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Valuation Models

Valuation Models. Bonds Common stock. Key Features of a Bond. Par value : face amount; paid at maturity. Assume $1,000. Coupon interest rate : stated interest rate. Multiply by par value to get dollar interest payment. Generally fixed.

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Valuation Models

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  1. Valuation Models • Bonds • Common stock

  2. Key Features of a Bond • Par value: face amount; paid at maturity. Assume $1,000. • Coupon interest rate: stated interest rate. Multiply by par value to get dollar interest payment. Generally fixed.

  3. Maturity: years until bond must be repaid. Declines over time. • Issue date: date when bond was issued.

  4. How can we value assets on the basis of expected future cash flows? CF1 (1 + k)1 CF2 (1 + k)2 CFn (1 + k)n Value = + . . . .

  5. How is the discount rate determined? The discount rate k is the opportunity cost of capital and depends on: • riskiness of cash flows. • general level of interest rates.

  6. The cash flows of a bond consist of: • An annuity (the coupon payments). • A lump sum (the maturity, or par, value to be received in the future). Value = INT(PVIFAi%, n ) + M(PVIFi%, n).

  7. Find the value of a 1-year 10% annual coupon bond when kd = 10%. 0 1 100 1,000 $1,100 1.10 Value = = $1,000.

  8. Find the value of a similar 10-year bond. 0 1 2 10 100 100 100 1,000

  9. Way to Solve Using tables: Value = INT(PVIFA10%,10)+ M(PVIF10%,10). = 100*0.9090 + 100*0.9091 = 1000

  10. Rule:When the required rate of return (kd) equals the coupon rate, the bond value (or price) equals the par value.

  11. What would the value of the bonds be if kd = 14%? 1-year bond Using tables: Value = INT(PVIFA14%,1)+ M(PVIF14%,1). = 100*0.9772 + 1000*0.8772 = 964.92

  12. 10-year bond Using tables: Value = INT(PVIFA14%,10)+ M(PVIF14%,10). = 100*5.2164 + 1000*0.2697 = 791.34 When kd rises above the coupon rate, bond values fall below par. They sell at adiscount.

  13. What would the value of the bonds be if kd = 7%? 1-year bond Using tables: Value = INT(PVIFA7%,1)+ M(PVIF7%,1). = 100*0.9346 + 1000*0.9346 = 1028.06

  14. 10-year bond Using tables: Value = INT(PVIFA7%,10)+ M(PVIF7%,10). = 100*7.0236 + 1000*0.5083 = 1210.66 When kd falls below the coupon rate, bond values rise above par. They sell at apremium.

  15. Value of 10% coupon bond over time: kd = 7% 1372 1211 1000 791 775 kd = 10% M kd = 13% 30 20 10 0 Years to Maturity

  16. Summary If kd remains constant: • At maturity, the value of any bond must equal its par value. • Over time, the value of a premium bond will decrease to its par value. • Over time, the value of a discount bond will increase to its par value. • A par value bond will stay at its par value.

  17. Semiannual Bonds 1. Multiply years by 2 to get periods = 2n. 2. Divide nominal rate by 2 to get periodic rate = kd/2. 3. Divide annual INT by 2 to get PMT = INT/2. 2n kd/2 OK INT/2 OK N I/YR PV PMT FV INPUTS OUTPUT

  18. Find the value of 10-year, 10% coupon, semiannual bond if kd = 14%. 2(10) 14/2 100/2 20 7 50 1000 N I/YR PV PMT FV 788.10 INPUTS OUTPUT Using tables: Value = INT(PVIFA7%,20)+ M(PVIF7%,20). = 50*10.5940 + 1000*0.2584 = 788.10

  19. What is the cash flow stream of a perpetual bond with an annual coupon of $100? 8 0 1 2 3 . . . 100 100 100 . . . 100

  20. A perpetuity is a cash flow stream of equal payments at equal intervals into infinity. PMT k Vperpetuity = .

  21. $100 0.10 V10% = = $1000. V13% = = $769.23. V7% = = $1428.57. $100 0.13 $100 0.07

  22. Stock value = PV of dividends D1 (1 + k) D2 (1 + k)2 Dฅ (1 + k)ฅ ^ P0 = + + . . . .

  23. Future Dividend Stream: D1 = D0(1 + g) D2 = D1(1 + g) . . .

  24. If growth of dividends g is constant, then: D1 ks - g D0 (1 + g) ks - g ^ P0 = = . • Model requires: • ks > g (otherwise results in negative price). • g constant forever.

  25. What is the value of Bon Temps’ stock given ks = 16%? Last dividend = $2.00; g = 6%. D0 = 2.00 (already paid). D1 = D0(1.06) = $2.12. P0 = = =$21.20. D1 ks - g $2.12 0.16 - 0.06 ^

  26. What is Bon Temps’ value one year from now? ^ P1 = D2/(ks - g) = 2.247/0.10 = $22.47. ^ Note: Could also find P1 as follows: P1 = P0 (1 + g) = $21.20(1.06) = $22.47. ^

  27. Constant growth model can be rearranged to solve for return: D1 P0 ^ ks = + g = + 0.06 = 16%. $2.12 $21.20

  28. Zero growth If a stock’s dividends are not expected to grow over time (g = 0), then it is a perpetuity. Pmt k V = = = $13.25. $2.12 0.16

  29. Subnormal or Supernormal Growth • Cannot use constant growth model • Value the nonconstant & constant growth periods separately

  30. If we have supernormal growth of 30% for 3 years, then a long-run constant g = 6%, what is P0? ^ 0ks=16% 1 2 3 4 g = 30% g = 30% g = 30% g = 6% D0 = 2.00 2.60 3.38 4.394 4.658 2.241 2.512 2.815 P3 = = 46.58 29.842 37.41 = P0 4.658 0.10

  31. Suppose g = 0 for 3 years, then g is constant at 6%. ฅ 0 1 2 3 4 . . . 0% 0% 0% 6% $2.00 $2.00 $2.00 $2.12

  32. What is the price, P0? (1) PV 3-year, $2 annuity, 16% PV = PMT(PVIFA 16%,3) = 2 * 2.2459 = $4.492. $2.12 0.10 (2)P3 = = $21.20. PV(P3) = $13.58. P0 = $4.49 + $13.58 = $18.07.

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