Are Amazon.com prices Real?

Calculating Stock Prices Using Real-Time Data

• By walking you through a set of real-time financial data for IBM, this assignment will help you better understand how theoretical stock prices are calculated; and how prices may react to market forces such as risk and interest rates. You will use both the CAPM and the Constant Growth Model (CGM) to arrive at IBM's stock price. To get started, complete the following steps. First, find an estimate of the risk-free rate of interest, krf. To calcuate this rate, first go to Bloomberg.com: Market Data [http://www.bloomberg.com/markets/index.html], to find the 10-year Treasury bond rate. Use this interest rate as the risk-free rate. In addition, you also need a value for the market risk premium. Use an assumed market risk premium of 7.0%. Download this IBM Stock Information document (.doc file). This document was generated from recent financial data for IBM. Using this document, find an estimate of: a) IBM's beta (?) b) IBM's current annual dividend c) IBM's 3-year dividend growth rate (g) d) Industry P/E e) IBM's EPS. Also find IBM's current annual dividend and its 3-year growth rate, or g. With the information you now have, use the CAPM to calculate IBM's required rate of return or ks. Use the CGM to find the current stock price for IBM. We will call this the theoretical price or Po. Now use appropriate Web resources to find IBM's current stock quote, or P. Compare Po and P. Do you see any differences? Can you explain what factors may be at work for such a difference in the two prices? This section is especially important?with more weight in grading?so you may want to do some study before answering such a question. Explain your thoughts clearly. Now assume the market risk premium has increased from 7.0% to 10%; and this increase is due only to the increased risk in the market. In other words, assume krf and stock's beta remains the same for this exercise. What will the new price be? Explain what happened? Recalculate IBM's stock using the P/E ratio model (pp. 350-1) and the needed info found on the Web. Explain why the present stock price is different from the price arrived at using CGM. Please show all work, including formulae and calculations used to arrive at financial values. Submit your work to your instructor via the drop box.

• Answer:

  I do not have access to the document to which you referred, so I have sought data from other sources. I obtained Kf from the Bloomberg website you provided. Today (April 15, 2005) the 10 year Treasury yield is 4.24%. From Yahoo Finance ("International Business Machines Corp" http://finance.yahoo.com/q/ks?s=IBM), I obtained the current annual dividend of IBM of $0.72/sh. and its Beta of 1.638. Beta is typically calculated by taking the slope of the line that best fits a plot of the returns of IBM stock versus the market's returns for a set of periods. A discussion of this is found, along with examples, on pages 183-185 of Brealey & Myers. Presumably appropriate data detailing the performance of IBM stock versus the market is found in the document referenced in your question. From the IBM website ("Stock Information" http://www.ibm.com/investor/stock/index.phtml), I obtained details regarding its annual dividend for the last three years. Using the Compound Annual Growth Rate formula from Investorwords.com ("CAGR" http://www.investorwords.com/666/CAGR.html), I calculated the CAGR of IBM's dividend: (0.72/0.60)^(1/3) - 1 = 6.27%. Using the CAPM model: Ks = Beta(Km - Kf) + Kf, I obtained Ks = 1.638(7 - 4.24) + 4.24 = 8.76 (page 162 of Brealey & Myers) The Constant Growth Model: Po = DIV1/r-g = $0.72/(8.76% - 6.27%) = $28.91 (page 62 of Brealey & Myers). From the Yahoo Finance source above, IBM's current stock price is $76.70. Possible reasons for the difference: The market risk premium is currently lower than the estimate we used. Another possibility is that investors expect IBM's growth rate to increase in the future, making the estimate of its future growth rate from its previous history inaccurate. With the new Km of 10%, Ks = 1.638(10-4.24)+4.24 = 13.67. Po = $0.72/(13.67%-6.27%) = $9.73. A riskier stock (increase stock market risk makes each individual stock riskier) with the same growth prospects results in the share price being reduced. The P/E ratio model is Po = P/E ratio * EPS. From the Yahoo Finance source above, IBM has a current P/E ratio of 15.74 and an EPS of $4.873. Therefore, the share price is $76.70. Source: "P/E Ratio - Price to Earnings" http://www.valuebasedmanagement.net/methods_PEratio.html. If IBM has had a significantly different PE ratio in the past that is more representative of its expected future prospects, then of course use of this PE ratio would result in a different Po. You will want to consult the document that you have been provided to ensure that you are not to use a different PE ratio for this calculation, such as the industry one. It is important to note that "[t]here is no reliable association between a stock's price-earnings ratio and the capitalization rate [Ks]. The ratio of EPS to Po measures [Ks] only if [the present value of growth opportunities] = 0 and only of reported EPS is the average future earnings the firm could generate under a no-growth policy." (Page 61 of Brealey & Myers). Sincerely, Wonko Source: "Principles of Corporate Finance" Fourth Edition by Brealey & Myers, McGraw-Hill Inc. (1991)