Unformatted text preview: Bond Valuation
Bond What are they worth?
What
Suppose you were promised the following
Suppose
cash flow: $100 in one year, $100 in two
years, $100 in three years, and $1000 in
three years.
three
s What would these be worth to you if you
What
discounted them at 10%? At 12%?
discounted
s Characteristics of Bonds
Characteristics
• Bonds pay fixed coupon (interest)
Bonds
coupon
payments at fixed intervals (usually
every 6 months) and pay the par value
par
at maturity.
maturity
$I
0 $I
1 $I $I
2 $I
... $I+$M
n example: AT&T 10s of 2007
example:
s par value = $1000
$1000
s coupon = 10% of par value per year.
10% =$100 per year (use annual payments).
=$100
s maturity = 3 years.
years.
s issued by AT&T.
$100
$100
0 $100 1 2 $100+$1000
3 Security Valuation
Security
KNOW THIS!!!!
s In general, the value of any asset = the present
value
value of the stream of expected cash
value
flows discounted at an appropriate
required rate of return.
required Bond Valuation
Bond
s Simply discount the cash flows at the
Simply investor’s required rate of return.
investor’s
1) the coupon payment stream (an annuity).
1)
(an
2) the par value payment (a single sum).
2)
(a Bond Valuation
Bond
n Vb = Σ t=1 $I
(1 + k b ) t $M
+
n
(1 + kb) $I = the coupon interest payment.
the
s kb = the investor’s required rate of return
(which depends on the riskiness of the bond).
(which
s Vb = the value of the bond.
the
s Bond Valuation
Bond
n Vb = Σ t=1 $I
(1 + kb) t + $M
n
(1 + kb) Vb = $I (PVIFA i, n) + $M (PVIF i, n) So, what is the ATT bond
worth?
worth?
s Recall, par = $1000, coupon
Recall, rate = 10%, and maturity = 3
years.
years.
s Suppose investors require a
Suppose
10% rate of return? 12%?
10%
s Value = ????? WITH THE FINANCIAL
CALCULATOR
CALCULATOR
s
s s
s Bonds are a “5 find 4” game
Enter the 4 things you know, and solve for the
Enter
fifth.
fifth.
Pmt = 100, FV = 1000, I/Yr = 12, N = 3
Solve for PV = 951.96 s Tip: enter PV as a negative.
s Q: Are you going to have ugly grandchildren?
Q: THERE ARE 2 KINDS OF
BOND QUESTIONS
BOND
s Questions 1: Given the discount rate,
find the market price
find s Question 2: Given the market price, find
the discount rate (aka “Yield to
Maturity”)
Maturity”) Yield To Maturity
Yield
s The average annual rate of return
The investors expect to receive on a bond
if they hold it to maturity.
if Yield To Maturity
Yield
s The average annual rate of return
The investors expect to receive on a bond
if they hold it to maturity.
if Vb = $I (PVIFA i, n) + $M (PVIF i, n)
$I
n)
Just solving for i !!! YTM Example
YTM
Suppose we paid $898.90 for a $1,000
Suppose
par 10% coupon bond with 8 years
to maturity and semiannual
coupon payments.
coupon
What is our yield to maturity? Using the Financial Calculator
Using
P/YR = 1
P/YR
Mode = end
N = 16 (huh?)
PV = 898.90
PMT = 50 (why?)
PMT is an
This ant
port
im
ide!!
sl Types of Bonds
Types
s Debentures  unsecured bonds.
unsecured
s Subordinated debentures  unsecured “junior” debt.
“junior”
s Mortgage bonds  secured bonds.
secured
s Zeros  bonds that pay only par value at
maturity; no coupons.
maturity;
s Junk bonds  speculative or belowspeculative
investment grade bonds; rated BB and
investment
below.
below. Types of Bonds
Types
s Eurobonds  bonds denominated in one currency and sold in another country.
(Borrowing overseas).
(Borrowing
s example  suppose Disney decides to sell
$1,000 bonds in France. These are U.S.D.
denominated bonds trading in a foreign
country. Why do this?
country.
s If borrowing rates are lower (very unlikely),
s To avoid SEC regulations. Convertibility
Convertibility
s Some bonds may be converted to common stock.
common
s Is this a benefit to the investor?
Yes!
Yes! The Bond Indenture
The
s The bond contract.
s Lists all of the bond’s features: coupon, par value, maturity, etc.
etc.
s Lists covenants which are
covenants
designed to protect bondholders.
designed
s Describes repayment provisions. Bond Example
Bond
s S’pose our firm decides to issue 20year
S’pose
20year bonds with a par value of $1,000 and
$1,000
annual coupon payments. The return
on other bonds of similar risk is
currently 12%, so we decide to offer a
12% coupon interest rate.
12%
s What would be a fair price for these
What bonds?
bonds? 120
120
0 120 120 ... 1000
120 1 2 3 ... 20 P/YR = 1
N = 20
I%YR = 12
FV = 1,000
PMT = 120
Solve PV = $1,000 Point: If the coupon rate = discount
Point
coupon
discount
rate, the bond will sell for par value.
rate the
par s Suppose interest rates fall immediately
Suppose interest after we issue the bonds. The required
return on bonds of similar risk drops
to 10%.
10%.
s What would happen to the bond
What price?
price? P/YR = 1
Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
FV
Solve PV = Solve
$1,170.27
Point: If the coupon rate > discount rate, the
Point
coupon
discount
the
bond will sell for a premium.
premium s Suppose interest rates rise immediately
Suppose interest after we issue the bonds. The required
return on bonds of similar risk rises to
14%.
14%.
s What would happen to the bond price? P/YR = 1
Mode = end
N = 20
I%YR = 14
PMT = 120discount
Point: If the coupon rate < discount rate, the
coupon
the
FV discount
bond will sell for a discount.
FV = 1000 Prices vs. Yields
Prices
s Big point: There is an inverse
relationship between prices and yields. If interest increase, the price of
If
existing bonds will fall
existing
s If interest rates fall, the price of
If
existing bonds will increase
existing
s Remember the pencil trick
s Zero Coupon Bonds
Zero
No coupon interest payments.
No
The bond holder’s return is
determined entirely by the
price discount.
price Zero Example
Zero
Suppose you pay $508 for a zeroSuppose
$508
coupon bond that has 10 years left to
coupon
10
maturity. What is your YTM?
maturity. Zero Example
Zero
Suppose you pay $508 for a bond that
Suppose
has 10 years left to maturity. What
is your yield to maturity? This is
just a lumpsum problem.
just
$508
0 $1000
10 Zero Example
Zero
P/YR = 1
Mode = End
N = 10
PV = 508
FV = 1000
Solve: I/YR = 7%
Solve:
7% Duration
Duration
s Two factors influence price
Two
sensitivity
sensitivity
– Longer maturity = greater sensitivity
– Lower coupon = greater sensitivity Duration captures both effects
s Literally, a weighted average time to
Literally,
maturity
maturity
s More details in lab
s The Financial Pages:
The
Corporate Bonds
Bonds Cur
Yld Vol Close Net
Chg Eckerd 9 1/4 04
Eckerd 8.6 20 107 1/2 ... What is Eckerd’s yield to maturity (today=00)?
s P/YR = 1, N = 8 (4years x 2 pay/yr),
P/YR
(4years
s FV = 1000, PV = $1,075,
FV 1000 PV $1,075
s PMT = 46.25
PMT
46.25
Solve: I/YR = 7.06% (I.e., 3.5324 x 2)
Solve:
7.06% The Financial Pages:
The
Corporate Bonds
Bonds AlldC zr 09
AlldC Cur
Yld ... Vol Close 30 43 5/8 Net
Chg +2 What is Allied Chemical’s yield to maturity?
s P/YR = 1, N = 9, FV = 1000, PV = $436.25,
P/YR
FV 1000 PV $436.25
s PMT = 0
PMT
s Solve: I/YR = 9.655%
Solve:
9.655% The Financial Pages:
The
Treasury Bonds
Maturity
Rate Mo/Yr
Bid
Asked
Rate
9
Nov 18 128:18 128:24 Chg
+13 Ask
Ask
Yld
Yld
6.43 What is the yield to maturity of this Treasury
What
bond? (note: tbonds are traded in 32nds)
bond?
s P/YR = 2, N = 40, FV = 1000, PMT = 45,
P/YR
40 FV 1000 PMT 45
PV =  1,287.50 (128.75% of par)
1,287.50
s s Solve:
Solve: I/YR = 6.43%
6.43% ...
View
Full
Document
This note was uploaded on 03/06/2012 for the course BUS M 201 taught by Professor Mcgregor during the Fall '11 term at BYU.
 Fall '11
 McGregor
 Valuation

Click to edit the document details