Bond Valuation

Corporate Finance
Bond Valuation – Session 2
Bonds – Fixed Income Securities



“ Fixed income securities, promises to pay a stream of
semiannual or annual payments for a given number of
years and then repay the loan amount at the maturity
date.”

Types of Financial Instruments

 Treasury Bonds

 Corporate Bonds or TFC

 Treasury Bills


Key Characteristics of Bonds
 Par Value
 Coupon payment
 Coupon interest rate
 Floating Rate Bond
 Zero coupon bond
 Original issue discount / premium bonds
 Maturity Date

Bond Indenture
 The bond indenture is the contract between the
issuer and the holder. It specifies:

 Details regarding payment terms
 Collateral
 Positive & negative covenants
 Par or face value (usually increments of $1,000)
 Bond pricing – usually shown as the price per $100 of par
value, which is equal to the percentage of the bond’s face
value

Security & Protective Provisions
 Covenants
 Positive covenants – things the firm agrees to do
 Supply periodic financial statements
 Maintain certain ratios

 Negative covenants – things the firm agrees not to do
 Restrictions on the amount of debt the firm can take on
 Prevents the firm from acquiring or disposing of assets

Bond Valuation
 Kd = The bond market rate of interest. Discount to use to
calculate the present value of bond.

 N = The number of years before the bond matures.

 INT = Rupee amount of interest paid annually or semiannually.

 M or FV = the or maturity value of the bond.

Bond Valuation


Bond Value = VB = INT + INT + … + INT + M
(1+Kd)¹ (1+Kd)² (1+Kd) ⁿ (1+Kd) ⁿ

or



| |
n n
r
FV
r r
r
C PV
) 1 ( ) 1 (
1 1
+ +
+ ÷ =
Bond Valuation
 N = 3
 Kd = 12%
 INT = 10
 M or FV = 100
 Find out Bond value.
 Semi annual coupon.


Current Yield
 It is the yield based on bond’s annual coupon
payment.

 It does not reflect the total return on bond.

 It does not reflect the capital gain or loss on bond.
Current Yield
 Current Yield = Annual Coupon Payment
Current Price of Bond

Example: A semi annual bond with a FV = 100, market
price Rs.98 and coupon rate of 9.50%. Compute
current yield.


Yield to Maturity
 The rate of return earned on a bond if it is held till
maturity.
 It is the total rate of return on a bond.
 YTM equals the expected rate of return only if:
1. The probability of default is ZERO.
2. The bond cannot be called.
Yield to Maturity

 YTM approx. = Annual Cpn + (FV – PV ) / N
(FV + PV ) / 2

E.g. N = 10, annual coupon 10%, FV = Rs.100, PV =
Rs.105.
Find out YTM.
Yield to Call
 The rate of return earned on a bond if it is called
before its maturity.

 Can be called if interest rates falls below the bond
coupon rate.

Yield to Call
YTC = Annual Cpn + (Call price – PV ) / N
(Call price + PV ) / 2

E.g. N = 10, FV = 100, PV = 105, Coupon rate = 10%,
Call price = 108, Kd = 5%. The bond can be called
after 5 Years.

Factors Affecting Bond Prices
 There are three factors that affect the price volatility
of a bond

 Yield to maturity

 Time to maturity

 Size of coupon
CHAPTER 6 – Bond Valuation and
Interest Rates
6 - 17
Coupon Rate Relationship to Yield-to-
Maturity
 The relationship between the coupon rate and the bond’s
yield-to-maturity (YTM) determines if the bond will 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
Other Types of Bonds/Debt Instruments
CHAPTER 6 – Bond Valuation and
Interest Rates
6 - 19
Treasury Bills
 Short-term obligations of government with an initial term to
maturity of one year or less
 Issued at a discount & mature at face value
 The difference between the issue price and the face value is
treated as interest income
 To calculate the price of a T bill, use the following formula:

1
T Bill
F
P
n
BEY
B
=
| |
+
|
\ .
Where:
P = market price of the T Bill
F = face value of the T Bill
BEY = the bond equivalent yield
n = the number of days until maturity
B = the annual basis (365 days in
Pakistan)
CHAPTER 6 – Bond Valuation and
Interest Rates
6 - 20
Solving for Yield on a T Bill
 To solve for the yield on a T bill, rearrange the previous
formula and solve for BEY.
 Example: What is the yield on a Rs.100 T-bill with 180 days
to maturity and a market price of Rs.98.20?


CHAPTER 6 – Bond
Valuation and Interest
Rates
6 - 21
Zero Coupon Bonds
 A zero coupon bond is a bond issued at a discount
that matures at par or face value
 A zero coupon bond has no reinvestment rate risk,
since there are no coupons to be reinvested
 To calculate the price of a zero coupon bond, solve
for the PV of the face amount
CHAPTER 6 – Bond Valuation and
Interest Rates
6 - 22
Zero Coupon Bonds
 Example: What is the market price of a Rs.100 zero
coupon bond with 25 years to maturity that is currently
yielding 14%?