FINANCIAL ECONOMICS CLEMSON UNIVERSITYCOMPUTING THE DISCOUNT RATEThe Risk and Cash FlowWhat we have discovered over that last month and a half is that the stock price of a company is based on the Discounted Cash Flow that the firm is expected to enjoy over the foreseeable future.There are two elements of the DCF equation. One, the cash flows must be forecast. Two, the appropriate discount rate must be chosen. Market participants are constantly working to evaluate the price of each stock to determine whether it correctly reflects its fundamental DCF value. PCashFlowrttt( )10Insiders and information gatherers acquire knowledge about the cash flows that a company can anticipate. These people study markets and products, managerial decisions, and corporate policies. From this study, they make informed opinions about the future cash flows of a company. Uninformed investors are investors with no special knowledge about the future cash flows of a company. They know what is publicly available and do not spend resource to discover new information. They are risk averse. They form portfolios of assets in order to achieve the highest possible utility by trading off return for lower risk. Portfolio diversification has the effect of lowering risk holding return constant. In the process of choosing among assets to hold in their portfolios, uninformed investors minimize variance by holding many, many different assets. In the limit, they hold all assets. The amount of each asset that they hold is based on the correlation of the return of that asset to all other assets. In choosing among assets, investors force the returnsof each asset to obey the Capital Asset Pricing Model. That is, the CAPM identifies the expected return to each asset:1E r r E r ri f m f( ) [ ( ) ]   .This expected return is the rate of return at which the firm's cash flows are discounted.We can think of the CAPM "market model" 2r rit i i mt it    as embodying these two components of the price of a stock. The parameters  and  are the discount rate component of the stock price and e is the information component. If the company has good management or a unique computer system or a crook for a bookkeeper, all this goes in epsilon. For instance, at the instant that the market recognizes that a firm's management is better than it was heretofore supposed, the stock price jumps and for that instant, e is positive. To the extent that the company is in textiles which vary with auto sales, this affects the rate at which thefirm's cash flows should be discounted and this is captured in .; Revised: January 14, 2019; M.T. Maloney1FINANCIAL ECONOMICS CLEMSON UNIVERSITYThe Risk PremiumCash flows come over time, and therefore they must be adjusted to reflect their current or presentvalue. The adjustment requires the estimation of an appropriate discount rate. The crucial issue isthat the discount rate should match the riskiness of the cash flows expected to accrue to the firm.If the future cash flows were known with certainty, the proper discount rate for a firm with a longlife would be the 30-year U.S. Treasury bond rate (that is, an almost risk free investment). Since the nominal cash flows resulting from purchasing a U.S. Treasury bond are expected to occur with a probability close to 1, this rate measures the risk free portion of the discount rate. This is the time value of money component of the overall discount rate.For firms, however, cash flows are not expected to occur with absolute certainty. Consequently, arisk premium must be added to the risk free rate in order to account for the imbedded uncertainty.This risk premium will vary from firm to firm and across industries. Computer software companies have high discount rates whereas public utilities (traditionally) have low rates. It is well known that the overall stock market is substantially riskier than the U.S. Treasury bond market. Investors require a risk premium in order to willingly hold the portfolio of common stocks. This expected risk premium is roughly 7.5 percentage points and is based on the difference in returns provided by U.S. Treasury bonds and the returns on the S&P 500 over the years 1926 through the present. Thus, an investor that choose to hold the stocks comprising the S&P 500 expects a return on the order of:Current T-Bond Rate + Expected Risk Premium on Market =5.9 percent + 7.5 percent,or 14.4 percent.Financial economists and experts have shown that risk varies across firms and industries. William Sharpe of Stanford University won the Nobel Prize in Economics in 1990 for helping to develop the Capital Asset Pricing Model (CAPM). This model describes how risk varies across firms. It is widely used on Wall Street and in estimating discount rates for the valuation of firms.As we have discussed and as is shown in (2) above, the CAPM applies the risk premium idea to individual stocks:E ri i( ) [  Treasury Bond Rate Market Risk Premium]where the Market Risk Premium is the historical difference between returns of U.S. Treasury bonds and the S&P 500 as discussed above.; Revised: January 14, 2019; M.T. Maloney2FINANCIAL ECONOMICS CLEMSON UNIVERSITYThe Calculation of BetaThe theory is that high betas have greater risk than low betas. In this context, one would expect computer software firms to have higher betas than utilities. This is true and is an explanation of why investors demand higher returns for holding computer software stocks than utilities.To provide a brief example, consider AMR, the parent of American Airlines. AMR has a beta of about 1.3. This beta is based on the historical relation between movements in AMR stock and movements in the overall market. Since the beta exceeds one, it suggests that holding AMR stockis riskier than holding a portfolio of stocks that resemble the S&P 500. The interpretation of beta is that when the market increases 10 percent, AMR stock is expected to increase on the order of 13 percent. However, when the market declines by 10 percent, the price of AMR is expected to fall by 13 percent.When we forecast the expected return for a particular stock like AMR that is publicly traded we can use the information contained in the trades to asset beta. We estimate the market model as in (2) to give us beta. Publicly traded firms are being evaluated all the time in terms of their price relative to the two components of the DCF formula. The current price of an asset can be