Running head: PRICING MODELS Pricing Models Adam F. Thornton FIN 501 – 3 TUI University Dr. William Anderson Chipotle Mexican Grill (CMG) is one of the fastest growing restaurant chains in the United States. Self proclaimed as “fast-casual,” CMG offers a dining experience that is unique, organic, and which draws from the local economy. For the investor, CMG is a wise investment for the aggressive and fast growing portion of a portfolio. When determining an appropriate model to evaluate CMG’s potential, the Capital Asset Pricing Model (CAPM) is the best choice.

This model offers the best amount detail while maintaining the simplicity needed for a model outlining investment decisions in CMG. The Pricing Models There are three pricing models to discuss when evaluating CMG: dividend growth, CAPM, and the Arbitrage Pricing Theory (APT). Each of these models has both advantages and disadvantages, easily tailoring one model to different situations. However, the CAPM is best suited for this case with CMG. Below is a further review on each of models’ advantages and disadvantages, and applicability to CMG’s market position and financial situation.

The Gordon Growth Model The Gordon Growth Model (GGM) is a very simple model for estimating the value of a stock. This equation works by calculating the stock value from dividends per share, the required rate of return for the equity investor, and growth rate in dividends (Gordon, 2008). The equation looks like this: Stock Value (P) = D / (k-G). Where D is the expected dividend per share one year from now, k is the required rate of return for the equity investor, and G is the growth rate in perpetuity.

This dividend growth model is best suited for a firm growing at a rate comparable to or lower than the nominal growth rate in the economy and which have well established dividend payout policies that they intend to continue in the future (Dividend). In addition, the dividend growth model is also suited for businesses that are in a stable market (Dividend). A good example of this type of company could be 3M or General Electric. Both of these companies are stable and have a steady growth rate.

Moreover, these two companies are subject to various regulations and restrictions from multiple government agencies that also have a factor in limiting the growth of the corporation. The GGM is not the preferred analysis tool for CMG for a few reasons. First, CMG has only been a public company for almost six years. This does not give enough data points to convince the investor on the direction of the company. The investor is unable to judge what CMG will do in the near and long-term regarding the growth of the company. Currently, CMG has a very high growth rate.

CMG is adding over 130 restaurant locations in 2010 alone, not to mention beginning business ventures in the international market (Annual, 2009). This high growth rate deters the wise investor from using the GGM to analyze CMG. Lastly, CMG is not in a market regulated on the rate of company growth. CMG can legally build as many new restaurants that are humanly possible (fair financial practices assumed). The high growth rate that CMG has creates a mathematical problem for the GGM because it will drive the price exponentially higher. This also invalidates the accuracy of the assessment and drives the investor to use a different tool.

The Arbitrage Pricing Theory The Arbitrage Pricing Theory (APT) also is not the right choice for CMG, though it came in close second place. The APT works by calculating the expected return of an asset with the following equation: E[Ra] = R f + ? a(E[Rm] – R f). In this equation, E[Ra] is the expected return of the investment, Rf is the risk free rate, ? a is the beta of the investment, and E[Rm] is the expected return on the market. Furthermore, this theory produces another equation: r = rf + ? 1f1 + ? 2f2 + ? 3f3 + … In this equation, r is the return, rf is the risk free rate and ? is the beta of each f1, or factor. This equation shows that there are an infinite number of factors, independent of the expected performance of the market. Although the APT accounts for many more variables than the following model, it is still not the wisest choice as the analysis tool for the investor. The argument in favour of APT is that it can account for multiple factors, and is not a “one-size fits all” tool. This tool is designed to give the investor a “custom fit” style of portfolio instead of a broad spectrum risk application (Goetzmann, 1996).

However, the real question lies in how many of these factors should be included in the spectrum of the portfolio. Corporations spend countless man-hours and funding to determine which factors apply to their stock. There are also other assumptions for APT, for example, risk drives the price of securities in a linear fashion, investors perceive these risks and can estimate the sensitivity of the security to them, investors are risk takers, and investors will exploit differences in expected return through risk arbitrage (Goetzmann, 1996). Regarding CMG, the APT is not the best choice.

Although the equation is built to account for multiple factors, there are too many factors for CMG to realistically compute. A truly in depth equation would account for every factor affecting the CMG security price. However, some factors are not going to be completely independent. Rather, they are inter-dependent and a change in one will incur a change in the other. Second, the APT is very difficult to understand for the majority of people and is far less widely used than other models (Money, 2007). Additionally, the more factors that are identified then the more betas there are that must be calculated.

This does assume that a finite number of factors are noted, which can be a point of contention. Lastly, CMG must also realize that the more factors associated with the end-result, the more statistical noise that will be associated. This means that the figures will be washed out by one another, diminishing the effect of changes in effects. The Capital Asset Pricing Model The Capital Asset Pricing Model (CAPM) is an easy to use pricing model. The formula is simple and can be calculated quickly, but can also be in depth enough to accurately estimate a security price, or required return.

The equation looks like this: Req ROI = RF + (RM – RF)* ?. The basic premise of the CAPM is that the required return on a portfolio or security equals the risk free rate plus a risk premium (Financial, 2007). Clearly, the risk free rate and the market rates are easy to calculate, or at least find on the internet. The risk free rate is typically low and can be estimated by using the one-year Treasury bill rate (although not truly “risk free”). The market rate can be estimated by determining the expected return on the S&P500 index (SPX). The only thing left to calculate is the beta, or the overall risk of the investment. A beta of 1. equals the risk of the market while great than one is more risky than the market. For example, a beta of 1. 2 would be 20 percent more risky than the market baseline. While this equation only allows for one beta and factor to be calculated, the beta should encompass the overall risk of the company, instead of calculating individual betas for every factor affecting the company, like what was done in the APT. For CMG, the CAPM is the best course of action. It is a widely used and accepting way to estimate returns. First, CMG is holding a high growth rate currently. The CAPM is ideal for companies that maintain this level of growth.

However, historically speaking, higher growth rate typically means a higher beta and companies with a higher beta have not performed well in the long-term (Financial, 2007). There are potentially some unrealistic assumptions with CAPM also. It may be difficult to accurately assess the specific beta, and the company specifics could have changed over the evaluation period. This is why it is imperative that the calculation and evaluation period be compressed for CMG. The growth rate is not maintainable forever and figures need to reflect the financial status as accurately as possible.

Lastly, although the real world is not linear, we can assess a company and risk on a relatively linear basis using the CAPM. CAPM is the best choice for CMG. In conclusion, Chipotle Mexican Grill is best suited to use the Capital Asset Pricing Model. This model gives the most amount of flexibility to the company while still accounting for market factors. CMG can best display the financial capability of the stock by using the CAPM method and pricing the stock appropriately. CAPM is the method CMG needs. References Annual Report, 2009. Chipotle Mexican Grill. Retrieved on 16 May 2010 from http://phx. orporate-ir. net/phoenix. zhtml? c=194775&p=irol-reportsAnnual Clark, T. (2000). Earnings Growth and Stock Returns. Retrieved 4 Jun 10 from http://www. dfaus. com/library/articles/earning_growth_stock/ Dividend discount models. Retrieved 4 Jun 10 from http://pages. stern. nyu. edu/~adamodar/pdfiles/valn2ed/ch13. pdf Financial Concepts: Capital Asset Pricing Model. (2007). Retrieved 4 Jun 10 from http://www. investopedia. com/university/concepts/concepts8. asp Goetzmann, W. (1996). Chapter Six: The Arbitrage Pricing Theory. An Introduction to Investment Theory. Yale School of Management [Online].

Retrieved 4 Jun 10 from http://viking. som. yale. edu/will/finman540/classnotes/class6. html The Gordon Growth Model, (2008). Retrieved 4 Jun 10 from http://www. investopedia. com/terms/g/gordongrowthmodel. asp Money Terms (2007). Arbitrage Pricing Theory. Money Terms[Online]. Retrieved 4 Jun 10 from http://moneyterms. co. uk/apt/ Otuteye, E. (1998). The arbitrage pricing dichotomy. Canadian Investment Review. Winter 1998. Retrieved 4 Jun 10 from ProQuest database, Touro Cyberlibrary. Value Based Management Net, Capital Asset Pricing Model. Retrieved 4 Jun 10 from http://www. valuebasedmanagement. net/methods_capm. html