Principles of Bond and Stock Valuation Estimating value by discounting future cash flows

Bond Price (semiannual coupons) P = bond price C = annual coupon ($) F = face value (par, principal) r = yield (annual) T = years to maturity

Bond Price Relative to Par C/F > rBond sells above par (premium bond) C/F = rBond sells at par (par bond) C/F < rBond sells below par (discount bond)

Zero Coupon Bonds Zeros make only one payment at maturity z n is the price today of $1 to be delivered n semiannual periods from today We can represent any bond price in terms of zero coupon bond prices

Recall Applying Discount Factors to Cash Flow Streams Discount factors are like prices (exchange rates)

Price of Coupon Bond in Terms of Zeros

Common Stock Valuation I buy a stock now for P 0 I expect to sell one year from now for P 1 I collect the dividend DIV 1 paid in Year 1 My opportunity cost rate of return is r

The One-Year Rate of Return First term represents dividend yield, second term represents capital gains Stock will be priced so that investors can expect to earn their opportunity cost rate of return

What Determines Future Stock Prices?

The Dividend Discount Model Carrying this process on out indefinitely: But how can we estimate all future dividends?

Constant Growth Dividend Discount Model Suppose dividends grow at a constant rate g each year forever:

Stock Price Grows at rate g in Constant Growth Model

Dividends Growing at Sustainable Growth Rate If dividends grow because the firm pays out the fraction (1-b) of each year t’s earnings E t as dividends and retains the fraction b, reinvesting to earn the rate ROE, dividends will grow at the sustainable rate = bROE:

Price-Earnings Ratio PE ratio  as discount rate , growth rate , and dividend payout , other things equal However, other things are not equal. An increase in payout lowers the growth rate

Investment Opportunities, Growth and Stock Prices

Dividend Discount Model Left-hand equation is general version of Dividend Discount Model (DDM) Right-hand equation is special case of DDM when there is constant perpetual growth General CaseConstant Growth Case

Dividends Growing at Sustainable Growth Rate If dividends grow because the firm pays out the fraction (1-b) of each year t’s earnings E t as dividends and retains the fraction b, reinvesting to earn the rate ROE, dividends will grow at the sustainable rate = bROE:

Growth Opportunities Model Growth Opportunities Model is an alternative but equivalent model to the DDM First term is the value of the earnings stream from existing assets VGO is value of growth opportunities

Growth Opportunities Model Second term in both expressions above is VGO (PV of NPVs of all future investments) Value is added from positive-NPV future projects rather than a higher growth rate per se General CaseConstant Growth Case

Equivalent Approaches to Stock Valuation Growth Opportunities Approach General Case Constant Growth Case Dividend Discount Approach