Chapter 16

1. Chapter 16 The Valuation of Fixed Income Securities

2. Current Value • The current value of a bond: the present value of cash flows • Interest and principal • discounted back to the present • at the going rate of interest on comparable debt

3. Comparable Debt • Same term to maturity • Same risk class

4. Comparable Debt • Comparable bonds • can have different coupons • can have different prices • have same yields

5. Perpetual Bond • The perpetual bond illustrates the process of valuation • P = PMT / i = $80/0.1 = $800

6. Perpetual Bond • Illustrates the inverse relationship between • bond prices • changes in interest rates

7. Valuation • Valuation of a bond that pays interest and matures • Unknown: PV • PMT = 100 • FV = 1000 • N = 3 • I = 10 Answer: $1,000

8. Same Bond at a Discount • Unknown: PV • PMT = 100 • FV = 1000 • N = 3 • I = 12 • The discount is the result of interest rates rising Answer: $952

9. Same Bond at a Premium • Unknown: PV • PMT = 100 • FV = 1000 • N = 3 • I = 8 • The premium is the result of interest rates declining Answer: $1,052

10. Relationship • The inverse relationship between • bond prices and • interest rates

11. Relationship

12. Fluctuations in Bond Prices • Prices of bonds with lower coupons fluctuate more • Prices of bonds with longer terms to maturity fluctuate more

13. Zero Coupon Bond Pricing • Unknown: PV • PMT = 0 • FV = 1000 • N = 10 • I = 7 Answer: $508

14. The Current Yield • Annual interest payment/Price of the bond • Current flow of interest (as a %) • $100 / $952 = 10.5%

15. The Yield to Maturity • The rate which equates • the present value of the cash inflows:the interest payment and principal repayment • the cash outflow:the cost of the bond

16. Yield to Maturity • Unknown: I • PV = $952 • PMT = $100 • FV = 1000 • N = 3 Answer: 12%

17. Current Yield and Yield to Maturity • Current yield exceeds yield to maturity • if bond sells for a premium • Yield to maturity exceeds the current yield • if the bond sells for a discount

18. Current Yield and Yield to Maturity • The current yield does not consider the premium or discount • The premium reduces the yield to maturity • The discount increases the yield to maturity

19. Yield to Call • Substitutes • the anticipated call date for the maturity date • the principal plus the call penalty for the principal repayment • A call will most likely occur • after interest rates have declined

20. Fluctuations in Yields • The yield spread between bonds of different quality increases when interest rates rise

21. Fluctuations in Yields

22. The Reinvestment Assumption • Yield to maturity assumes all cash inflows are reinvested at the yield to maturity • If the assumption holds, the realized rate and the yield to maturity are the same

23. The Reinvestment Assumption • If yields decrease, the realized rate over the lifetime of the bond • less than the yield to maturity • If yields increase, the realized rate over the lifetime of the bond • exceeds the yield to maturity

24. The Reinvestment Assumption

25. Duration • The average time required to collect • the interest and principal repayment • Weights the present value of each payment by the timing of the payment • A measure of price volatility

26. Duration • The larger the numerical value, the greater is the price volatility

27. Duration • Duration facilitates comparisons of price volatility of bonds with • different coupons and • different terms to maturity

28. Duration • Duration facilitates managing reinvestment rate risk • acquiring bonds whose duration matches when the funds will be needed erases reinvestment rate risk

29. Convexity and Duration • Duration may be used to forecast change in a bond’s price • The forecast become less accurate the greater the change in interest rates

30. Convexity and Duration • Duration forecasts along a straight line • Actual price changes are convex

31. Convexity and Duration Forecasted Prices Actual Prices

32. Management of Bond Portfolios • Bond swapping • The laddered strategy • The barbell strategy • The matching strategy • The swapping of variable for fixed payments

33. Features of Preferred Stock • Fixed dividend payments • Payment from earnings • Not a legal obligation • Cumulative preferred stock • Non-cumulative preferred stock • Arrearage

34. Valuation of Preferred Stock • The fixed dividend implies the model for valuation of bonds applies • Valuation of perpetual preferred stock • P = D / k

35. Valuation of Preferred Stock with Finite Life • The same model used for bond valuation: present value of dividends and the repayment of par value

36. Preferred Stock • Prices fluctuate inversely with changes in interest rates • Preferred stock prices tend to fluctuate more than bond prices

37. Comparisons of Bonds and Preferred Stock • Both make fixed payments • Both use the same valuation model • Bonds are debt but preferred stock is equity • Virtually all bonds have a maturity date; preferred stock may be perpetual

38. Comparisons of Bonds and Preferred Stock • Bonds are riskier than preferred stock • from the issuing company's perspective • Preferred stock is riskier than bonds • from the investor's perspective

39. Analysis of Preferred Stock • Based on the capacity of the company to pay the dividend • Times-dividend-earned ratio • Earnings after taxes / preferred dividend payment

40. Analysis of Preferred Stock • Earnings per preferred share • Earnings after taxes / number of preferred shares