 Earlier we have seen that how cost of debt and cost of preferred stock can be determined. Now it's time to learn that how cost of common equity can be determined. By cost of common equity, we mean the rate of return required by a company's common stockholders over holding of its equity instruments. A company can raise common equity in two different ways like through flowing bag of its retained earnings. This means that retained earnings are reinvested in the business of the company or a firm can raise its equity through the new issue. Now to determine cost of equity, certain approaches can be used by a financial analyst like a capital asset pricing model or KPMM, two dividend discount model, pre-bond yield plus risk premium can be used. First approach is capital asset pricing model or the KPMM. In fact in KPMM, the model works as that the required rate of return on a particular project with reference to the cost of equity is basically the sum of risk pre-rate and the premium for bearing the stock market risk. Now what these terms are, if we see the KPMM model, the first term on the left hand side is the required rate of return or the R bar, then we have in the right hand side the first term SRF or the risk pre-rate, then we have beta. Beta in fact the mayor or variable that mayors the responsiveness of a particular stock with reference to variation in the prices of the stock market. Then we have RM that is the return on market portfolio or it is the market return but a risk free rate is in this KPMM model by risk free rate we means a rate that is earned on a risk free asset and by risk free asset we mean an asset that has no default risk option. To proxied risk free rate we generally use yield on default free government date instruments that has similar duration of the project cash flows. If we are working in Pakistan and we want to determine the risk free rate then we can use the T bills rate as a proxy for the risk free rate. Now the difference between market return and the risk free rate is the equity risk premium which is demanded by any investor for investing in the risky market portfolio. So that is the market risk premium which is in fact demanded by a rational investor over and above the risk free rate in a market. Now how to determine ERP or equity risk premium there are certain approaches. The first approach is the historical ERP. In historical ERP it is assumed that the realized ERP observed over a longer period of time or the historical risk premium is a good measure or indicator to determine an expected risk premium. This means that we are using a historical equity risk premium to compute the expected risk premium for the future. Using the historical data we determine an average return on the market portfolio and the risk free rate in the country is then determined. This means that using these historical returns on the market portfolio we are determining the market return or RM and using the historical yields on T bills we are determining the risk free rate. How to determine this ERP? These ERPs can be determined using average or arithmetic means or these ERPs can also be determined using geometric means. An example to determine risk free rate using the arithmetic mean we see that in the example we have T bonds data over the past 100 years that an average is 5.4%. The arithmetic mean on market observed or RM is the 9.3%. Now if we need to determine the equity risk premium we need to determine take the difference between market return which is 9.3% and risk free rate which is 5.4%. So deducting 5.4% from 9.3% comes to 3.9% and this is the equity risk premium that we determine using the arithmetic averages or arithmetic means. We can use also historical geometric means. In this example example 2 the historical geometric mean for US equity of 4.8% to value Citibank as of early June January 2006. So this is basically the market return RM putting to the standard and poor Citibank had a beta that is the beta of this Citibank or particular entity which is 1.32. Using the 10 years US trading bond yield of 4.38% to represent the risk free rate. So this is the RF which is 4.3% if we determine cost of equity then we add this risk free rate to the risk premium which is 4.8% and the cost of equity is 10.72%. So we can use both arithmetic mean and geometric mean to determine either the market return or the risk free rate to determine the cost of equity. The second approach that can be used to determine cost of equity is the dividend discount model. Dividend discount model that was delivered by the famous Gordon which is also known as Gordon growth model. It assumes a long term growth trend in the firms earning because the model is based on firms earning and it uses the relationship between the value of an index expected dividend and a constant growth in the corporate dividends. So when we develop a relationship between these variables we develop a model in which current price or P0 is equal to the dividend divided by RE minus G. Here G is the growth rate of dividend RE is the return on the cost of equity, D1 is the next period dividend and P0 is the current market price of the stock. If we rearrange this particular equation to determine RE then RE is equal to D1 plus D1 divided by P0 and this is basically the dividend yield plus the G. G is the growth rate. So RE basically then is equal to the sum of dividend yield plus the dividend growth rate. Therefore we can say that the ERBR equity risk premium is basically the difference between RM and RF that we are producing here. The third approach that is used to determine equity risk premium is the survey approach. In fact we get a survey on this equity risk premium from different financial experts and then we make an average of these opinions and this average value is then used as the equity risk premium for determining the cost of equity. The second model that can be used to determine a cost of equity is the dividend discount model or the garden growth model. It can be directly used to obtain an estimate of the cost of equity. Earlier we used this model to determine the equity risk premium but this model can also be used to directly determine the cost of equity. In fact this dividend discount model states that intrinsic value of the stock is basically the present value of its expected dividend. This means that this model determines a rate of return at which the present value of the future dividend becomes equal to the current market price of the company's stock. This garden growth model or dividend discount model assumes expected dividends to grow at a constant rate at a fixed rate throughout the life of the company because it is an infinity equity instrument. So we also assume that prices in fact reflect the intrinsic value of the particular stock. This means that value of the firm is equal to the current market price of its stock. Now to determine RE we have to rearrange the dividend discount model which is basically P0 is equal to D1 divided by RE minus G. In fact we need to determine RE then we solve RE through dividing the expected dividend over the current price and adding the growth to this figure. This means again that the cost of equity or required rate of return on equity is the sum of dividend yield in the growth rate. But here in this particular case the G does not mean the growth rate in the dividend. In fact here G is the growth in the company's earnings. This is earnings growth rate. To estimate this G is a little challenging because it is not as simple. We have two different ways to determine this G. The first is to get the value of this G from the published sources of the firm or it may be obtained from certain vendors or financial analyst firms or it may be developed through building a relationship between the G which is the retention rate in fact. So G here is the retention rate that the rate at which the firm is retaining its retain earning for its internal growth and in fact this G is basically the sustainable growth rate and to determine this sustainable growth rate or G we need to divide the retained earnings over the company's overall earnings and then multiply this retention ratio with the return on equity. So if we multiply return on equity with the retention ratio of the firm the resulting figure is the sustainable growth rate the rate at which internally firm can grow. Firm can grow at its internal financing and adding this G to the dividend yield gives the figure of cost of equity or RE. The third approach that can be used to determine cost of equity is the bond yield plus risk premium approach. In this approach we assume that cost of capital of riskier cash flows is higher than that of a lesser riskier cash flows. Higher the riskiness of a cash flow higher is the cost of capital. We use a risk premium that basically captures the additional yield on a company's stock in relation to its bonds this means that we determine the cost of equity through the submission of the company's cost of debt plus the risk premium in relation to its debt riskiness. This means that we can determine the risk premium using historical spread between the bond yield and the stock yield of a particular corporate firm.