Valuing Bonds

1
Chapter 5

• Valuing Bonds

2
Chapter 5 Topic Overview

• Bond Characteristics
• Reading Bond Quotes
• Annual and Semi-Annual Bond Valuation
• Finding Returns on Bonds
• Bond Risk and Other Important Bond Valuation
  Relationships

3
Bond Characteristics

• Face (or Par) Value stated face value that is
  the amount the issuer must repay, usually 1,000
• Coupon Interest Rate
• Coupon (cpn) Coupon Rate x Face Value
• Maturity Date when the face value is repaid.
• This makes a bonds cash flows look like this

4
Characteristics of Bonds

• Bonds pay fixed coupon (interest) payments at
  fixed intervals (usually every 6 months) and pay
  the face value at maturity.

5
The Financial Pages Treasury Bonds

• Maturity Ask
• Rate Mo/Yr Bid Asked Chg Yld
• 6.5 Oct 06n 11217 11218 -2 2.23
• Most values expressed as a age of par (1000).
• xxx xxx and /32nd of par
• Asked investor purchase price 112 18/32 of
  1000 1,125.625
• Bid investor selling price 1,125.3125
• Rate Annual coupon rate 6.5 of par 65/year
  32.50 semiannually
• Chg change in price from previous day in 32nds
  of of par
• Ask Yld 2.23 annual rate of return if
  purchased and held until maturity in Oct 2006

6
Bonds

• WARNING
• The coupon rate IS NOT the discount rate used in
  the Present Value calculations.
• The coupon rate merely tells us what cash flow
  the bond will produce.
• Since the coupon rate is listed as a , this
  misconception is quite common.

7
Bond Pricing

• The price of a bond is the Present Value of all
  cash flows generated by the bond (i.e. coupons
  and face value) discounted at the required rate
  of return.

8
Bond Valuation

• Discount the bonds cash flows at the investors
  required rate of return.
• the coupon payment stream (an annuity).
• the face (par) value payment (a single sum).
• PV cpn (PVAF r, t) par /(1r)t

9
Bond Valuation Example 1

• Duffs Beer has 1,000 par value bonds
  outstanding that make annual coupon payments.
  These bonds have an 8 annual coupon rate and 12
  years left to maturity. Bonds with similar risk
  have a required return of 10, and Moe Szyslak
  thinks this required return is reasonable.
• Whats the most that Moe is willing to pay for a
  Duffs Beer bond?

10
P/Y 1 12 N 10 I/Y
1,000 FV 80 PMT CPT PV
-863.73

• Note If the coupon rate lt discount rate, the
  bond will sell for less than the par value a
  discount.

11
Lets Play with Example 1

• Homer Simpson is interested in buying a Duff Beer
  bond but demands an 8 percent required return.
• What is the most Homer would pay for this bond?

12
P/Y 1 12 N 8 I/Y
1,000 FV 80 PMT CPT PV
-1,000

• Note If the coupon rate discount rate, the
  bond will sell for its par value.

13
Lets Play with Example 1 some more.

• Barney (belch!) Barstool is interested in buying
  a Duff Beer bond and demands on a 6 percent
  required return.
• What is the most Barney (belch!) would pay for
  this bond?

14
P/Y 1 12 N 6 I/Y
1,000 FV 80 PMT CPT PV
-1,167.68

• Note If the coupon rate gt discount rate, the
  bond will sell for more than the par value a
  premium.

15
Bond Prices and Interest Rates have an inverse
relationship!
16
Bonds with Semiannual Coupons

• Double the number of years, and divide required
  return and annual coupon by 2.

VB annual cpn/2(PVAFr/2,2t) par /(1r/2)2t
17
Semiannual Example

• A 1000 par value bond with an annual coupon rate
  of 9 pays coupons semiannually with 15 years
  left to maturity. What is the most you would be
  willing to pay for this bond if your required
  return is 8 APR?
• Semiannual coupon 9/2(1000) 45
• 15x2 30 remaining coupons

18
P/Y 1 15x2 30 N 8/2
4 I/Y 1,000 FV 90/2 45
PMT CPT PV -1,086.46
19
Bond Yields

• Current Yield - Annual coupon payments divided by
  bond price.
• Yield To Maturity - Interest rate for which the
  present value of the bonds payments equal the
  price.

20
Bond Yields

• Calculating Yield to Maturity (YTMr)
• If you are given the price of a bond (PV) and
  the coupon rate, the yield to maturity can be
  found by solving for r.

21
Yield to Maturity Example

• 1000 face value bond with a 10 coupon rate paid
  annually with 20 years left to maturity sells for
  1091.29.
• What is this bonds yield to maturity?

22
P/Y 1 -1091.29 PV 20
N 1,000 FV 100 PMT CPT I/Y 9 YTM

23
Bond Yields

• Rate of Return - Earnings per period per dollar
  invested.

24
Lets try this together.

• Imagine a year later, the discount (required)
  rate for the bond from the YTM example fell to
  8.
• What is the bonds expected price?
• What is the rate of return, if we sell the bond
  at this time assuming we bought the bond a year
  earlier at 1091.29?
• PMT 100, FV 1000

25
YTM for semiannual coupon bonds back to our
T-bond

• Maturity Ask
• Rate Mo/Yr Bid Asked Chg Yld
• 6.5 Oct 06n 11217 11218 -2 2.23
• 1000 par value, todays price 1125.625 PV
• Semiannual coupon 1000(6.5/2) 32.50
• Assume 2006-2003 3 years to maturity x 2 6
  semiannual payments left.
• -1,125.625 PV, 32.50 PMT, 1000 FV, 6 N,
  CPT I/Y 1.1 semiannually
• Annual YTM 2(1.1) 2.2 APR

26
Bond Value Changes Over Time

• Returning to the original example 1, where k
  10, N 12, cpn (PMT) 80, par (FV) 1000,
  PV 863.73.
• What is bond value one year later when N 11 and
  r is still 10?
• 80 PMT, 1000 FV, 11 N, 10 I/Y, CPT PV
  870.10
• PV 80(PVAF10,11) 1000/(1.10)11 870.10

27
What is the bonds return over this year?

• Rate of Return (Annual Coupon Price
  Change)/Beg. Price
• Annual Coupon 80
• Beg. Price 863.73, End Price 870.10
• Price Change 870.10 - 863.73 6.37
• Rate of Return (80 6.37)/863.73 10

28
Bond Prices over time approach par value as
maturity date approaches assuming same YTM
29
Interest Rate Risk

• Measures Bond Price Sensitivity to changes in
  interest rates.
• In general, long-term bonds have more interest
  rate risk than short-term bonds.

30
Interest Rate Risk Example

• Recall from our earlier example (1), the
  12-year, 8 annual coupon bond has the following
  values at kd 6, 8, 10. Lets compare with
  a 2-yr, 8 annual coupon bond.
• 12-year bond 2-year bond
• r6 PV 1,167.68 PV 1,036.67
• r8 PV 1,000 PV 1,000
• r10 PV 863.73 PV 965.29

31
Bond Price Sensitivity Graph
32
Default Risk

• Credit risk
• Default premium
• Investment grade
• Junk bonds

33
Default Risk
34
Other Types of Bonds

• Zero Coupon Bonds no coupon payments, just par
  value.
• Convertible Bonds can be converted into (fixed
  of) shares of stock.
• Floating Rate (Indexed) Bonds coupon payments
  and/or par value indexed to inflation.
• TIPs Indexed US Treasury coupon bond, fixed
  coupon rate, face value indexed.
• Callable Bonds Company can buy back the bonds
  before maturity for a call price. More likely as
  interest rates fall.
• Yield to Call calculate like yield to maturity
  but use time to earliest call date as N, and call
  price as FV.