# Essay on Stock prices

There exist several approaches to determining of stock prices, the major of them being CAPM (capital asset pricing model) and CGM (constant growth model). The purpose of this paper is to evaluate XYZ stock price, using both models and company data on prices, growth trends, financial strength and management effectiveness.

CAPM model of evaluating required rate of return is based on the following equation:  where  is the required return rate,  – risk-free rate,  – expected market return (and – is referred to as market risk premium), and  is beta of the security (Geddes, 2011). Risk-free rate is most often determined as the return rate of 10-year US Treasury bonds, and beta is the coefficient determining the sensitivity of the particular stock to market fluctuations.

In constant growth model, also referred to as Gordon model, current price of the stock is determined using current annual dividends value (D), required rate of return (k) and dividend growth rate (g):  (Madura, 2009).

In order to determine the required return rate for XYZ stock using CAPM model and evaluate XYZ stock price using Gordon model, the following values are required:

Risk-free rate �� equals to 1.875% (assumed as indicated in assignment data; although Bloomberg.com lists 1.75% as of May 12, 2012) (Bloomberg.com, 2012)

Expected market return rate �� 7.5% (assumed as indicated in assignment data)

XYZ’s beta �� equals to 1.64 (company data)

XYZ’s current annual dividend �� equals to \$0.80 (company data)

XYZ’s 3-year dividend growth rate (g) �� equals to 8.2% (company data)

Industry P/E �� equals to 23.2 (company data)

XYZ’s EPS �� equals to \$4.87 (company data)

Using these data, it is possible to apply CAPM to calculating the required rate of return:  Thus, the required rate of return for XYZ stock is 14.175%.

Using the risk-free rate, it is possible to determine the current (theoretical) stock price for XYZ stock using CGM (Gordon) model:

Theoretical price of XYZ stock is \$14.487, and the current price of XYZ stock is \$76.28, which is significantly greater compared to theoretically evaluated price.

The difference between these prices is conditioned by a variety of factors. First of all, the limitations of CAPM model used to estimate required rate of return and the limitations of CGM model used to calculate the theoretical evaluation of stock price. Betas of the companies change over time, and the relationship between betas and returns is not linear, contrary to the assumptions of CAPM model (Geddes, 2011). Significant difference between theoretical and real stock price might also be conditioned by the incorrect estimates of future dividend value, and by the changes of dividend payments, contrary to constant growth model assumptions (Madura, 2009). If the estimates of the existing stock price were based on nonlinear growth of dividends with optimistic forecast, the significantly higher stock price could emerge due to this assumption.

If market risk premium increased from 7.5% to 10%, the calculations would be the following:

Required rate of return:  Theoretical stock price:  With the increase of market risk premium, the expected rate of return increased, and as a result, theoretical value of the stock decreased.

Another method used for estimating stock value is P/E model (Geddes, 2011): Earnings per share (EPS) for XYZ stock is \$4.87 (company data). Price/earnings ratio for XYZ company is 15.65 (company data). Therefore, estimated market value of XYZ stock, according to P/E model:

This price estimate is significantly different from the price estimate obtained using CGM model. The difference emerged due to different assumptions and data used for stock valuation: P/E ratios are based on market pricing of the stocks and earnings associated with this stock, but do not relate to future periods or to dividends paid. CGM model, on the contrary, uses forecasts of dividend value and dividend growth for future periods, and is not related to current P/E ratios and EPS ratios of the company. Therefore, these two models yield significantly different results.