Bond valuation is the determination of the fair price of a bond

1. Corporate Finance
Bond Valuation – Session 2

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.”

3. Types of Financial Instruments

Treasury Bonds

Corporate Bonds or TFC

Treasury Bills

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

5. 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

6. 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

7. 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.

8. Bond Valuation
Bond Value = VB = INT + INT + … + INT + M
(1+Kd) ⁿ (1+Kd) ⁿ
(1+Kd)¹ (1+Kd)²
[
or
]
1
PV = C 1 − r (1+ r ) n + (1FV) n
r
+r

9. Bond Valuation






N=3
Kd = 12%
INT = 10
M or FV = 100
Find out Bond value.
Semi annual coupon.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. 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

17. Coupon Rate Relationship to Yield-toMaturity

The relationship between the coupon rate and the bond’s yieldto-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
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CHAPTER 6 – Bond Valuation and
Interest Rates

18. Other Types of Bonds/Debt Instruments

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:
P Bill
T
6 - 19
Where:
P = market price of the T Bill
F
=
F = face value of the T Bill
n
BEY = the bond equivalent yield
1 + BEY  ÷
n = the number of days until maturity
B
B = the annual basis (365 days in
Pakistan)
CHAPTER 6 – Bond Valuation and
Interest Rates

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?
6 - 20
CHAPTER 6 – Bond Valuation and
Interest Rates

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
6 - 21 CHAPTER 6 – Bond
Valuation and Interest

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%?
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CHAPTER 6 – Bond Valuation and
Interest Rates