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

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

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

7. 01 100 1,000 Value = = $1,000. Find the value of a 1-year 10% annual coupon bond when k d = 10%. $1,100 1.10

8. 010 100 1,000 12 100 Find the value of a similar 10-year bond.

9. Way to Solve Using tables: Value = INT(PVIFA 10%,10 )+ M(PVIF 10%,10 ). = 100*6.1446 + 1000*0.3855 = 1000 (approx.)

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

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

12. 10-year bond When k d rises above the coupon rate, bond values fall below par. They sell at a discount. Using tables: Value = INT(PVIFA 14%,10 )+ M(PVIF 14%,10 ). = 100*5.2164 + 1000*0.2697 = 791.34

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

14. 10-year bond When k d falls below the coupon rate, bond values rise above par. They sell at a premium. Using tables: Value = INT(PVIFA 7%,10 )+ M(PVIF 7%,10 ). = 100*7.0236 + 1000*0.5083 = 1210.66

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

16. Summary If k d 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 = k d /2. 3.Divide annual INT by 2 to get PMT = INT/2. INPUTS OUTPUT 2nk d /2 OK INT/2OK NI/YR PV PMT FV

18. 2(10) 14/2 100/2 20 7 50 1000 NI/YR PV PMTFV 788.10 Find the value of 10-year, 10% coupon, semiannual bond if k d = 14%. INPUTS OUTPUT Using tables: Value = INT(PVIFA 7%,20 )+ M(PVIF 7%,20 ). = 50*10.5940 + 1000*0.2584 = 788.10

19. 00112233... 88 100100100... 100 What is the cash flow stream of a perpetual bond with an annual coupon of $100?

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

21. V 10% = = $1000. V 13% = = $769.23. V 7% = = $1428.57. V 10% = = $1000. V 13% = = $769.23. V 7% = = $1428.57. $100 0.10 $100 0.10 $100 0.13 $100 0.13 $100 0.07 $100 0.07

22. P 0 = + +.... ^ D 1 (1 + k) D 2 (1 + k) 2 D n (1 + k) n Stock value = PV of dividends

23. D 1 = D 0 (1 + g) D 2 = D 1 (1 + g)...... Future Dividend Stream:

24. P 0 = =. ^ D 1 k s - g D 0 (1 + g) k s - g If growth of dividends g is constant, then: Model requires: k s > g (otherwise results in negative price). g constant forever.

25. D 0 = 2.00 (already paid). D 1 = D 0 (1.06) = $2.12. P 0 = = =$21.20. Last dividend = $2.00; g = 6%. What is the value of Bon Temps’ stock given k s = 16%? ^ D 1 k s - g $2.12 0.16 - 0.06

26. P 1 = D 2 /(k s - g) = 2.247/0.10 = $22.47. ^ What is Bon Temps’ value one year from now? Note: Could also find P 1 as follows: P 1 = P 0 (1 + g) = $21.20(1.06) = $22.47. ^ ^

27. k s = + g = + 0.06 = 16%. D1P0D1P0 $2.12 $21.20 Constant growth model can be rearranged to solve for return: ^

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

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 P 0 ? ^ 0 k s =16% 12 3 4 g = 30% g = 30% g = 30% g = 6% D 0 = 2.00 2.60 3.38 4.394 4.658 2.241 2.512 2.815 P 3 = = 46.58 29.842 37.41 = P 0 4.658 0.10

31. 0011223344 $2.00 $2.12 0% 6%... Suppose g = 0 for 3 years, then g is constant at 6%. ฅ

32. (1) PV 3-year, $2 annuity, 16% PV = PMT(PVIFA 16%,3 ) = 2 * 2.2459 = $4.492. (2)P 3 = = $21.20. PV(P 3 ) = $13.58. P 0 = $4.49 + $13.58 = $18.07. $2.12 0.10 What is the price, P 0 ?