BOND VALUATION
Lecture 09
“It is a debt agreement in which one party (Borrower) agrees to pay the principle amount and
specific interest to the other party (lender) up till certain point of time period”
Important Terms
1) Face value 2) Coupon Rate 3) Market value
4) Maturity date
6) Yield to Maturity
7) Current yield 8) Discount Rate / Interest Rate 9) Coupon value 10) Fair value
Explanation:
N#1. What if a company sells a piece of paper for $ 1000 and promises to pay the buyer 5% of
face value i.e. $1000 ($50) per year for 3 years & promises to pay whole $1000 at the end of the
3 year?
Here:
Face value is = 1000
Coupon rate is 5%
Coupon Payment= $50
Let’s us suppose company sells it to original buyer for $1000 and original buyer send it to
someone else for another price say $913
1. Is new bond value is $1000 or $913??
Both are bond value: $1000 is face value of bond and it will always remain the same. $913 is
a market value and will change.
2. Now new bond holder will get $50 per year (5% of bond face value) is he still
getting 5%?
No he is not getting 5%
50/913 is 0.0548 = 5.48%
So which one is Coupon rate??
“Remember”
Coupon rate ~ Face value
Prepared by: Usman Ali,
Lecturer Bakhtar University.
Current yield ~ Market value
Page 1
Bond Valuation
It is a technique used for determining the fair value of a particular bond.

Bond valuation includes calculating the present value of the bond's future interest
payments, and the bond's value upon maturity.
Bond Value = PV of coupons + PV of par value
Bond Value = PV of annuity + PV of lump sum

Bond valuation is only one of the factors investors consider in determining whether to
invest in a particular bond.

Other ways to evaluate bond are: the issuing company's creditworthiness, the bond's
price appreciation potential, as determined by the issuing company's growth prospects;
and prevailing market interest rates.

Interest rates increase present values decrease

Interest rates increase, bond prices decrease and vice versa
N#2 If 3 year bond has a face value of $1000 and coupon rate is 5% then that means that you
get $50 per year and will get back $1000.
What is YTM if you buy it in the beginning of the 2nd year (So bond will still have to pay 2 more
coupon payment) for only 913?
1. What is the %profit (Rate of return)?
913 = 50 / (1+ R)1 + 50 / (1+ R)2 + 1000 / (1+ R)2
913 = 50 / (1+ 0.10)1 + 50 / (1+ 0.10)2 + 1000 / (1+ 0.10)2
913 = + 913
10% (Yield to maturity)
______________________________________________
Prepared by: Usman Ali,
Lecturer Bakhtar University.
Page 2
N#3 ABC Company issued a 3 year bond with a $1000 face value and a 5% coupon rate, with
coupons paid once a year at the end of the year and the first coupon has already been paid.
Banks are giving 4% interest rate for deposit. The bond market value is $913. Yield is 10%. What
is the bonds fair value?
Solution
Bond Fair Value =$50 / (1+ 0.04)1 + $50 / (1+ 0.04)2 +$1000 / (1+ 0.04)2
Bond Fair Value =$50 / (1.04)1 + $50 / (1.04)2 +$1000 / (1.04)2
Bond Fair Value = $1018.86
Suppose deposit rate changes from 4% to 6%, Then
Bond Fair Value =$50 / (1+ 0.06)1 + $50 / (1+ 0.06)2 +$1000 / (1+ 0.06)2
Bond Fair Value =$50 / (1.06)1 + $50 / (1.06)2 +$1000 / (1.06)2
Bond Fair Value = $981.67
Numerical #1
Consider a bond with a coupon rate of 10% annual coupons. The par value is $1,000 and the
bond has 5 years to maturity. The yield to maturity is 11%. What is the market value of the
bond?
Solution:
Bond Market Value = PV of annuity + PV of lump sum
Where, PV of Annuity = FV [1-1/ (1+i) n]/i
&
PV of Par value = Face value/ (1+i) n
Bond Market Value = 100[1 – 1/ (1.11)5] / 0.11 + 1,000 / (1.11)5
Bond Market Value = 369.59 + 593.45 = 963.04
Prepared by: Usman Ali,
Lecturer Bakhtar University.
Page 3
Numerical #2 (Assignment)
Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000.
There are 20 years to maturity and the yield to maturity is 8%. What is the fair value of this
bond?
Numerical #3
Global Mills Corporation is selling a new issue of bonds to raise money. The bonds will pay a
coupon rate of 10% and will mature in 6 years. The face value of the bonds is $1,000; interest is
paid semi-annually. The market rate of interest is currently 8% for similar bonds.
a. What is the fair price for an investor to pay for one of these bonds?
b. If you pay the current price of $1,100 for a bond, what will be your yield-to-maturity?
Numerical #4
You have a chance to buy a BB-rated bond that has a face value of $1,000. The bond has a 5%
coupon rate of interest and matures in four years. Interest is paid semi-annually. The market
rate of interest is currently 6% per year for similar bonds.
a. How much should you be willing to pay for the bonds?
b. If you pay the current price of $950 for a bond, what will be your yield-to-maturity?
Prepared by: Usman Ali,
Lecturer Bakhtar University.
Page 4
Prepared by: Usman Ali,
Lecturer Bakhtar University.
Page 5