Bonds Valuation and Interest Rates - Premium or Discount Bonds

Imagine you borrow $10,000 now at a rate of 12% interest annually, for the next 30 years. You will therefore pay 0.12 x $10,000 = $1200 per year for the next 30 years. At the end of the 30 years, you will also pay back the original $10,000 (principal amount). What is the total amount you have paid?

$1200 per year x 30 years = $36000 (interest payments)
$10,000 (original principal)
Total payments = $36,000 + $10,000 = $46,000

This sounds like a pretty simple example right? Yep, bonds are simple debt financing activities, however they have a rich blend of terminology that you must learn (in order to become a successful financial manager).

1) Coupons: In the above example, the $1200 a year payments you must make are also known as "coupons." They are the annual interest payments made on a bond.
Note: Payments can be monthly, quarterly, semi-annually or annually, depending on how the interest terms are set out.

2) Face Value: In the above example, the $10,000 that must be repaid back at the end of the 30 years is known as the "Face Value" of the bond. It is the original price at which the bond was issued.

3) Coupon Rate: In the above example, the interest rate was 12% annually. Therefore, this 12% is known as the "Coupon Rate." It is the pre-determined interest rate on the bond. It can also be determined by diving 1200 / 1000 = 12%

4) Maturity Date: The total # of years until the original principal (face value) is repaid back is called the "Maturity Date". Therefore, the above bond example has a maturity of 30 years.

5) Yield-to-Maturity (YTM): The yield to maturity is the interest rate that brings a bond's original value, principal payments and interest payments into equilibrium. It is the prevailing market interest rate (subject to economic conditions and government policies).

Bond Terminology

Bonds can be sold either at Par, Discount or Premium.

	Discount	PAR	Premium
Price of Bond	Sold for less than face value	Sold for equal to face value	Sold for more than face value
Investor Requirement	Higher return than coupon rate	Equal to coupon rate	Less return than coupon rate

i) Bonds sold at Discount

For example, consider a bond selling in 2005 for $10,000 with an annual coupon payment of $1000. What is the coupon rate? $1000 / 10,000 = 10%

Now suppose that in 2006, the same bond yields only 8% interest payments annually. What is the coupon payment? 8% x 10,000 = $800 per year.

Which one would you prefer buying? At 10% coupon rate or 8% coupon rate? Since the value of the bond (cash flows produced) has depreciated from $1000 per year to only $800 per year, this bond will have to be sold at a cheaper price (or at DISCOUNT).

ii) Bonds sold at Premium

For example, consider a bond selling in 2005 for $10,000 with an annual coupon payment of $1000. What is the coupon rate? $1000 / 10,000 = 10%

Now suppose that in 2006, the same bond yields an insane 15% in interest payments annually. What is the coupon payment? 15% x 10,000 = $1500 per year.

Which one would you prefer buying? At 10% coupon rate or 15% coupon rate? Since the value of the bond (cash flows produced) has appreciated (gone up) from $1000 per year to a huge $1500 per year, this bond will have to be sold at a PREMIUM price (higher than its original value).

iii) Bonds sold at Par

For example, consider a bond selling for $10,000 with an annual coupon payment of $1000. Similar type of bonds are also offering interest payments of $1000 a year. What is the coupon rate?

The coupon rate in this case is $1000 / $10,000 = 10%. Since similar bonds are also offering a 10% interest rate, this bond is sold at the original price of $10,000 (at Par).

Discount (Less than Original)	Premium (More than Original)
Bonds sold at 97.5 of Face Value =	Bonds sold at 101.5 of Face Value =
Bond Price = $1000 Sold at 97.5 = 0.975 x $1000 Discounted Bond Price = $975	Bond Price = $1000 Sold at 101.5 = 1.015 x $1000 Premium Bond Price = $1015

Bond Valuation using Financial Analyst BAII Plus Calculator:

To perform bond calculations, we will use the above mentioned calculator. Here are the calculator keys we will use:

N = # of Years x Interest Payment Periods
I/Y = Market Rate of Return (Investor's Yield)
PV = (+) Cash Received by issuing firm NOW (Discount, Par or Premium)
PMT = (-) Interest payment by company to investors each period
FV = (-) Face value to be repaid back to Investors
P/Y = # of Interest Payments per Year
C/Y = # of Interest Payments per Year