Bonds and Bond Valuations

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Bonds and Bond Valuations

Shivam Gupta
Financial Sector Research
June 8, 2014

1 Introduction
Corporations and municipal governments use bonds to borrow money from the
public. In this research, we will define a bond, how to value a bond, and the effect of
interest rates on bonds. Since this research is brief, we have not covered all possible
material related to bonds; however, we have laid the foundation for future inquiries
and subsequent research projects on the topic

2 Definition
A bond is a debt security where an investor (public) will loan money to a borrower
(corporation or government). Typically, a bond is an interest-only loan, meaning that
the borrower will pay interest on the loan every period. If the bond is held until
maturity (when the term for the loan expires), then the face value, which is the original
investment for the bond, will be paid out to the investor. As we will see, if the bond

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is sold earlier then maturity, then the value of the bond fluctuates based on
marketplace interest rates.

3 Valuation of a Bond
When valuing a bond, we must take into consideration two distinct parts: the face
value portion and the bond’s coupons. Let’s look at an example. Kabra Corporation
issues a $5000 bond with 20 years to maturity and a coupon rate of 10%. Thus, the
bond will pay an annual coupon of $500 and in 20 years, Kabra Corporation will pay
the holder of the bond $5000. In order to value the bond, we must calculate the
present value of the bond.
PV= FV
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!

= 5000
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= $743.22
The present value of $5000 paid after 20 years at a 10% interest rate is $743.22. Now,
we must calculate the present value of the coupons.
Annuity Present Value= C * (
!!!!!!!
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!
)
= 500 * (
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!!
)
= $4256.78
Total Value of Bond= $4256.78 + $743.22 = $5000
If the interest rate matches the coupon rate (10%), then the value the bond sells for
is equal to the face value the investor receives at the end of maturity.
4 Effects of Fluctuating Market Interest Rates
Let’s assume the scenario above, but pretend that after one year the interest rate
rises to 15%. We now have 19 years until maturity and a higher interest rate.
PV= FV
!
!!!!!
!

=5000
!
!!!!!"!
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=$817.54

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The present value of $5000 paid after 19 years at a 10% interest rate is $817.54. Now
we look at the coupons.
Annuity Present Value= C * (
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)
= 500 * (
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)
= $3099.12
Total Value of Bond= $3099.12 + $817.54 = $3916.66
When the interest rate rises above the coupon rate, Kabra bond sells for less than its
face value. In this case, the bond sells for $3916.66. Investors are less willing to
invest money in a security that returns 10% when they can get a return of 15%
elsewhere. Thus, the discount bond makes up for this by offering a bond for a cheaper
price and having a built-in profit ($5000-$3916.66=$1083.64). Subsequently, when
interest rates go below coupon rates, premium bonds sell at an excess amount
compared to face value because investors wish to take advantage of the favorable
coupon rate.

5 Generalized Equation for Bond Value
Bond Value= C * (
!!!!!!!
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!
) + FV
!
!!!!!
!