Capital Asset Pricing Model - Research Paper Example

Capital Asset Pricing Model Purpose of the Paper: The purpose of the paper is to understand and workout the cost of equity of a given company. The cost of equity of a company is associated with risk associated in investing in that company. Higher the risk associated in equity investment, higher will be the cost of equity for shareholders. Capital asset pricing model can be employed to work out the cost of equity. The minimum rate of return that shareholders would ask for is also known as the cost of equity. Answer 1. The company under consideration is Nvidia. The systematic risk coefficient is available from the site yahoo.com, which shows beta of the company, Nvidia as 1.54 (Key Statistics1) The current Yield to Maturity (YTM) on a U.S government bond (issued date 5.5.2011 and maturity date 5.3.2012) that matures in one year is given as 0.20 (Recent Bill…) Based on above details, expected rate of return or the cost of Nvidia can be now calculated as per the following. Rj = RF + βj [RM - RF] (Capital Asset… 2011) = 0.20 + 1.54 [7] = 10.98 Answer 2. The average cost of capital in the S&P 500 is 10.2 percent. It can be said that the cost of capital of Nvidia is almost on par with S&P 500 companies. It is pertinent to note that risk free rate varies time to time depending upon the yield of government Treasury bill. Usually, it is found to give 3% in normal conditions and based on this treasury rate, the cost of equity can also be calculated using the same formula Rj = RF + βj [RM - RF] It is assumed that difference between the expectation on rate of return for market portfolio and available risk-free rate of return, [RM - RF] factor is 7.0 Then, Rj, the cost of equity = 3+ 1.54 [7] = 13.78 Based on this, the cost of capital of Nvidia is certainly higher than average cost of S&P 500 companies. Answer 3. The cost of equity of Chevron (CVX) can be calculated in the similar fashion. Beta of Chevron is 0.70 (Key Statistics 2) The cost of equity = 3+ 0.7 [7] (Assuming risk free return of 3%) = 7.9 The cost of equity is remarkably low in case of Chevron compared to the average cost of S&P 500 companies. It would be further interesting to find the cost of equity whose beta is 1.76 Wipro Ltd. (in NASDAQ known as WIP) The cost of equity of Wipro = 3 + 1.76 [7] (Key Statistics 3) = 15.32 Thus, Wipro has higher cost of equity than Nvidia and Nvidia’s cost of equity is higher than Chevron. With rising beta the cost of equity also goes up. Answer 4. Dividend Growth Model It can be described as a stock valuation model that takes into consideration dividends and their growth, discounted to present value. Under this model, the valuation depends on 1. The Current Dividend 2. The Growth of Dividend at constant rate 3. Required Rate of Return For more clarity, it will be worthwhile to have some real life situation. The company is paying dividend of $2 per year and it is growing at the constant average rate of 3% per year. The only variable component in this model is required rate of return, if it is assumed as 15% Then, value under this model can be given as, Value= Current Dividend / (Required Return - Dividend Growth) (Gordon Growth…2011) = 2 / (0.15 – 0.03) = 2 / 0.12 = 16.66 Above calculation tells that under the given assumptions, this stock at the price of $16.66 should yield average annual 15% rate of return. At this juncture, it will also be prudent to look at the required rate of return and its basis. The required rate or return is given as the risk free return (such as U.S Treasury bill gives) adding to the return required for taking the risk in investing the stock. Thus, required rate (RR) is given as RR = risk free return + β (RM-RF) = 3+ 1.7 (10-3) {Beta for the industry under calculation is 1.70} = 15 That is how required rate of return was assumed as 15% (Dividend Growth…) Arbitrage Pricing Theory – APT This theory was propounded by Stephen Ross in 1976. This theory has more flexible assumptions to describe as and taken as an alternative to (CAPM) capital asset pricing model. In contrast to CAPM, which takes into consideration market's expected return, APT takes into account the expected return of risky assets associating risk premium to a number of macro-economic factors. Thus, jobbers or Arbitrageurs act taking a cue from APT model to take advantage of mispriced securities. A mispriced security is one when its price deviates from the calculated theoretical price proposed by the model. When security is overpriced, the arbitrageur goes short by selling the scrip or conversely, when security is underpriced, the arbitrageur takes long position on the scrip, thus making the profit on both sides. (Goetzmann, 1996) Arbitrage pricing theory does not depend on the performance of the market; it takes into account the fundamental factors that drive the price of the security. Unfortunately, theory does not provide any indication of what these fundamental factors are; instead, they need to be found empirically. Interest rates or economic growth are some of the factors which give some cue regarding its valuation. These factors are at times, company specific and need to be settled accordingly. Mathematically, this can be represented as R = Rf + β1f1 + β2f2 + β3f3 + ⋅⋅⋅ βnfn Where, R is the expected return from the security. Rf is the risk free rate of return; and F1, f2, f3 … fn are the factors affecting the valuation of the stock. β1, β2, β3… are the factor betas for different influences to the stocks. As can be seen, there may be several factors to affect change creating complexity in its application and the reason for it is less widely used in comparison to CAPM. (Goetzmann, 1996) Conclusion It is clear that the cost of equity of a listed and traded company depends upon the risk parameters (beta value) even APM models take into consideration risk factors associated at macro level. These models employ past prices to estimate the risk parameters. Private companies do not have any trade history hence their cost of equity cannot be estimated through these models hence a totally different approach is needed to calculate the cost of equity of such firms. References 1. Key Statistics 1, [Online] available at http://finance.yahoo.com/q/ks?s=NVDA [Accessed 17 May 2011] 2. Key Statistics 2, [Online] available at http://finance.yahoo.com/q/ks?s=CVX+Key+Statistics [Accessed 18 May 2011] 3. Key statistics 3, [Online] available at http://finance.yahoo.com/q/ks?s=WIT+Key+Statistics [Accessed 18 May 2011] 4. Recent Bill Auction Results (2011), [Online] available at http://www.treasurydirect.gov/RI/OFBills [Accessed 17 May 2011] 5. Capital Asset Pricing Model (CAPM) (2011), Financial Concepts: Capital Asset Pricing Model (CAPM). [Online] available at http://www.investopedia.com/university/concepts/concepts8.asp [Accessed 17 May 2011] 6. Gordon Growth Model (2011) [Online] available at http://www.investopedia.com/terms/g/gordongrowthmodel.asp [Accessed 17 May 2011] 7. Valuebasedmanagement.net, (2011), Capital asset pricing model (CAPM) [Online] available at http://www.valuebasedmanagement.net/methods_capm.html [Accessed 17 May 2011] 8. Money Terms (2011), Arbitrage pricing theory, [Online] available at http://moneyterms.co.uk/apt/ [Accessed 17 May 2011] 9. Boehme, R. (n. d.), Chapter 11: Arbitrage Pricing Theory (APT), [Online] available at http://www.rdboehme.com/MBA_CF/Chap_11.pdf [Accessed 17 May 2011] 10. Goetzmann, W. (1996), An Introduction to Investment Theory, Chapter six: the arbitrage pricing theory. Yale School of Management [Online] available at http://viking.som.yale.edu/will/finman540/classnotes/class6.html [Accessed 17 May 2011] Read More