Download Bonds

Chapter 4
Bond Valuation
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1
Key Features of a Bond





Par value: Face amount; paid at maturity. Assume
$1,000.
Coupon interest rate: Stated interest rate. Multiply
by par value to get dollars of interest. Generally
fixed.
Maturity: Years until bond must be repaid. Declines.
Issue date: Date when bond was issued.
Default risk: Risk that issuer will not make interest or
principal payments.
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2
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 higher returns, on callable bonds.
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3
Value of a 10-year, 10% coupon bond if
rd = 10%
0
1
2
10%
V=?
VB =
10
...
100
$100
100
$100
100 + 1,000
$1,000
.
.
.
+
+
+
1
N
(1 + rd)
(1 + rd)
(1 + rd)N
= $90.91 +
= $1,000.
. . . + $38.55 + $385.54
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4
The bond consists of a 10-year, 10%
annuity of $100/year plus a $1,000 lump
sum at t = 10:
PV annuity
PV maturity value
Value of bond
INPUTS
OUTPUT
10
N
10
I/YR
= $ 614.46
=
385.54
= $1,000.00
PV
-1,000
100
PMT
1000
FV
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
5
What would happen if expected inflation
rose by 3%, causing r = 13%?
INPUTS
OUTPUT
10
N
13
I/YR
PV
-837.21
100
PMT
1000
FV
When rd rises, above the coupon rate, the
bond’s value falls below par, so it sells at
a discount.
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6
What would happen if inflation fell, and rd
declined to 7%?
INPUTS
OUTPUT
10
N
7
I/YR
PV
-1,210.71
100
PMT
1000
FV
If coupon rate > rd, price rises above par,
and bond sells at a premium.
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7
Bond Value ($) vs. Years remaining to
Maturity


Suppose the bond was issued 20 years ago and now
has 10 years to maturity. What would happen to its
value over time if the required rate of return
remained at 10%, or at 13%, or at 7%?
See next slide.
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8
Bond Value ($) vs. Years remaining to
Maturity
1,372
1,211
rd = 7%.
rd = 10%.
1,000
M
837
rd = 13%.
775
30
25
20
15
10
5
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0
9




At maturity, the value of any bond must equal its par
value.
The value of a premium bond would decrease to
$1,000.
The value of a discount bond would increase to
$1,000.
A par bond stays at $1,000 if rd remains constant.
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10
What’s “yield to maturity”?


YTM is the rate of return earned on a bond held to
maturity. Also called “promised yield.”
It assumes the bond will not default.
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11
YTM on a 10-year, 9% annual coupon,
$1,000 par value bond selling for $887
0
rd=?
1
10
...
90
PV1
.
.
.
PV10
PVM
9
90
90
1,000
887
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12
Find rd
VB =
INT
INT
M
... +
+
+
N
1
(1 + rd)
(1 + rd)
(1 + rd)N
1,000
90
90
...
887 =
+
+
+
1
N
(1 + rd)
(1 + rd) (1 + rd)N
INPUTS
OUTPUT
10
N
I/YR
10.91
-887
PV
90
PMT
1000
FV
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
13
Coupon Rate vs. Yield to Maturity





If coupon rate < rd, bond sells at a discount.
If coupon rate = rd, bond sells at its par value.
If coupon rate > rd, bond sells at a premium.
If rd rises, price falls.
Price = par at maturity.
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14
Find YTM if price were $1,134.20.
INPUTS 10
N
OUTPUT
I/YR
7.08
-1134.2 90
PV
PMT
1000
FV
Sells at a premium.
Because coupon = 9% > rd = 7.08%
bond’s value > par.
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15
Definitions
Current yield =
Annual coupon pmt
Current price
Capital gains yield =
Exp total
return
Change in price
Beginning price
Exp
Exp cap
= YTM =
+
Curr yld
gains yld
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16
9% coupon, 10-year bond, P = $887, and
YTM = 10.91%
Current yield
$90
= $887
= 0.1015 = 10.15%.
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17
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 10.15%
= 0.76%.
Could also find values (prices) in Years 1 and 2, get
difference, and divide by value in Year 1. Same answer.
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18
Semiannual Bonds
1. Multiply years by 2 to get periods = 2N.
2. Divide nominal rate by 2 to get periodic
rate = rd/2.
3. Divide annual INT by 2 to get PMT = INT/2.
INPUTS
2N
N
rd/2
I/YR
OK
PV
INT/2
PMT
OK
FV
OUTPUT
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19
Value of 10-year, 10% coupon,
semiannual bond if rd = 13%.
2(10)
INPUTS
20
N
OUTPUT
13/2
6.5
I/YR
PV
-834.72
100/2
50
PMT
1000
FV
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20
Callable Bonds and Yield to Call

A 10-year, 10% semiannual coupon,
$1,000 par value bond is selling for
$1,135.90 with an 8% yield to maturity.
It can be called after 5 years at $1,050.
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21
Nominal Yield to Call (YTC)=?
INPUTS 10
N
OUTPUT
-1135.9 50
I/YR
PV
PMT
3.765 x 2 = 7.53%
1050
FV
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22
If you bought bonds, would you be more
likely to earn YTM or YTC?



Coupon rate = 10% vs. YTC = rd = 7.53%. Could
raise money by selling new bonds which pay 7.53%.
Could thus replace bonds which pay $100/year with
bonds that pay only $75.30/year.
Investors should expect a call, hence YTC = 7.5%,
not YTM = 8%.
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23
rd = r* + IP + DRP + LP + MRP.
Here:
rd
r*
IP
DRP
LP
MRP
= Required rate of return on a debt
security.
=
=
=
=
=
Real risk-free rate.
Inflation premium.
Default risk premium.
Liquidity premium.
Maturity risk premium.
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24
Estimating IP


Treasury Inflation-Protected Securities (TIPS) are
indexed to inflation.
The IP for a particular length maturity can be
approximated as the difference between the yield on
a non-indexed Treasury security of that maturity
minus the yield on a TIPS of that maturity.
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25
Bond Spreads, the DRP, and the LP

A “bond spread” is often calculated as the difference
between a corporate bond’s yield and a Treasury
security’s yield of the same maturity. Therefore:


Spread = DRP + LP.
Bond’s of large, strong companies often have very
small LPs. Bond’s of small companies often have LPs
as high as 2%.
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26
Bond Ratings
S&P and Fitch
Moody’s
% defaulting within:
1 yr.
5 yrs.
Investment grade bonds:
AAA
Aaa
0.00
0.00
AA
Aa
0.03
0.19
A
A
0.08
0.76
BBB
Baa
0.20
2.45
BB
Ba
1.05
6.91
B
B
2.02
10.52
CCC
Caa
24.88
36.84
Junk bonds:
© 2016Fitch
Cengage Ratings
Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as
Source:
permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
27
Bond Ratings and Bond Spreads
(December
2013)
Long-term Bonds
10-Year T-bond
AAA
AA
A
BBB
BB
B
CCC
Yield (%)
2.87
3.65
3.65
3.87
4.81
5.87
6.26
7.40
Spread (%)
0.78
0.78
1.00
1.94
3.00
3.39
4.53
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28
Interest rate (or price) risk for
1-year and 10-year 10% bonds
Interest rate risk:
Rising rd causes bond prices to fall
1-Year
rd
Price
Change
5.0% $1,048
4.8%
10.0% $1,000
4.5%
15.0% $957
10-Year
Price
Change
$1,386
38.6%
$1,000
33.5%
$749
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29
What is reinvestment rate risk?


The risk that CFs will have to be reinvested in the
future at lower rates, reducing income.
Illustration: Suppose you just won $500,000 playing
the lottery. You’ll invest the money and live off the
interest. You buy a 1-year bond with a YTM of 10%.
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30
What is reinvestment rate risk?


Year 1 income = $50,000. At year-end get back
$500,000 to reinvest.
If rates fall to 3%, income will drop from $50,000 to
$15,000. Had you bought 30-year bonds, income
would have remained constant.
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31
The Maturity Risk Premium




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!
Yields on longer term bonds usually are greater than
on shorter term bonds, so the MRP is more affected
by interest rate risk than by reinvestment rate risk.
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32
Term Structure Yield Curve


Term structure of interest rates: the relationship
between interest rates (or yields) and maturities.
A graph of the term structure is called the yield
curve.
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33
Hypothetical Treasury Yield Curve
14%
Interest Rate
12%
10%
MRP
IP
r*
8%
6%
4%
2%
19
17
15
13
11
9
7
5
3
1
0%
Years to Maturity
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34
Bankruptcy

Two main chapters of Federal Bankruptcy Act:



Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company (stock holders) wants Chapter 11,
creditors may prefer Chapter 7.
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35
Bankruptcy


If company can’t meet its obligations, it files under
Chapter 11. That stops creditors from foreclosing,
taking assets, and shutting down the business.
Company has 120 days to file a reorganization plan.


Court appoints a “trustee” to supervise reorganization.
Management usually stays in control.
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36
Assignment


Review slides of chapter 7 from FINC3131
Chapter 4 problems: 1,2,3,4,5,6,7,8,9,10,11,12,13,16
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permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
37