bonds, bond valuation, and interest rates
TRANSCRIPT
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Designed by: Salah Anwar Skaik
Saed Fathi Abdel Wahhab
Copyright © 2011 - S.A.S & S.F.AW
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5CHAPTER
BONDS, BOND VALUATION, AND
INTEREST RATES
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(Part A) Topics In Chapter:
Who Issues Bonds?
Key Characteristics Of Bonds.
Bond Valuation.
Changes In Bond Values Over Time.
Bonds With Semiannual Coupons.
The Pre-Tax Cost Of Debt:
Determinants Of Market Interest
Rates.
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(Part B) Topics In Chapter:
The Real Risk-Free Rate Of Interest.
The Inflation Premium(IP).
The Nominal, Or Quoted, Risk-Free Rate Of Interest.
The Default Risk Premium(DRP).
The Liquidity Premium(LP).
The Maturity Risk Premium(MRP).
The Term Structure Of Interest Rates.
Financing With Junk Bonds.
Bankruptcy And Reorganization.
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What is a Bond?
A bond is a long-term contract under which
a borrower agrees to make payments of
interest and principal, on specific dates,
to the holders of the bond.
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Classification Of Bonds
i. Treasury Bonds. (Government Bonds)
ii. Corporate Bonds.
iii. Municipal Bonds.
iv. Foreign Bonds.
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Key Characteristics Of Bonds
Par Value:
It is the stated face value of the bond. Generally represents the amount of money the firm borrows and promises to repay on the maturity date.
(Assume $1,000).Copyright © 2011 - S.A.S & S.F.AW
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Key Characteristics Of Bonds
Coupon Payment
The specified number of dollars of
interest paid each period, generally
each six months.
Coupon Interest Rate
The stated annual interest rate on a bond.
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Key Characteristics Of Bonds
Floating Rate BondA bond whose interest rate fluctuates
with shifts in the general level of
interest rates.
Zero Coupon Bond
A bond that pays no annual interest but is sold at
a discount below par, thus providing compensation
to investors in the form of capital appreciation.Copyright © 2011 - S.A.S & S.F.AW
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Key Characteristics Of Bonds
Original Issue Discount Bond(OID)
Any bond originally offered at a
price below its par value.
Payment-In-Kind Bond(PIK)
No cash coupon payments, but pay
coupons consisting of additional bonds,
or a percentage of an additional bond.Copyright © 2011 - S.A.S & S.F.AW
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Key Characteristics Of Bonds
Maturity Date
A specified date on which the par
value of a bond must be repaid.
Original Maturity
The number of years to maturity at
the time a bond is issued.
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Key Characteristics Of Bonds
Call Provision
A provision in a bond contract that
gives the issuer the right to redeem
the bonds under specified terms
prior to the normal maturity date.
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Key Characteristics Of Bonds
Call Provision (Cont.)
The call provision generally states that
the company must pay the bondholders
an amount greater than the par value if
they are called. The additional sum,
which is termed a call premium=(INT/M).
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Example: Call Premium
Suppose the following characteristics of a bond:
Par value = $1,000
Original Maturity = 10 years
Interest Rate = 10%
Solution:
if it were called during the first year, then the call premium would be $100, and $90 during the second year (calculated by reducing the $100, or 10%, premium declining by one-tenth).
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Key Characteristics Of Bonds
Deferred Call & Call Protection
Bonds are often not callable until
several years (generally 5 to 10) after
they are issued. This is known as a
deferred call, and the bonds are said
to have call protection.
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Key Characteristics Of Bonds
Refunding Operation
Using the proceeds of the new issue
to retire the high-rate issue and thus
reduce the firm’s interest expense.
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Key Characteristics Of Bonds
Sinking Funds
Some bonds include a sinking fund provision
that facilitates the orderly retirement of the
bond issue.
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Key Characteristics Of Bonds
Sinking Funds (Cont.)The firm is given the right to administer the
sinking fund in either of two ways:
i. The company can call in for redemption (at par value) a certain percentage of the bonds each year.
ii. The company may buy the required number of bonds on the open market.
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Key Characteristics Of Bonds
Sinking Funds (Cont.)
Note: The firm will choose the least-cost method.
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Key Characteristics Of Bonds
Convertible Bonds
Owners of convertible bonds have the
option to convert the bonds into a fixed
number of shares of common stock.
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Key Characteristics Of Bonds
Warrants
are options that permit the holder to
buy stock at a fixed price.(lower rate)
Income Bond
Is required to pay interest only if earnings
are high enough to cover the interest
expense.(risky)
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Key Characteristics Of Bonds
Indexed Bonds Or Purchasing Power Bonds
The interest payments and maturity
payment rise automatically when the
inflation rate rises.
(TIPS = Treasury Inflation-Protected Securities)
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Bond Markets
Corporate bonds are traded
primarily in electronic/telephone
markets rather than in organized
exchanges. (few players)
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Bond Valuation
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The value of any financial asset
is simply the present value of
the cash flows the asset is
expected to produce.
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Bond Valuation (Cont.)
rd = The bond’s required rate of
return, which is the market
rate of interest for that type of bond.
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Bond Valuation (Cont.)
rd = It is also called the “yield” or“going rate of interest.”
Note that rd is not the coupon interest rate.
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Bond Valuation (Cont.)
N = Number of years before the bond matures.
Note that N declines each year after the bond was issued.
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Bond Valuation (Cont.)
INT = Dollars of interest paid each year = (Coupon rate)*(Par value).= PMT
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Bond Valuation (Cont.)
M = Par, or maturity, value of the bond.
This amount must be paid off at maturity
Often equal to $1,000
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Bond Valuation (Cont.)
Equ. (5-1C)
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VB
Equ. (5-1B)
Equ. (5-1A)
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Example: Solving for the Bond Price
Suppose the following characteristics for MicroDrive Inc.’s Bonds: Par value = $1,000 Original Maturity = 15 years Interest Rate = 10% Find the Bond’s value (price)
Solution:
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VB
= $1,000
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Example: Solving for the Bond Price
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Interest Rate Changes and Bond Prices
An increase in the market interest rate
(rd) will cause the price of an outstanding
bond to fall, whereas a decrease in rates
will cause the bond’s price to rise.
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Example: Solving for the Bond PriceInterest Rate Increase
Suppose the following characteristics for MicroDrive Inc.’s Bonds: Par value = $1,000 Original Maturity = 15 years Interest Rate = 10% 15%Find the Bond’s value (price)
Solution:
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VB
= $707,63
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RESULT No.1
Whenever the going rate of interest rises
above the coupon rate, a fixed-rate bond’s
price will fall below its par value, and it is
called a Discount Bond.
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Example: Solving for the Bond PriceInterest Rate Decrease
Suppose the following characteristics for MicroDrive Inc.’s Bonds: Par value = $1,000 Original Maturity = 15 years Interest Rate = 10% 5%Find the Bond’s value (price)
Solution:
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VB
= $1,518.98
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RESULT No.2
Whenever the going interest rate falls
below the coupon rate, a fixed-rate
bond’s price will rise above its par value,
and it is called a Premium Bond.
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Changes In Bond Values Over Time
A bond that has just been issued is
known as a New Issue.
Once the bond has been on the market for a
while, it is classified as an Outstanding Bond,
also called a Seasoned Issue.
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Changes In Bond Values Over Time(Cont.)
Suppose the following characteristics for MicroDrive Inc.’s Bonds: Par value = $1,000 Original Maturity = 15 years Interest Rate = 10%
what would the value of the bond be 1 year after it was issued for the following cases?
i. Interest rate is constant i.e. = 10%ii. Interest rate decreases 5% i.e. = 5%iii. Interest rate increases 5% i.e. = 15%
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Case No. 1:
Interest rate is constant i.e. rd= 10%
Changes In Bond Values Over Time(Cont.)
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VB
= $1,000
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Case No. 2:
Interest rate Decreases 5% i.e. rd = 5%
Changes In Bond Values Over Time(Cont.)
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VB
= $1,494.93
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Case No. 3:
Interest rate Increases 5% i.e. rd = 15%
Changes In Bond Values Over Time(Cont.)
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VB
= $ 713.78
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Case No. 2: Current Yield & Capital Gains Yield
Interest rate Decreases 5% i.e. rd= 5%
Interest, Or Current, Yield = $100/$1,494.93 = 0.0669 = 6.69%
Capital gains yield = -$25.25/$1,494.93 = -0.0169 = -1.69%
Total rate of return, or yield = $74.75/$1,494.93 = 0.0500 = 5.00%
Changes In Bond Values Over Time(Cont.)
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Case No. 3: Current Yield & Capital Gains Yield
Interest rate Increases 5% i.e. rd= 15%
Interest, Or Current, Yield = $100 / $713.78 = 0.1401 = 14.01%
Capital gains yield = $7.06 / $713.78 = 0.0099 = 0.99%
Total rate of return, or yield = $107.06/$713.78 = 0.1500 = 15.00%
Changes In Bond Values Over Time(Cont.)
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Changes In Bond Values Over Time(Cont.)
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Bonds With SemiAnnual Coupons
Although some bonds pay interest
annually, the vast majority actually
pay interest semiannually.
To evaluate semiannual payment
bonds, we must modify the
valuation model as follows:
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Bonds With SemiAnnual Coupons (Cont.)
i. Divide the annual coupon interest payment by 2 to determine the dollars of interest paid every 6 months.
ii. Multiply the years to maturity, N, by 2 to determine the number of semiannual periods.
iii. Divide the nominal (quoted) interest rate, rd, by 2 to determine the periodic (semiannual) interest rate.
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EQUATION (5-2)
Bonds With SemiAnnual Coupons (Cont.)
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Example: Solving for Semiannual Bond Price
Suppose the following characteristics for MicroDrive Inc.’s Bonds: Par value = $1,000 Original Maturity = 15 years Interest Rate = 5% Find the Semiannial Bond’s value (price)
Solution:
VB =
=
= $ 1,523.26 > $ 1,518.98 for 15 periods previously calculated
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Unlike the coupon interest rate, which is fixed,
the bond’s yield varies from day to day
depending on current market conditions.
The yield can be calculated in three different
ways, and three “answers” can be obtained.
Bond Yields
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What rate of interest would you earn on your investment
if you bought the bond and held it to maturity?
This rate is called the bond’s yield to maturity (YTM).
The yield to maturity is usually the same as the
market rate of interest, rd.
i. Yield To Maturity (YTM)
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i. Yield To Maturity (YTM)
Bond Price =
To find the YTM for a bond with annual interest
payments, Equation 5-1 should be solved for rd.
EQUATION (5-3A)
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i. Yield To Maturity (YTM)
Bond Price =
To find the YTM for a bond with Semiannual interest payments, Equation 5-2 should be
solved for rd.
EQUATION (5-3B)
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If current interest rates are well below an
outstanding bond’s coupon rate, then a callable
bond is likely to be called, and investors will
estimate its expected rate of return as the yield
to call (YTC) rather than as the yield to maturity.
To calculate the YTC, solve this equation for rd
ii. Yield To Call (YTC)
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To calculate the YTC, solve this equation for rd
Here N is the number of years until the company can call
the bond, rd is the YTC, and “Call price” is the price the
company must pay in order to call the bond (it is often set
equal to the par value plus 1 year’s interest).
ii. Yield To Call (YTC)
Price Of Callable Bond
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=EQU. (5-4)
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The current yield is the annual interest payment
divided by the bond’s current price.
For example, if MicroDrive’s bonds with a 10% coupon were currently selling at $985, then the bond’s current
yield would be:
$100/$985 = 0.1015 = 10.15%
iii. Current Yield
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The relation between current yield, capital
gains yield (which can be negative for a
capital loss), and the yield to maturity:
Current Yield + Capital Gains Yield = Yield to Maturity.
iii. Current Yield (Cont.)
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THE END
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OF PART 1