Junior Philippine Institute of Accountants and Auditors – United
Financial Markets
Bond Valuation
Bonds
2 Main Components of Bonds
o Coupon – periodic receipts of cash
o Par Value - Lump sum payment of face value
(stated amount in bond)
Example. HAU issued a 3-year bond with Face
value 10,000 PHP which has a coupon rate at 8%
paid annually. Investors require a 6% yield to
maturity.
This is because a bond is basically an instrument
where the issuer will pay
1. Periodic Cash Flow
2. Lump-sum at the end of the bond’s life.
Difference between Coupon Rate and YTM
Components (Given)
Coupon Rate – Percentage used in determining
- Coupon Rate = 8%
- Coupon = 800 PHP per year payment (10,000 X
8%)
- Par Value (Face Value) = 10,000 PHP Paid at the
end of the Bond’s Life.
the Coupon.
Yield to Maturity – The required market interest
rate.
Let’s further break down the formula for Bond
- YTM (yield to maturity) = 6%
Value.
2 Distinct Components
1. Annuity (coupon) – Periodic payments
2. Lump-sum component – Paid at the end of the
bond’s life.
Case with solving for the PV of a bond (Bond
Coupon = Face Value X Coupon Rate /
Value)
compounding rate (if stated in the problem)
r = Yield to Maturity
c = Compounding rate
Annually = 1
Semi-annually = 2
As you can see the Formula for Bond Valuation is
Quarterly = 4
a combination of PV for Annuity and PV for Lumpsum payments.
Monthly = 12
Face Value = Par Value
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Junior Philippine Institute of Accountants and Auditors – United
Financial Markets
To further Illustrate let’s use the same example a
while ago.
HAU issued a 3-year bond with Face value 10,000
PHP which has a coupon rate at 8% paid annually.
Example 3.
Investors require a 6% yield to maturity.
Carolina issued a bond with a 10% coupon rate
Coupon = 10,000 X 8% / 1 = 800
paid Semi-annually, with a Face value of 7,000.
r = 6%
The bond matures in 5 years. If the required yield
c=1
is 12%, what is the bond value of the said bond?
Face value = 10,000
Given:
After listing the given, we can now solve for bond
Coupon = 7,000 X 10% / 2 = 350
value.
r = 12%
c=2
Face Value = 7,000
Let’s see the difference if the bond was
compounded quarterly
Example 2. Compounded Quarterly
Current Yield
HAU issued a 3-year bond with Face value 10,000
Current yield is the bond’s annual coupon
PHP which has a coupon rate at 8% paid
divided by its price.
quarterly. Investors require a 6% yield to
maturity.
Example 4. (using Example 3)
Coupon = 10,000 X 8% / 4 = 200
r = 6%
c=4
= 10.79
Face value = 10,000
•
Make sure that the annual coupon is used.
After listing the given, we can now solve for bond
In the problem the Annual coupon is paid
value.
Semi-annually, as such 350 * 2 = 700
annual coupon
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Junior Philippine Institute of Accountants and Auditors – United
Financial Markets
Approximate YTM
Variables
R = Nominal Rate
A formula used when solving for the YTM for a
r = Real rate
bond
h = Inflation rate
1 + 𝑅 = (1 + 𝑟) 𝑋 (1 + ℎ)
Example 6.
Example 5. Approx YTM
Interest rates If an investor required a 10% real
Find the approximate YTM of a bond with a face
rate of return, and the inflation rate is 8% what is
value of P1,000 and pays P100 coupon payment.
the approximate nominal rate?
1 + 𝑅 = (1 +. 10) 𝑋 (1 +. 08)1 + 𝑅 = 1. 188R
It sells at 105 and will mature in 4 years
Given:
Coupon = 100
Par value = 1,000
Bond value = 1,050 (105 in the problem means
the bond can be sold at 105% of its face value)
105% X 1000 = 1,050
t=4
c=1
Real Rate vs Nominal Rate
Real Rate – Interest rate that has been adjusted
for inflation.
Nominal Rate - Interest rate that has not been
adjusted for inflation.
The Fisher Effect - The relationship among
nominal returns, real returns, and inflation.
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