Emgt 452 Advanced Financial Management

1
Emgt 452 Advanced Financial Management

• Chapter 9
• Bonds and their Valuation

2
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 holders of the
bond.
3
Types of Bonds

• 1. Treasury bonds
• Corporate bonds
• Municipal bonds
• Foreign bonds

4
Key Features of a Bond
1. Par value Face amount paid at maturity.
Assume 1,000. 2. Coupon interest rate Stated
interest rate. Multiply by par value to get
dollars of interest. Generally fixed.
(More)
5
Key Features of a Bond
3. Maturity Years until bond must be repaid.
Declines. 4. Issue date Date when bond was
issued. 5. Default risk Risk that issuer will
not make interest or principal payments.
6
How does adding a call provision affect a bond?

• Issuer can refund if rates decline. That helps
  the issuer but hurts the investor.
• Therefore, borrowers are willing to pay more, and
  lenders require more, on callable bonds.
• Most bonds have a deferred call and a declining
  call premium.

7
Whats a sinking fund?

• Provision to pay off a loan over its life rather
  than all at maturity.
• Similar to amortization on a term loan.
• Reduces risk to investor, shortens average
  maturity.
• But not good for investors if rates decline after
  issuance.

8
Sinking funds are generally handledin 2 ways
1. Call x at par per year for sinking fund
purposes. 2. Buy bonds on open market. Company
would call if kd is below the coupon rate and
bond sells at a premium. Use open market
purchase if kd is above coupon rate and bond
sells at a discount.
9
Financial Asset Valuation
k
...
CF
CF
CF
1
n
2



PV

.
.
.

.
(
)
(
)
(
)
1
2
n
1

k
1

k
1
k

10

• The discount rate (ki) is the opportunity cost of
  capital, i.e., the rate that could be earned on
  alternative investments of equal risk.

ki k IP LP MRP DRP
for debt securities.
11
Whats the value of a 10-year, 10 coupon bond if
kd 10?
10
...
100 1,000
100
100
V ?
100
1
,
000
100
V

.
.
.




B
1
10
10
(
)
(
)
(
)
k
k
1
1
1
k



d
d
d
90.91 . . . 38.55 385.54
1,000.
12
The bond consists of a 10-year, 10 annuity of
100/year plus a 1,000 lump sum at t 10
INPUTS
10 10 100 1000 N I/YR PV
PMT FV -1,000
OUTPUT
13
What would happen if expected inflation rose by
3, causing k 13?
INPUTS
10 13 100 1000 N I/YR PV
PMT FV -837.21
OUTPUT
When kd rises, above the coupon rate, the bonds
value falls below par, so it sells at a discount.
14
What would happen if inflation fell, and kd
declined to 7?
INPUTS
10 7 100 1000 N I/YR PV
PMT FV -1,210.71
OUTPUT
If coupon rate gt kd, price rises above par, and
bond sells at a premium.
15
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?
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Bond Value ()
kd 7.
1,372
1,211
kd 10.
M
1,000
837
kd 13.
775
30 25 20 15 10 5 0
Years remaining to Maturity
17

• 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 kd remains constant.

18
Bond Yields

• Yield to Maturity
• Yield to Call
• Current Yield

19
Whats yield to maturity?

• YTM is the rate of return earned on a bond held
  to maturity. Also called promised yield.
• YTM equals expected rate of return (assumes the
  probability of default is zero and the bond
  cannot be called

20
Whats the YTM on a 10-year, 9 annual coupon,
1,000 par value bond that sells for 887?
0
1
9
10
kd?
...
90
90
90
1,000
PV1 . . . PV10 PVM
Find kd that works!
887
21
Find kd
INT
M
INT
...
V




B
(
)
(
)
(
)
N
N
1
k
k
1
1
1

k


d
d
d
90
1
000
90
,
...
887





(
)
(
)
(
)
1
10
10
1
1
k
k
1

k


d
d
d
INPUTS
10 -887 90 1000 N I/YR
PV PMT FV 10.91
OUTPUT
22

• If coupon rate lt kd, bond sells at a discount.
• If coupon rate kd, bond sells at its par value.
• If coupon rate gt kd, bond sells at a premium.
• If kd rises, price falls.
• Price par at maturity.

23
Find YTM if price were 1,134.20.
INPUTS
10 -1134.2 90
1000 N I/YR PV PMT FV 7.08
OUTPUT
Sells at a premium. Because coupon 9 gt kd
7.08, bonds value gt par.
24
What is Yield to call?

• If the bond has a call provision, the yield to
  call is more appropriate
• The yield to call is the rate of return earned on
  a bond held to the time when it can be called

25
What is Current Yield ?

• Current yield is the annual interest payment
  divided by the bonds current price

26
Definitions
Annual coupon pmt Current price
Current yield Capital gains yield
YTM
Change in price Beginning price
Exp total return
Exp Curr yld
Exp cap gains yld
27
Find current yield and capital gains yield for a
9, 10-year bond when the bond sells for 887 and
YTM 10.91.
90 887
Current yield 0.1015 10.15.
28
YTM Current yield Capital gains yield. Cap
gains yield YTM - Current yield 10.91
- 10.15 0.76.
Could also find values in Years 1 and 2, get
difference, and divide by value in Year 1. Same
answer.
29
Whats interest rate (or price) risk? Does a
1-year or 10-year 10 bond have more risk?
Interest rate risk Rising kd causes bonds
price to fall.
kd
1-year
Change
10-year
Change
5
1,048
1,386
4.8
38.6
10
1,000
1,000
4.4
25.1
15
956
749
30
Value
10-year
1,500
1-year
1,000
500
kd
0
0
5
10
15
31
Semiannual Bonds
The vast majority of bonds pay interest
semi-annually
32
Semiannual Bonds
1. Multiply years by 2 to get periods
2n. 2. Divide nominal rate by 2 to get periodic
rate kd/2. 3.Divide annual INT by 2 to get
PMT INT/2.
INPUTS
2n kd/2 OK INT/2 OK N I/YR
PV PMT FV
OUTPUT
33
Find the value of 10-year, 10 coupon, semiannual
bond if kd 13.
2(10) 13/2 100/2 20 6.5
50 1000 N I/YR PV
PMT FV -834.72
INPUTS
OUTPUT
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• In general, if a bond sells at a premium, then
  (1) coupon gt kd, so (2) a call is likely.
• So, expect to earn
• YTC on premium bonds.
• YTM on par discount bonds.

35
Bond Ratings Provide One Measureof Default Risk
Investment Grade
Junk Bonds
Moodys
Aaa
Aa
A
Baa
Ba
B
Caa
C
SP
AAA
AA
A
BBB
BB
B
CCC
D
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What factors affect default risk and bond
ratings?

• Financial performance
• Debt ratio
• Current ratios

37
Bond Provisions

• Provisions in the bond contract
• Secured versus unsecured debt
• Senior versus subordinated debt
• Guarantee provisions
• Sinking fund provisions
• Debt maturity