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Chapter 6 Valuing Bond. The Application of the Present Value Concept. 1. Bond Characteristics. Bond - Security that obligates the issuer to make specified payments to the bondholder. Coupon - The interest payments made to the bondholder. - PowerPoint PPT Presentation
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11
Chapter 6Valuing Bond
The Application of the
Present Value Concept
3
Bond Characteristics
Bond - Security that obligates the issuer to make specified payments to the bondholder.
Coupon - The interest payments made to the bondholder.
Face Value - (Par Value, Principal or Maturity Value) - Payment at the maturity of the bond.
Coupon Rate - Annual interest payment as a percentage of face value.
4
Bond Characteristics
A bond also has (legal) rights attached to it: If the borrower doesn’t make the required
payments, bondholders can force bankruptcy proceedings
In the event of bankruptcy, bond holders get paid before equity holders
5
An Example of A Bond
Example A coupon bond that pays coupon of 5% annually, with
a face value of $1000, has a discount rate of 2.15% and matures in three years.
The coupon payment is $50 annually In the third year, the bondholder is supposed to get $50
coupon payment plus the face value of $1000. The discount rate is different from the coupon rate.
6
Bond Cash Flows
7
Coupon Rate vs. Discount Rate
WARNINGWARNINGThe coupon rate IS NOT the discount rate used in the Present Value calculations.
The coupon rate merely tells us what cash flow the bond will produce.
Since the coupon rate is listed as a %, this misconception is quite common.
8
Bond Pricing – Zero Coupon Bonds
Example
How much is a 10-yr zero coupon bond worth today if the face value is $1,000 and the effective annual rate is 8% ?
P0=1000/1.0810=$463.2 present value of the face value paid at the maturity Zero coupon bonds are also called zeros or
stripped bonds.
9
Bond Pricing – Coupon Bonds
The price of a coupon bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
10
Bond Pricing
Example
What is the price of a 5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.
95.081,1$
)0215.1(
050,1$
)0215.1(
50$
)0215.1(
50$321
PV
PV
11
Bond Pricing
Another way to think of bond pricing
PV = PV (coupons) + PV (face value)
$1,081.95$938.18$143.77PV
(1.0215)
1$1,000
215)0.0215(1.0
1
0.0215
1$50PV
33
PV of An Annuity
Financial calculator: n=3, i=2.15, PMT=50, FV= 1,000 PV=(-)1,081.95
12
Bond Pricing
Example
What is the price of the 5% coupon bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?
13
Bond Pricing
Example
What is the price of the 5% coupon bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?
37.082,1$
)01075.1(
025,1
)01075.1(
25
)01075.1(
25
)01075.1(
25
)01075.1(
25
)01075.1(
25654321
PV
PV
Financial calculator: n=6, i=1.075, PMT=25, FV= 1,000 PV=(-)1,082.37
14
Interest Rates and Bond Prices
Example
What is the price of the 5% annual coupon bond if the required rate of return is 5 %?
000,1$
)05.1(
050,1
)05.1(
50
)05.1(
50321
PV
PV
Financial calculator: n=3, i=5, PMT=50, FV= 1,000 PV=(-)1,000
15
Interest Rates and Bond Prices
Example (continued)
What is the price of the bond if the required rate of return is 15 %?
68.771$
)15.1(
050,1
)15.1(
50
)15.1(
50321
PV
PV
Financial calculator: n=3, i=15, PMT=50, FV= 1,000 PV=(-)771.68
16
Interest Rates and Bond Prices
Example (continued)
Q: How do bond prices vary with interest rates? Market interest rate > Coupon rate
Bond price < Face value : discount bond
Market interest rate < Coupon rate Bond price > Face value: premium bond
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Bond Prices Over Time
18
Interest Rates and Bond Prices
19
Interest Rate Risk
20
Bond Yields
Current Yield - Annual coupon payments divided by bond price.
The current yield does not measure the bond’s total rate of return. It overstates the return of premium bonds It understates the return of discount bonds
21
Bond Yields
Yield To Maturity (YTM) - Interest rate for which the present value of the bond’s payments equal the price.
22
Bond Yields
Calculating Yield to Maturity (YTM=r)
If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.
PVcpn
r
cpn
r
cpn par
r t
( ) ( )
....( )
( )1 1 11 2
23
Bond Yields
Example
What is the YTM of a 5% annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95.
1 2 3
50 50 1,050$1081.95
(1 ) (1 ) (1 )
2.15%
r r r
r
Financial calculator: n=3, PV=(-)1,081.95, PMT=50, FV= 1,000 i=2.15
24
Bond Yields
WARNINGWARNINGCalculating YTM by hand can be very tedious.
It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.
25
Bond Yields
Example
In the previous example, what is the YTM if the coupons are paid semiannually?
%082.1
95.081,1$
)1(
025,1
)1(
25
)1(
25
)1(
25
)1(
25
)1(
25654321
r
PV
rrrrrrPV
Financial calculator: n=6, PV=(-)1,081.95, PMT=25, FV=1,000 i=1.082
%18.210.01082)(1 Yield Annual Effective
2.164% 21.082 Maturity) to(Yield Yield Annual Quoted2
26
Bond Yields
Example
A 4-year maturity bond with a 14 percent coupon rate can be bought for $1,200. What is the YTM if the coupon is paid annually? What if it is paid semiannually?
If coupon is paid annually
If coupon is paid semiannually
Financial calculator: n=4, PV=(-)1,200, PMT=140, FV= 1,000 i=7.97
Financial calculator: n=8, PV=(-)1,200, PMT=70, FV= 1,000
i=4.026 per 6 month. It would be reported in the financial press as 8.05 percent annual yield (yield to maturity).
27
Bond Rates of Return
Rate of Return – Total income per period per dollar invested.
Rate of return =total income
investment
Rate of return =Coupon income + price change
investment
28
Bond Rates of Return
Rate of Return versus Yield to Maturity The yield to maturity
defined as the discount rate that equates the bond’s price to the present value of all its promised cash flows.
a measure of the average rate of return you will earn over the bond’s life if you hold it to maturity.
The rate of return can be calculated for any particular holding period
based on the actual income and the capital gain or loss on the bond over that period.
29
Bond Rates of Return
Example
Our 5.5 percent annual coupon bond currently has 3 years left until maturity and sells today for $1,056.03. Its yield to maturity is 3.5 percent. Suppose that by the end of the year (Note: at this time, the bond will have only 2 years to maturity), interest rates have fallen and the bond’s yield to maturity is now only 2.0 percent. What will be the bond’s rate of return?
6.34%or ,0634.003.056,1$
)03.056,1$95.067,1($$55 Return of Rate
95.067,1$)02.1(
055,1$
)02.1(
55$ 2.0%at PV
21
30
Bond Rates of Return
Example (Continued)
Suppose that the bond’s yield to maturity had risen to 5 percent during the year. What will be the bond’s rate of return?
0.78%or ,0078.003.056,1$
)03.056,1$30.009,1($$55 Return of Rate
30.009,1$)05.1(
055,1$
)05.1(
55$ 5%at PV
21
The Yield Curve
Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date.
Yield Curve - Graph of the term structure.
The term structure of interest rates (Yield curve)
YTM for corporate and government bonds
The YTM of corporate bonds is larger than the YTM of government bonds
Why does this occur?
34
Default Risk
Default (or credit) risk The risk that a bond issuer may default on its
bonds.Default premium
The additional yield on a bond investors require for bearing credit risk.
Investment grade bonds Bonds rated Baa or above by Moody’s or BBB or
above by S&P’s.Junk bonds
Bonds with a rating below Baa or BBB
35
Default Risk
StandardMoody' s & Poor's Safety
Aaa AAA The strongest rating; ability to repay interest and principalis very strong.
Aa AA Very strong likelihood that interest and principal will berepaid
A A Strong ability to repay, but some vulnerability to changes incircumstances
Baa BBB Adequate capacity to repay; more vulnerability to changesin economic circumstances
Ba BB Considerable uncertainty about ability to repay.B B Likelihood of interest and principal payments over
sustained periods is questionable.Caa CCC Bonds in the Caa/CCC and Ca/CC classes may already beCa CC in default or in danger of imminent defaultC C C-rated bonds offer little prospect for interest or principal
on the debt ever to be repaid.
36
Default Risk
37
Corporate Bonds
Zero couponsFloating rate bondsConvertible bondsCallable bonds
