Bond Valuation

1
Bond Valuation

• FIL 404
• Keldon Bauer, PhD

2
Introduction

• The valuation of all financial securities is
  based on the expected PV of future cash flows.

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Introduction

• ECFt Expected cash flow at time t.
• r The required return (based on economic
  conditions riskiness).
• Value increases as cash flow increases or r
  decreases.

4
Capital Market Instruments

• There are two forms of capital
• Debt The right to an agreed cash flow.
• Equity The ownership interest in the business
  (therefore the residual cash flow).
• A bond is a long-term promissory note by business
  or government.

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Bond Terminology

• Principal Amount Face Value Maturity Value
  Par Value The amount borrowed and the principal
  that will be returned at maturity.
• Coupon (Interest) Payment Payment of promised
  interest (typically at six month intervals).
  Payment/Face value is the coupon interest rate.

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Bond Terminology

• Maturity Date Date when the principal and any
  outstanding interest payments are remitted.
• Issue date Date when bond was issued.
• Default risk Risk that issuer will not make
  interest or principal payments.

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Bond Terminology

• Call Provision Clause in the indenture giving
  the issuer the right to early redemption (or
  recall).
• New Issue versus Outstanding Bonds Bonds in the
  primary or secondary markets

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Call Provision

• Issuer can refund if rates decline. That helps
  the issuer but hurts the investor.
• Therefore, borrowers are willing to pay more, and
  lenders require more, on callable bonds.
• Most bonds have a deferred call and a declining
  call premium.

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Whats a sinking fund?

• Provision to pay off a loan over its life rather
  than all at maturity.
• Similar to amortization on a term loan.
• Reduces risk to investor, shortens average
  maturity.
• But not good for investors if rates decline after
  issuance.

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Sinking Funds Two Ways

• 1. Call x at par per year for sinking fund
  purposes.
• 2. Buy bonds on open market.
• Company would call if rd is below the coupon rate
  and bond sells at a premium. Use open market
  purchase if rd is above coupon rate and bond
  sells at a discount.

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Bond Valuation

• Two major components
• Interest payments (an annuity).
• Principal (future lump-sum).

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Bond Valuation Interest Review

• The discount rate (rBond) is the opportunity cost
  of capital, i.e., the rate that could be earned
  on alternative investments of equal risk.
• For debt securities
• rBond r IP LP MRP DRP

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Bond Valuation - Example 1

• The value of a 15 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  10.

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Bond Valuation - Example 2

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  10.

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Bond Valuation - Example 3

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  8.

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Bond Valuation - Example 4

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  12.

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Some Conclusions

• Return or loss on bonds comes from two
  components.
• Interest Payment (Current Yield) (Interest
  Payment)/VB
• Change in Face Value (Capital Gain) (VEnding -
  VBeginning)/VBeginning

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Current Yield - Example

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  8.

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Capital Gains Yield - Example

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  8.

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Total Yield - Example

• The value of a 7 year 10,000 bond, paying
  semi-annual payments of 500, when market rate is
  8.

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Some Conclusions

• When market rate rB the bond sells at par or
  face value.
• When market rate lt rB the bond sells at a
  premium.
• When interest rates go down, bond prices go up.
• When market rate gt rB the bond sells at a
  discount.

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Some Conclusions

• As time to maturity approaches zero, market value
  approaches face value.
• If a 15 year, 10 coupon bond at 5 10 and 15
  market rates were sold on the market, the values
  of the bond would be as shown in the following
  graph.

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Value of a 10 Coupon Bond
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Some Conclusions

• As time to maturity approaches zero, market value
  approaches the face value of the bond.

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Yield to Maturity (YTM)

• Yield to Maturity (YTM) The effective interest
  rate earned on the bond.
• The text has a formula to estimate the YTM, but
  your calculator can calculate it directly.
• Input the n, PV (Market Value), PMT (semi-annual
  payments), FV (Par Value), and have it compute i
  (then adjust).

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YTM - Example

• What is the yield-to-maturity of a bond with
  current market value of 950.51, a par value of
  1,000 (which is returned in seven years), making
  a coupon payment of 45 every six months?

Answer 10.00
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Bond Values - Example

• What is the market value of a bond with current
  market rate of 10, a par value of 1,000 (which
  is returned in seven years), making a coupon
  payment of 54 every six months?

Answer 1,039.59
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Interest Rate Risk

• Two types of interest rate risk associated with
  bond value.
• Price Risk
• Reinvestment Risk
• Price Risk The risk of change in price give
  change in interest.
• As interest increases, value decreases.

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Price Risk - Effect of Maturity
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Price Risk - Effect of Payment
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Interest Rate Risk

• Reinvestment Risk The risk of worse
  reinvestment opportunities when repaid.
• When interest rates increase reinvestment
  opportunities improve.
• Note Price and Reinvestment Risks go in
  opposite directions.

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Bond Market

• Long-term bonds High interest rate risk, low
  reinvestment rate risk.
• Short-term bonds Low interest rate risk, high
  reinvestment rate risk.
• Nothing is riskless!

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Bond Market

• True or False All 10-year bonds have the same
  price and reinvestment rate risk.
• False! Low coupon bonds have less reinvestment
  rate risk but more price risk than high coupon
  bonds.

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Default Risk

• Bond indenture
• Trustee
• Restrictive covenants
• Mortgage bonds
• Debentures
• Subordinated debentures
• Development bonds
• Municipal bond insurance

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Default Risk

• Bond Ratings
• Standard and Poors (SP)
• Moodys
• Investment Grade vs Speculative Grade
• Rating Criteria