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Principles of Bond and Stock Valuation

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.

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Principles of Bond and Stock Valuation

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

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

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

  4. Zero Coupon Bonds • Zeros make only one payment at maturity • zn 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

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

  6. Price of Coupon Bond in Terms of Zeros

  7. Common Stock Valuation • I buy a stock now for P0 • I expect to sell one year from now for P1 • I collect the dividend DIV1 paid in Year 1 • My opportunity cost rate of return is r

  8. 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

  9. What Determines Future Stock Prices?

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

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

  12. Stock Price Grows at rate g in Constant Growth Model

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

  14. 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

  15. Investment Opportunities, Growth and Stock Prices

  16. Dividend Discount Model General Case Constant Growth Case • 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

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

  18. 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

  19. Growth Opportunities Model General Case Constant Growth Case 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

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

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