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By walking you through a set of 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 (Capital Asset Pricing Model) and the Constant Growth Model (CGM) to arrive at IBM's stock price. To get started, complete the following steps. Find an estimate of the risk-free rate of interest, krf. To obtain this value, go to : Market Data [ and use the "U.S. 10-year Treasury" bond 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 7.5%. Download this IBM Stock Information document (.pdf file).( please see link below for pdf file) Please note that the following information contained in this document must be used to complete the subsequent questions.IBM's beta (?) IBM's current annual dividend IBM's 3-year dividend growth rate (g) Industry P/E IBM's EPS. ? 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 7.5% 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 and the needed info found in the IBM pdf file. Explain why the present stock price is different from the price arrived at using CGM (Constant Growth Model). To receive full credit on this assignment, please show all work, including formulae and calculations used to arrive at financial values.Solution:(a) An estimation of the risk-free rate of interest, krf.Steps:"U.S. 10-year Treasury" bond rate = 3.64% = the risk-free rate -------- (1)(U.S. 10-Year Treasury from Market Snapshot available at )(b) Calculation of IBM’s financial parameters:Steps:IBM's beta (?) : β= 1.64 which is 60 month beta given in “price and valuation” section of IBM Stock Information document.IBM's current annual dividend: Current dividend Div0= $0.80 which is Annual dividend /Share given in “Growth Trend” section of IBM Stock Information document.IBM's 3-year dividend growth rate (g): g= 8.20% which is 3-year dividend growth rate given in “Growth Trend” section of IBM Stock Information document.Industry P/E: P/E = 23.2 which is Price/Earnings for Industry given in “price and valuation” section of IBM Stock Information document.IBM's EPS: EPS = $4.87 which is EPS for IBM given in “price and valuation” section of IBM Stock Information document.(c) With the information you now have, use the CAPM to calculate IBM's required rate of return or ks.Steps:Required rate of return or Ks = r f + β (r m – r f) r m -r f = market risk premium = 7.5% (provided in question)r f = risk free rate 3.64% … from (1)β= 1.64 Hence, Ks =3.64%+1.64*7.5% = 15.94% --------------------- (2)(d) Use the CGM to find the current stock price for IBM. We will call this the theoretical price or Po. Steps:The theoretical price or Po = Div1/ (r-g)Div1 = Div0*(1+g) =(1+8.2%)*0.8 = $0.8656r= 15.94% ----------- From (2) g= 8.20% Hence,Po= Div1/ (r-g) = 0.8656*100/(15.94-8.2) = $11.18 (e) 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. Steps:Current Price is 76.28 which is current price of IBM given in “price and valuation” section of IBM Stock Information document.Hence, Current Price = P= $76.28 Theoretical Price = Po = $11.18 Following is the list of factors which can be reason behind differences between two prices:There are scopes of error in estimating the value of the dividend growth rate, the dividend value or the discount rate. As CGM model fluctuates highly even by slight variation of these parameters, it can create difference between actual and theoretical price of share.There are chances of increment in growth rate of IBM’s dividend and current market risk premium is much lower than assumed market risk premium for calculation. Hence, it is making the difference due to incorrect assumptions. Investors can increase the prices by high after bidding seeing the current growth trend of industry and extrapolated it too far which results in overprice of the stocks.There can be mistake from investor in assessment of risk which raises the price of stocks.(f) Now assume the market risk premium has increased from 7.5% 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. Steps:Recalculation after risk premium has increased from 7.5% to 10%Required rate of return or Ks = r f + β (r m – r f) r m -r f = market risk premium = 10% (provided in question)r f = risk free rate 3.64% … from (1)β= 1.64 Hence, Ks =3.64%+1.64*10% = 20.04% ---------------------------------- (3)The theoretical price or Po = Div1/ (r-g)Div1 = Div0*(1+g) = (1+8.2%)*0.8 = $0.8656r= 20.04% ----------- From (3) g= 8.20% Hence,Po= Div1/ (r-g) = 0.8656*100/(20.04-8.2) = $7.31 There is decrement in the price of share for dividend value as value of Ks or required rate of return has increased. This kind of stock is considered risk prone as price of share has decreased with having same growth for increased rate of return.(g) Recalculate IBM's stock using the P/E ratio model and the needed info found in the IBM pdf file. Explain why the present stock price is different from the price arrived at using CGM (Constant Growth Model). Steps:Industry P/E: P/E = 23.2 which is Price/Earnings for Industry given in “price and valuation” section of IBM Stock Information document.IBM's EPS: EPS = $4.87 which is EPS for IBM given in “price and valuation” section of IBM Stock Information document.Recalculate IBM's stock:Price of IBM’s stock = IBM’s EPS * Industry P/E = $4.87*23.2 = $112.98Brealey and Myers (2002) in his book “Corporate Finance: Capital Investment and Valuation”finds that price- earnings ratio of stock and required rate of return does not have higher degree of correlation which can define the strength of linear association between these two variables. The CGM model’s assumption that there will be constant growth of dividends every year is not valid in real market scenario. There are many growth opportunities which make the growth rate as variable. Hence, the present stock price is different from the price arrived at using CGM. ................
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