Pricing Financial Assets Timing and Amount of Cash Flows Risk of the Cash Flows Present Value of the Cash Flows discounted at the appropriate level of risk How do we determine timing and amount of cash flows? How do we determine the level of risk? How do we determine the risk premium and therefore the discount rate of the cash flows?

Stock Pricing What cash flows are we trying to price? The future dividends of the stock… The future dividends of the stock… cash dividends terminal price (liquidating dividend) What if the stock is to live forever? What if the stock is to live forever? terminal price has zero present value constant dividends look like perpetuity Pricing can only be done with some very restrictive assumptions...

Stock Pricing Some Constraints Constant Dividends Price = Dividends / k Price = Dividends / k Dividends that grow at a constant rate growth model…(Gordon’s Growth Model) growth model…(Gordon’s Growth Model) Price = Dividend x (1 + growth rate) / (discount rate minus growth rate) Price = Dividend x (1 + growth rate) / (discount rate minus growth rate) More formal: More formal: Price t = Div t (1 + g) / (k - g) = Div t+1 / (k - g)

Stock Pricing – Chapter 7 Problems With restricted models Must know dividends or be able to estimate dividend amount and timing… Must know dividends or be able to estimate dividend amount and timing… Problem 2 – Preferred Stock (fits model well) Problem 2 – Preferred Stock (fits model well) Problem 6 – Constant Growth Stock Problem 6 – Constant Growth Stock Problem 8 – Another Example Problem 8 – Another Example Problem 9 – Practice, Practice, Practice Problem 9 – Practice, Practice, Practice Problem 19 – Adding Beta to the mix… Problem 19 – Adding Beta to the mix…

CAPM - Security Market Line Capital Asset Pricing Model (CAPM) In return space it relates the expected return to the reward for taking on risk, the market premium In return space it relates the expected return to the reward for taking on risk, the market premium This is an ex-ante model… This is an ex-ante model… What is the relationship between an individual stock and the market in general? Covariance or Correlation Coefficient Covariance or Correlation Coefficient

Security Market Line The relationship is built through the OLS regression Return on Individual Stock vs. Market Return Return on Individual Stock vs. Market Return Ret i = α + β i (Market Return) Ret i = α + β i (Market Return) Beta is the relationship of the stock in a well diversified portfolio Beta is the relationship of the stock in a well diversified portfolio Market Premium (reward for risk) The difference between the market’s return and the risk-free return The difference between the market’s return and the risk-free return

Security Market Line Looking Forward… What is the expected reward for taking on risk? What is the expected reward for taking on risk? Beta measures risk Beta measures risk Standard Market risk has Beta of 1.0 Standard Market risk has Beta of 1.0 Expected Return is: Expected Return is: E(r i ) = r f + β i (E(r m ) – r f ) Chapter 5, Problem 20

Security Market Line All assets Plot on the Security Market Line Ex-Ante Ex-Ante The two dimensional graph The two dimensional graph Risk is measured by Beta and is the x-axis Return is the expected return and is the y-axis The Line is the Security Market Line The intercept is the risk-free rate The slope of the line is the market premium Chapter 5, Problem 22 Finally, beta in a portfolio – Linear Combination Chapter 5, Problem 18 Chapter 5, Problem 18