FINC 3310

1
FINC 3310

• Chapter Seven
• Bond Valuation and Interest Rate Basics

2
I. Bonds

• Features and Payment Patterns
• Bond Pricing
• Pricing Theorems and Interest Rate Risk
• Bond Markets and Interest Rate Basics

3

• The Bond Indenture
• The bond indenture is a three-party contract
  between the bond issuer, the bondholders, and the
  trustee. The trustee is hired by the issuer to
  protect the bondholders interests. (What do you
  think would happen if an issuer refused to hire a
  trustee?)
• The indenture includes
• The basic terms of the bond issue
• The total amount of bonds issued
• A description of the security (if any)
• Repayment arrangements
• Call provisions
• Details of the protective covenants

4
Features of a May Department Stores Bond

• Terms Explanations
• Amount of issue 125 million The company will
  issue 125 million worth of bonds.
• Date of issue 2/28/86 The bonds were sold on
  2/28/86.
• Maturity 3/1/16 The principal will be paid in 30
  years.
• Annual coupon 9.25 The denomination of the bonds
  is 1,000. Each bondholder will receive 92.50
  per bond per year (9.25 of the face value).
• Offer price 100 The offer price will be 100 of
  the 1,000 face value per bond.

5
Features of a May Department Stores Bond
(concluded)

• Terms Explanations
• Coupon payment dates 3/1, 9/31 Coupons of
  92.50/2 46.25 will be paid on these dates.
• Security None The bonds are debentures.
• Sinking fund Annual The firm will make annual
  payments beginning 3/1/97 toward the sinking
  fund.
• Call provision Not callable The bonds have a
  deferred call before 2/28/93 feature.
• Call price 106.48 initially, After 2/28/93, the
  company can buy back declining to 100 the bonds
  for 1,064.80 per bond, declining to 1,000 on
  2/28/05.
• Rating Moodys A2 This is one of Moodys higher
  ratings. The bonds have a low probability of
  default.

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Bond Ratings

• Low Quality, speculative
• Investment-Quality Bond
  Ratings and/or Junk
• High Grade Medium Grade Low Grade
  Very Low Grade
• Standard Poors AAA AA A BBB
  BB B CCC CC C
  DMoodys Aaa Aa A Baa
  Ba B Caa Ca C C
• Moodys SP
• Aaa AAA Debt rated Aaa and AAA has the highest
  rating. Capacity to pay interest and principal
  is extremely strong.
• Aa AA Debt rated Aa and AA has a very strong
  capacity to pay interest and repay principal.
  Together with the highest rating, this group
  comprises the high-grade bond class.
• A A Debt rated A has a strong capacity to pay
  interest and repay principal, although it is
  somewhat more susceptible to the adverse
  effects of changes in circumstances and
  economic conditions than debt in high rated
  categories.

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Bond Ratings (concluded)

• Baa BBB Debt rated Baa and BBB is regarded as
  having an adequate capacity to pay interest and
  repay principal. Whereas it normally exhibits
  adequate protection parameters, adverse
  economic conditions or changing circumstances
  are more likely to lead to a weakened capacity
  to pay interest and repay principal for debt in
  this category than in higher rated categories.
  These bonds are medium-grade obligations.
• Ba, B BB, B Debt rated in these categories is
  regarded, on balance, as predominantly
  speculative with respect to capacity to pay
  interest and Ca, C CC, C repay principal in
  accordance with the terms of the obligation. BB
  and Ba indicate the lowest degree of
  speculation, and CC and Ca the highest degree
  of speculation. Although such debt will likely
  have some quality and protective
  characteristics, these are out-weighed by large
  uncertainties or major risk exposures to adverse
  conditions. Some issues may be in default.
• D D Debt rated D is in default, and payment of
  interest and/or repayment of principal is in
  arrears

8
Bond Pricing

• Given the characteristics of bonds outlined
  above, it is straightforward to arrive at the
  following bond pricing relationship
• B

9
Example

• Bond issued with 10 years to maturity. Coupon
  and current market rates are 9. What is price
  at issue? Coupon payments are annual.
• B C (PVIFA9,10) F (PVIF9,10)
• C 9 of 1000 90
• F 1000
• B 90(6.4177) 1000(.4224)
• 577.6 422.4
• 1000

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Pricing Fundamentals

• Since interest rates vary after bond's issue,
  but (usually) coupon doesn't, B will vary as
  rates rise and fall.
• 1) if r coupon, bond sells at a discount
• 2) if r
• 3) if r coupon, bond sells at F (regardless of
  maturity)

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Example, continued

• What if rates changes after issue? Two years
  later rates are now lower at 7. What price does
  the bond sell for now?
• B 90(PVIFA7,8) 1000(PVIF7,8)
• 90(5.9713 1000(.5820)
• 537.417 582.00
• 1,119.417

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Example, continued

• What is the economic intuition of the premium?
• Note that the coupon payment is 20 too high.
  What is the value of the extra 20?
• PVA 20(PVIFA7,8) 20(5.9713) 119.42

13
Example, continued

• What if rates had risen instead? Say r goes
  from 9 to 12 (still two years later, as in the
  previous example)
• B 90(PVIFA12,8) 1000(PVIF12,8)
• 90(4.9676) 1000(.4039)
• 447.084 403.90
• 850.984

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Example, continued

• What is the economic intuition of the discount?
• Here, the coupon is 30 too low. What is the
  value of the this?
• PVA 30(PVIFA12,8) 30(4.9676) 149.028

15
Bond Price Sensitivity to YTM
Bond price
1,800
Coupon 10020 years to maturity1,000 face
value
1,600
Notice bond prices and YTMs are inversely
related.
1,400
1,200
1,000
800
600
Yields to maturity, YTM
12
4
6
8
10
14
16
16
Adjusting for semi-annual payments

• Here we must be careful because the stated
  annual coupon rate is like an APR from the last
  chapter. That is, if the coupon rate is 10, the
  six month rate is 5, or 12 becomes 6 , and so
  on. Note that this means the actual yield and
  the APR yield to maturity will be different.
  We must be very clear just what rate we are using
  as the current market rate or yield. Is it the
  APR or EAR? If it is the APR, the adjustment is
  easy-just divide by two as we do for the coupon
  payment. If is is the EAR, we must solve for the
  appropriate six month rate.

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Example

• Current rates (APR) are at 8 annually, and you
  own a bond paying 10 on a semiannual basis. The
  bond has 5 years until maturity. B ?
• B 50 (PVIFA4,10) 1000(PVIF4,10)
• 50(8.1109) 1000(.6756)
• 405.545 657.60
• 1,081.145
• EAR (1.04)2 -1 8.16

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Bond Prices and Interest Rate Risk

• Interest Rate Risk - notice that when rates
  fall, prices , (or rates rise and prices ).
  Additionally, notice something price changes are
  asymmetric and the magnitudes depend on maturity
  and coupon rate of the bonds!
• a) all else equal, the longer maturity bond has
  greater D in price for a given D in interest
  rate
• b) all else equal, the lower coupon bond has
  greater D in price.

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Interest Rate Risk and Time to Maturity
Bond values ()
2,000
1,768.62
30-year bond
Time to Maturity
Interest rate 1 year 30
years 5 1,047.62 1,768.62
10 1,000.00 1,000.00 15 956.52 671.70
20 916.67 502.11
1,500
1-year bond
1,047.62
1,000
916.67
502.11
500
Interest rates ()
20
5
10
15
Value of a Bond with a 10 Coupon Rate for
Different Interest Rates and Maturities
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Solving for the Yield to Maturity - YTM

• Often we know a bonds price, coupon, and
  maturity. We want the yield to maturity that
  one rate over the bonds life that makes the PV
  of cash flows equal to the current price.
• B C (PVIFAr,n) F(PVIFr,n)
• This can be a trial and error process!

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YTM, continued

• We can't really solve this. But use what we
  know!
• If B coupon rate
• If B 1000 premium r
• So eliminate bad guesses!!

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YTM Example

• Assume
• 50 coupon, semiannually (annual 100)
• 6 years to maturity (n 12!)
• B0 841.15
• What is YTM? That rate that solves the
  following
• 841.15 50 (PVIFAr/2,12) 1000 (PVIFr/2,12)
• Coupon is 10, so do higher rate

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YTM Example, continued

• At 12 (6 per period)
• B 50(8.3838) 1000(.4970)
• 916.19 (too high, rate too
  ________)
• At 14 (7 per period)
• B 50(7.9427) 1000(.4440)
• 841.135 OK!!

24
Inflation and Interest Rates

• Real versus Nominal Rates
• The idea is that interest rates must include
  compensation for expected changes in purchasing
  power
• R r h rh

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Inflation and Interest Rates

• An example
• Suppose a friend wants to borrow 200 pizzas and
  will repay you 210 pizzas next period.
• What is your pizza return?
• Is there an easier way to do this?

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Example, continued

• Suppose pizzas cost 12 now. How much would your
  friend need to borrow?
• How much would you expect in return?
• This ignores inflation! Suppose you expect
  pizzas to cost 13.20 next period. What happens
  if your payoff is unchanged?

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Example, continued

• How many pizzas can you now buy?
• What return do you need?
• Summary Your nominal return is the percentage
  change in the amount of money you have. Your
  real return is the percentage change in the
  amount of stuff you can actually buy.

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Determinants of Observed Yields

• Term structure
• real rate
• expected inflation
• interest rate risk premium
• Default risk
• Taxability
• Liquidity