lecture’3’ bond’valuaon’ - simon foucher
TRANSCRIPT
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Lecture 3 Bond Valua0on
FINA 614
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Bond Defini0ons
• Bond • Par value (face value) • Coupon rate • Coupon payment • Maturity date • Yield or Yield to maturity
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Valuing a Discount Bond with Annual Coupons
• Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? – Using the formula:
• B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5 • B = 369.59 + 593.45 = 963.04
– Using the calculator: • N = 5; I/Y = 11; PMT = 100; FV = 1000 • CPT PV = -‐963.04
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The Bond-‐Pricing Equa0on
t
t
r)(1F
rr)(1
1-1C Value Bond
++
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡+
=
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Example – Semiannual Coupons • Most bonds in Canada make coupon payments
semiannually. • Suppose you have an 8% semiannual-‐pay bond with a
face value of $1,000 that matures in 7 years. If the yield is 10%, what is the price of this bond? – The bondholder receives a payment of $40 every six months (a total of $80 per year)
– The market automa0cally assumes that the yield is compounded semiannually
– The number of semiannual periods is 14
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Example – Semiannual Coupons con0nued
– Or PMT = 40; N = 14; I/Y = 5; FV = 1000; CPT PV = -‐901.01
01.90105.1000,1
05.01.05
1-140 Price Bond 14
14
=+⎥⎦
⎤⎢⎣
⎡
×=
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Bond Prices: Rela0onship Between Coupon and Yield
• If YTM = coupon rate, then par value = bond price
• If YTM > coupon rate, then par value > bond price – Why? – Selling at a discount, called a discount bond
• If YTM < coupon rate, then par value < bond price – Why? – Selling at a premium, called a premium bond
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Interest Rate Risk • Price Risk
– Change in price due to changes in interest rates – Long-‐term bonds have more price risk than short-‐term bonds
• Reinvestment Rate Risk – Uncertainty concerning the interest rates at which cash flows can be reinvested
– Short-‐term bonds have more reinvestment rate risk than long-‐term bonds
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Interest Rate Risk and Time to Maturity
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Interest Rate Sensi0vity
Bond Coupon Maturity Initial YTM
A 12% 5 years 10% B 12% 30 years 10% C 3% 30 years 10% D 3% 30 years 6%
A B C D Change in yield to maturity (%)
Perc
enta
ge c
hang
e in
bon
d pr
ice 0
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Bond Pricing Theorems • Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate
• If you know the price of one bond, you can es0mate its YTM and use that to find the price of the second bond
• This is a useful concept that can be transferred to valuing assets other than bonds
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Differences Between Debt and Equity Con0nued
• Equity – Ownership interest – Common shareholders vote for the board of directors and other issues
– Dividends are not considered a cost of doing business and are not tax deduc0ble
– Dividends are not a liability of the firm and shareholders have no legal recourse if dividends are not paid
– An all equity firm can not go bankrupt
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The Bond Indenture • Contract between the company and the bondholders; includes: – The basic terms of the bonds – The total amount of bonds issued – A descrip0on of property used as security, if applicable
– Sinking fund provisions – Call provisions – Details of protec0ve covenants
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Bond Classifica0ons • Registered vs. Bearer Forms • Security
– Collateral – secured by financial securi0es – Mortgage – secured by real property, normally land or buildings
– Debentures – unsecured debt with original maturity of 10 years or more
– Notes – unsecured debt with original maturity less than 10 years
• Seniority – Sinking Fund – Account managed by the bond trustee for early bond redemp0on
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Bond Classifica0ons Con0nued
• Call Provision – Call premium – Deferred call – Call protected – Canada plus call
• Protec0ve Covenants – Nega0ve covenants – Posi0ve covenants
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Bond Characteris0cs and Required Returns
• The coupon rate depends on the risk characteris0cs of the bond when issued
• Which bonds will have the higher coupon, all else equal? – Secured debt versus a debenture – Subordinated debenture versus senior debt – A bond with a sinking fund versus one without – A callable bond versus a non-‐callable bond
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Bond Ra0ngs – Investment Quality
• High Grade – DBRS’s AAA – capacity to pay is excep0onally strong – DBRS’s AA – capacity to pay is very strong
• Medium Grade – DBRS’s A – capacity to pay is strong, but more suscep0ble to changes in circumstances
– DBRS’s BBB – capacity to pay is adequate, adverse condi0ons will have more impact on the firm’s ability to pay
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Bond Ra0ngs -‐ Specula0ve • Low Grade
– DBRS’s BB, B, CCC, CC – Considered specula0ve with respect to capacity to pay.
• Very Low Grade – DBRS’s C – bonds are in immediate danger of default
– DBRS’s D – in default, with principal and/or interest in arrears
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Stripped or Zero-‐Coupon Bonds • Make no periodic interest payments (coupon rate = 0%)
• The en0re yield-‐to-‐maturity comes from the difference between the purchase price and the par value
• Cannot sell for more than par value • Some0mes called zeroes, or deep discount bonds • Bondholder must pay taxes on accrued interest every year, even though no interest is received
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Floa0ng Rate Bonds • Coupon rate floats depending on some index value • There is less price risk with floa0ng rate bonds
– The coupon floats, so it is less likely to differ substan0ally from the yield-‐to-‐maturity
• Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”
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Other Bond Types • Catastrophe bonds • Income bonds • Conver0ble bonds • Put bond (retractable bond) • There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns
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Bond Markets
• Primarily over-‐the-‐counter transac0ons with dealers connected electronically
• Extremely large number of bond issues, but generally low daily volume in single issues
• Makes gerng up-‐to-‐date prices difficult, par0cularly on small corporate issues
• Treasury securi0es are an excep0on
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Bond Quota0ons • From Figure 7.3 Canada 10.5 Mar 15/21 169.37 3.43
– Issue is a Government of Canada bond – Coupon rate is 10.5% (assumed to be semiannual)
– Maturity date is March, 15, 2021 – Price that a bondholder can sell for is $1,693.70 – Yield to maturity is 3.43% compounded semiannually
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Infla0on and Interest Rates • Real rate of interest – compensa0on for change in purchasing power
• Nominal rate of interest – quoted rate of interest, includes compensa0on for change in purchasing power and infla0on
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The Fisher Effect • The Fisher Effect defines the rela0onship between real rates, nominal rates and infla0on
• Exact rela0onship is (1 + R) = (1 + r)(1 + h), where: – R = nominal rate – r = real rate – h = expected infla0on rate
• Approxima0on of the above rela0onship is: – R = r + h
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Example – Fisher Effect • If we require a 10% real return and we expect infla0on to be 8%, what is the nominal rate?
• R = (1.1)(1.08) – 1 = .188 = 18.8% • Approxima0on: R = 10% + 8% = 18% • Since the real return and expected infla0on are rela0vely high, there is significant difference between the actual Fisher Effect and the approxima0on.
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Term Structure of Interest Rates • Term structure is the rela0onship between 0me to maturity and yields, all else equal
• It is important to recognize that we pull out the effect of default risk, different coupons, etc.
• Yield curve – graphical representa0on of the term structure – Normal – upward-‐sloping, long-‐term yields are higher than short-‐term yields
– Inverted – downward-‐sloping, long-‐term yields are lower than short-‐term yields
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– Upward-‐Sloping Yield Curve
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Downward-‐Sloping Yield Curve
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Government of Canada Yield Curve February 13, 2009
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Factors Affec0ng Required Return • Default risk premium – remember bond ra0ngs
• Liquidity premium – bonds that have more frequent trading will generally have lower required returns
• Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns
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