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Cost of Capital

# Cost of Capital - FINA537 Equity Valuation Professor Laura...

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1 FINA537 Equity Valuation Professor Laura Xiaolei Liu Cost of Capital – Risk and Return

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2 What is risk? Will I win??? \$\$\$\$\$\$
3 What is risk? Risk is the uncertainty about the outcome Risk in the stock market is the uncertainty about the return you can get from purchasing a stock

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4 Calculating Rates of Return Suppose you purchased a share of IBM common stock for \$100 on January 1 2009, if the stock pays \$4 in dividends, and if it has a market price of \$108 on December 31, 2007 The rate of return on this investment is r = 4 + 108 100 100 = 12%
5 Rate of return on risky asset What if the IBM price is \$96 at Dec 31, 2009 r = (4 + 96 100)/100 = 0% What if the IBM price is \$86 at Dec 31, 2009 r = (4 + 86 100)/100 = -10% What if the IBM go bankruptcy at Dec 31,2009 r = (0-100)/100 = -100% Realized return depends on the stock price at Dec 31, it also depends on the dividend paid during the year 2009

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6 Calculating Rates of Return Rates of return for most assets are random Looking backward, we can calculate realized rates of return Looking forward, we characterize random events with probabilities and probability distributions Probability distributions are often described by summary measures like the mean and variance, the mean of this distribution is called expected return
7 Rate of Return Distribution IBM monthly stock return (1980-2000) 0 10 20 30 40 -0.2 -0.1 0.0 0.1 0.2 Series: RET Sample 1 240 Observations 240 Mean 0.013393 Median 0.011645 Maximum 0.238180 Minimum -0.261900 Std. Dev. 0.074086 Skewness -0.067616 Kurtosis 3.528114 Jarque-Bera 2.971918 Probability 0.226285

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8 Return of risk-free asset On January 1, 2009, you deposit \$100 to the saving account of Hang Seng Bank, Hong Kong, which offers a 5% interest rate r = \$105 \$100 =5% 100 You will receive 5% return no matter what happens (assuming the government will not allow the bank go bankruptcy for various of reasons). It is risk-free
9 Investor Preferences We will make two fundamental assumptions about investor preferences ¾ Investors prefer more wealth to less ( other things equal, investors prefer higher expected returns) ¾ Investors are risk averse (other things equal, investors prefer a lower standard deviation of their wealth)

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10 Risk and Return Since investors are risk-averse, they must be compensated for taking risk E(R s ) = R f + Risk Premium Risk premium is higher if the stock is more risky How to measure risk?
11 Modern Portfolio Theory Before Harry Markowitz pioneered portfolio theory, risk was usually measured by the stock return variance or stock-return standard deviation Modern Portfolio theory points out that risk can be reduced by diversification

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12 Risk Reduction through Diversification Two firms located on an isolated Caribbean island Buy \$100 of A, you get expected return of 12% with uncertainty, assuming there is equal choice to get sunny, normal or rainy day. Similarly for buying \$100 of B 33% Rainy year 12% Normal year Disposable Umbrella Manufacture -9% Sunny year Company B -9% Rainy year 12% Normal year Suntan Lotion Manufacture 33% Sunny year Company A Return on Stock Weather Conditions
13 Risk Reduction through Diversification

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