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

Bonds, Interest Rates and Inflation Most bonds are “fixed income” instruments Their payments are specified in “nominal” terms – i.e., unadjusted for inflation Inflation hurts bondholders by eroding the purchasing power of future bond payments

The Fisher Effect (see p. 155) R is the nominal interest rate r is the real interest rate Investors care about real rates, so they demand that nominal rates compensate them for anticipated inflation

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

Total Return in the Constant Growth Dividend Discount Model Total return, R, consists of dividend yield and capital gains The growth rate, g, is the annual rate of expected capital gains

Where does Growth Come From? Earnings grow because funds retained and reinvested add new earnings: EPS 2 = EPS 1 + (bROE)EPS 1 bROE is the sustainable growth rate when ROE is measured as next year’s earnings divided by this year’s equity (see Chap. 3, p. 78)

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:

An Aside on the 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