20a. Bond Markets
Bonds are notes payable (notes that will be repaid in the future or rather at its maturity) that bear
interest during the life of the bond. Typically, bonds are viewed to be safe investments because of its
predictable and steady stream of payments (interest). The key difference between stocks and bonds is that
when stock is purchased, the stockholder is receiving a percentage of the company they have invested in.
In other words, stockholders, depending on the proportion of their investment or the shares they have
bought, has a percentage of company ownership and therefore, a certain level of involvement and
participation in the company. Another key difference is that bonds have a maturity date whereas stocks do
not. Purchasing a bond is simply a form of lending money and receives no such type of ownership as when
purchasing stock.
Market Value of Bonds
One of the most important factors in the bond market is the simple topic of determining the price
of a bond. For example, an individual who has 5,000 dollars might be interested in investing their money,
and in investing their money, they would be able to earn interest from their investment for a decided
number of years at which at the maturity of the bond are also repaid. In doing so, this individual would be
able to earn more money then they initially started with. Thus, the idea here is in answering the question of
how much one must invest today (with a given interest rate) in order to earn a desired amount x years from
now, or rather, what is the present value of the desired amount x years from now. Deriving the present
value is equivalent to finding the price of a bond which is possible through a method called discounting.
Discounting basically requires two steps:
1) Find the present value (PV) of a single sum.
PV of single sum = (FV)/(1+i) n
{PV = present value; FV = future amount desired or also called the future value; i is the
given interest rate and n is the number of periods (such as the number of years the life of
a bond is) }
2) Find the present value (PV) of an ordinary annuity.
PV of ordinary annuity = (pymt) (1+i) n / i
{pymt = the payment, or rather the interest amount one receives}
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Add the value of steps one and two (PV of single + PV of ordinary annuity) to find
the value of a bond.
It is necessary to find the present value of a single sum and an ordinary annuity because you are receiving
interest annually, semiannually or whatever the agreement is. Likewise, you are also receiving a sum of
money in the future as well.
There two similar yet different types of interest, the contractual interest rate and the market
interest rate, which are important factors to consider when selling bonds. The contractual interest rate is
the interest the borrower must pay and the interest the lender receives, or more simply, it is the interest rate
stated on a bond whereas the market interest rate is “the investors demand for loaning funds”. Therefore,
bonds can either be sold at a premium, face value, or discount. For example, if the market interest rate is
at 15 percent and the contractual interest rate on a bond is 12 percent, the bond would be sold at a discount
because the contractual interest is lower than the market rate, the value of the bond goes down. One would
pay a value less the than the face value of the bond. Likewise, with the same market rate but now with a
contractual interest rate of 18 percent, the bond would be sold at premium since the higher contractual
interest rate makes the value of the bond worth more, or rather compensates for the difference in the
different interest rates. Thus, when the market rate and contractual interest rate are equivalent, the bond
would be sold at its face value. Mathematically, the total discount is derived by subtracting the selling
price from the face value of the bond.
Discount = face value – selling price
Likewise, the total premium is derived by subtracting the face value of the bond from the selling market
price of the bond.
Premium = selling price – face value
Sample Bond Certificate
* In this sample, you can see that the contractual interest rate is 7 5/8 with a face value of $10,000. We can
also see that the issuer of the bonds is Phillips Petroleum Company and the lender is the person whose
signature appears at the bottom of the certificate.
Questions
1) What is a key difference between stocks and bonds?
2) How do you find the price of a bond?
3) Given an interest rate of 5% that pays once a year for 10 years, and it is given that the face value
of a bond is $50,000, calculate mathematically the market value of that bond?
4) What is the difference and importance between the contractual interest rate and market interest
rate?
5) If the market rate is 10% and the contractual interest rate is 12%, would the bond be sold for a
discount or a premium?
6) If the market rate is 50% and the contractual interest rate is 49%, would the bond be sold for a
discount or a premium?
Answers
1) Bonds basically have a maturity date in which money is due whereas stocks do not hold any maturity
date.
2) Price of a bond = PV of a single sum + PV of an ordinary annuity
3) PV of single sum = (50000)/ (1.05)10 = 30695.66
PV of ordinary annuity = (2500) [1-(1.05)/0.05] = 19304.34
30695.66 + 19304.34 = 50,000
4) The contractual interest rate is the interest the borrower must pay and the interest the lender receives,
or more simply it is the interest rate stated on a bond (as in the 7 5/8 interest rate on the sample bond
certificate above), and the market rate is the interest rate investors are demanding. These two interest
rates are what determine whether or not a bond is sold at discount or a premium.
5) PREMIUM
6) DISCOUNT