volatile as its stocks trade in the stock market unlike when a company is owner funded where the volatility of trade tends to be less as the stock prices trade in the exchange market.

The Arbitrage Pricing theory (APT) is a model that requires that the returns in stock are linearly related to one factor. APT is based on the same intuition as the CAPM, but is more general. The relationship between the APT, CAPM and the dividend growth model is that the prices of stock reflect all future market expected returns. All the three methods are used to calculate the cost of capital and can be used interchangeably. The dividend growth model can be applied in the valuation of stocks of firms that pay a constant annual dividend, zero dividend, annual dividend with a constant increasing rate of growth and annual dividend with a constant decreasing rate of growth (Pratt, 2002). Using this approach to find the cost of equity:

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 evaluation of the module 3 SLP shows the ways in which the cost of capital is derived and the returns to be expected by the investors of stocks. The module also shows the application of the different methods used to calculate the cost of capital and their overall effect on the asset prices. The relationship of the various concepts and their differences has also been emphasized. Different companies have different required rates of returns for their investors and, therefore, it is necessary for potential investors to know the best method to use in order to analyze the asset prices of a particular company of interest.