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Bond Valuation and InterestRates
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 2
The Basic Structure of Bonds
What is a bond?
a bond is any debt instrument that promises a
fixed income stream to the holder Fixed income securities are often classified
according to maturity, as follows:
Less than one yearBills or Paper
1 year < Maturity < 7 yearsNotes
< 7 yearsBonds
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 3
The Basic Structure of Bonds
A typical bond has the followingcharacteristics:
A fixed face or par value, paid to the holder of the
bond, at maturity A fixed coupon, which specifies the interest payable
over the life of the bond Coupons are usually paid either annually or semi-annually
A fixed maturity date
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 4
Bond indenture - the contract between theissuer of the bond and the investors who hold it
The market price of a bond is equal to the
present value of the payments promised by thebond
The Basic Structure of Bonds
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 5
The Basic Structure of BondsCash Flow Pattern for a Traditional Coupon-Paying Bond
0 1 2 3 n
I I I I I
F
FIGURE 6-1
I = interest payments, and F = principal repayment
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 6
Cash Flow Pattern of a Bond
The Purchase Price or Market Price of a bond is simply the present
value of the cash inflows, discounted at the bonds yield-to-maturity
0 2 3 4 n1
Coupon Coupon Coupon Coupon Coupon +
Face Value
Purchase
Price
Cash Inflows
to the Investor
Cash Outflows
to the Investor
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 7
Term-to-maturitythe time remaining to thebonds maturity date
Coupon ratethe annual percentage interestpaid on the bonds face value; to calculate the
dollar value of the annual coupon, multiply thecoupon rate by the face value If the coupon is paid twice a year, divide the annual
coupon by two
Example: A $1,000 bond with an 8% coupon rate willhave an $80 coupon if paid annually or a $40 couponif paid semi-annually
The Basic Structure of Bonds
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 8
Bond Valuation
The value of a bond is a function of:
Par value
Term to maturity Coupon rate
Investors required rate of return (discount rate is also
known as the bonds yield to maturity)
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 9
Bond Valuation: Example
What is the market price of 15-years,$1,000 bond with a 10% coupon, if the
bonds yield-to-maturity is 10%?
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 10
Bond ValueGeneral Formula
[ 6-1]
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Bond ValueGeneral Formula
VB= 100* 7.6061 + 1000* 0.2394 = 760.61+ 239.4= 784.55 $
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6 - 13
Bond ValueGeneral Formula
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Bond ValueGeneral Formula
1- INT= 1000 *8%= 80$N= 19 yearsM= 1000Kd= 6%VB= 80/(1+6%) + 1000 /(1+6%)VB= 80 * 11.1581+ 100 * 0.3305= 1223.148$
19 19
2- INT= 1000 *8%= 80$N= 19 years
M= 1000Kd= 10%VB= 80/(1+10%) + 1000 /(1+10%)VB= 80 * 8.3649+ 100 * 0.1635= 832.692$
19 19
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 15
Factors Affecting Bond PricesBond Price-Yield Curve
Market Yield (%)
FIGURE 6-2
Price($)
When interest rates increase, bond prices fall
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 16
Factors Affecting Bond PricesBond Price-Yield Curve
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 17
Factors Affecting Bond PricesBond Price-Yield Curve
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 18
The relationship between the coupon rate and thebonds yield-to-maturity (YTM) determines if the bondwill sell at a premium, at a discount, or at par
If Then Bond Sells at a:
Coupon < YTM Market < Face Discount
Coupon = YTM Market = Face Par
Coupon > YTM Market > Face Premium
Factors Affecting Bond Prices
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CHAPTER 6 Bond Valuation and Interest Rates6 - 19
Bond Valuation: Semi-Annual Coupons
So far, we have assumed that all bonds haveannual pay coupons. While this is true for manybonds, it is not true for other bond issues, whichhave coupons that are paid semi-annually
To adjust for semi-annual coupons, we mustmake three changes:
Size of the coupon payment (divide by 2)
Number of periods (multiply by 2) Yield-to-maturity (divide by 2)
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 20
For example, suppose you want to value a 5-years, $10,000 Government ofCanada bond with a 4% coupon, paid twice a year, given a YTM of 6%.
INT /2=( 10000 *4%)/2= 400/2= 200$N * 2=5 * 2=10M= 10000
Kd /2= 6% /2= 3%
VB= 200/(1+3%) + 10000 /(1+3%)VB= 200 * 8.5302+ 10000 * 0.7441 = 9147.04$
10 10
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 21
Factors Affecting Bond Prices
There are three factors that affect the pricevolatility of a bond
Yield to maturity
Time to maturity Size of coupon
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 22
Bond Yields
Yield-to-maturity (YTM)the discount rate usedto evaluate bonds
The yield earned by a bond investor who: Purchases the bond at the current market price Held the bond to maturity
Reinvested all of the coupons at the YTM
Is the bonds Internal Rate of Return (IRR)
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 24
Factors Affecting Bond PricesPrice and Yield: 25 Year Bond, 10% Coupon
Price/Yield Relationship
0
50
100
150
200
250
300
350
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Percent YTM
P
rice
per$100
ofFa
ce
Value
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 25
Factors Affecting Bond Prices
Time to maturity
Long bonds have greater price volatility than shortbonds
The longer the bond, the longer the period for which thecash flows are fixed
Size of coupon
Low coupon bonds have greater price volatility
than high coupon bonds High coupons act like a stabilizing device, since a greater
proportion of the bonds total cash flows occur closer to
today & are therefore less affected by a change in YTM
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 26
Interest Rate Risk & Duration
The sensitivity of bond prices to changes ininterest rates is a measure of the bondsinterest rate risk
A bonds interest rate risk is affected by: Yield to maturity
Term to maturity
Size of coupon
These three factors are all captured in onenumber called duration
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CHAPTER 6 Bond Valuation and Interest Rates 6 - 27
Duration
Duration is a measure of interest rate risk
The higher the duration, the more sensitive thebond is to changes in interest rates
A bonds duration will be higher if its: YTM is lower
Term to maturity is longer
Coupon is lower
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Bond ValueGeneral Formula
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Bond ValueGeneral Formula