The Valuation of Fixed Income Securities

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, and
• 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, and
• 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
The Inverse Relationship

• 10 3 year bond
• I PB
• 4 1,167
• 8 1,052
• 10 1,000
• 12 952
• 14 907

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 that 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

26
Duration

• A measure of price volatility
• 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
  bonds price.
• The forecast becomes 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
Actual Prices
Forecasted 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