19C. Bonds and Bond Pricing

19c. Bonds and Bond Pricing

When we think about investments (in layman’s terms), the two types of investments that often come to mind are stocks and bonds. These two types of investments, though often lumped together, are very different. While the stock market is based on the buying and selling of ownership of a company, the bond market is based on the buying and selling of owed debt. When a bond is written and issued, the issuer, or writer, is writing an IOU to some lender. The way the issuer of a bond attracts a lender and the reason a lender wants to lend is because bonds pay interest. The issuer is borrowing money now and promising to pay back more money in the future.

Why would a company or government or university choose to issue bonds? Well, bonds allow the issuer of the bond to borrow money or capital now and pay later. In this way, the government can use money now to fund a new program or a corporation can finance their new project and use later profits to pay back the bonds.

There are many types of bonds. Most pay interest periodically and then the principal, the amount borrowed, at maturity, the date upon which the writer of the bond must pay back the principal.

Bonds can vary based whether or not they are backed by collateral. Secured bonds are bonds “secured” with assets as collateral, meaning if the issuer cannot pay for the bonds, the issuer’s promised assets will be used. These assets can be land or real estate or other items of value. Unsecured bonds are not backed by anything but the general reputation and good credit of the borrower.

Bonds can also differ based on how they mature. Term bonds are paid back on a single appointed date while serial bonds are paid back in installments.

How corporations treat ownership of their bonds can differ. Until recently, most bonds were bearer bonds. This meant whoever had the bond in their possession could receive the interest payment by tearing off a coupon and exchanging the coupon from the bond for the interest payment from the corporation. Today, most bonds are registered bonds. If a corporation issues a bond to a specific owner, this is a registered bond. This means the corporation has on record the owner of the bond and sends him or her the interest payments.

The first step in the bond market is issuing the bonds. The number of bonds, the principal and interest rate must all be decided. The principal and interest rate of the bond will not change once the bonds are printed and these are what determine the amount beyond the principal the lender will receive. Then the bonds are sold.

Once on the market, the bond’s worth fluctuates with changing interest rates, but never will the printed interest rate or principal change. The interest will always be the same amount paid on the payment dates and the principal will always be the same amount paid at the end. So if the interest rates change, how does the value of the bond change if the printed values never change? The amount paid to acquire the bond that pays a specific interest rate on a specific principal changes with fluctuations in the bond market. For example, if today’s interest rate is higher than the printed rate, the person who wants to buy that bond will pay less than its printed worth to acquire it.

Let’s say that you have printed bonds worth $1000 in ten years that pay an interest rate of 10%. The market rate is now 9%. Will people pay more or less than the printed value for bonds with a 10% interest rate? More because your bonds pay a better rate than the market. What if the market rate was 12%? Then people would pay less than the printed value of the bond because they can get a better deal elsewhere unless the bond price is lowered.

The percentage of the printed value that the bond is worth right now is quoted as the bond price. For example, a $1000 bond with a quoted price of 103 is worth 103% of its printed value of $1000 or $1030. Bonds are traded like stocks on national securities exchanges but these markets do not affect the relationship between the corporation and its bonds. The corporation will pay only the printed interest rate and the stated principal that are on the face of the bond, making it the people selling and trading and buying in the bond market after the initial issuing to the first owner that pay these fluctuating bond prices. As you can see in Figure 19c.2., the market price of a 2 year bond for $1000 on this particular day in the market was $1000.63. ($1000 @ 100.0625 % = $1000 x 1.000625).

So how is the price of the bond determined? The type of bond will affect this answer and the method used to acquire it. In all the cases, the driving idea is that money today does not equal the same amount tomorrow. The concept of present value and future value is used to determine the price of a bond as it is an exchange of money today for money tomorrow + interest. The present value of a bond is that price which must be lent today at a given interest rate in order to yield a specified amount at the end of a specific period of time. This present value of a bond is its price. What affects this bond price? The future value or amount to be paid upon maturation, the period over which the money will be borrowed, and the current market interest rate demanded for the lending of funds by lenders all affect the price of a bond. When you start from a future value of a bond and determine its present value in today’s market, it is called discounting a bond.

Historical Method

Historically, bonds were bearer bonds, those that had coupons on the bottom which were torn off to receive interest payments. To determine the present value of the bonds, one had to consider the worth of the interest payments and the principal, or the final sum to be paid.

As above in Figure 19c.3, if the interest rate is 5% and the principal is $1000, then the interest paid annually will be $50. This means that each year the interest paid will be 5% of $1000 or $50. So the bearer of the bond can turn in the $50 coupons each year for his or her $50 and then the other half, the IOU at the end of ten years for his or her principal of $1000. This involved complicated calculations requiring tables to determine bond prices.

Historical Bond Pricing r = 5%

Present

B = $1000 Principal

$50 $50 $50 $50 $50 $50 $50 $50 $50 $50 Interest Payments

Bond Price Today = present value (PV) of principal ( B ) + PV of interest payments

= B/(1+r)n + [B/(1+r)1 + B/(1+r)2 + … + B/(1+r)n ]

Coupon Stripping

In the 1980’s, technology such as computers and high powered calculators made bond pricing and present value calculations much easier. The Saloman Brothers created what is called “coupon stripping.” The idea was that one could separate the coupons from the principal in order to please more lenders. Some people were only interested in the steady stream of interest payments found with the coupons, such as retired people, and others were much more interested in the long term receipt of the principal, so a “zero-coupon” or zero bond, which often attract parents investing in college funds. These slices of the bond became known as “tranches” which is French for “slice.” For example, the 4th tranche on a 30 year mortgage bond is the interest payments for years 16 through 30. This is a very risky type of bond investment because it is the part of the bond that is affected by many years of interest so that a small shift in the interest rates has a large effect on the price of this bond:

PV = B/(1+r)n

While looking at this formula for the interest payment, it is obvious that a large shift in n will affect the PV greatly because the larger n gets, the more it will affect the equation. If something is multiplied to the 18th power, that quickly becomes a large number! If interest rates increase even a little, the bond price will go down a lot, and if interest rates go down even a little, the bond price will go up very quickly. This makes sense if we think back to what a bond price means. Since a bond already has a printed interest rate and a printed principal, these amounts will not change. So if a bond has an interest rate higher than the market rate, one must pay extra for the bond to get the better interest rate. On the other hand, if the bond has a lower interest rate than the market, no one will want it unless they pay less to get it. So apply this logic to the 4th tranche case, a change in the interest rate multiplied exponentially can cause a big change in bond price! So the moral here is that 4th tranche is very sensitive to changes in the interest rates!

USEFUL BOND PRICING FORMULAS:

Lump sum over n periods:

For example, will pay $1000 in ten years (Generally the principal)

Bond Price = PV = B/(1+r)n

Perpetuity (forever):

For example, will pay $30 annually forever for bond bought for $1000.

Bond Price = PV = B/R

Annuity over n periods:

For example, will pay $100 each year for 30 years. (Generally interest payments)

Bond Price = PV = B/(1+r)1 + B/(1+r)2 + … + B/(1+r)n

PRACTICE QUESTIONS:

#1) A bond will pay $500 in 10 years and is quoted at 97 today. What is its bond price?

#2) A bond is issued with a printed value of $1000 to be paid in three years and will pay an interest of 10% annually. What will its interest payments be?

#3) A $100 bond is issued and will mature in 5 years. The market interest rate is 5%. What is the bond price?

#4) If a bond promises to pay $10 dollars a year forever if you buy the bond for a printed value of $500, how much is the interest rate?

#5) A mortgage bond promises to pay $10000 dollars a year for 3 years. The interest rate is 5 %. How much is borrowed/lent today?

Ch 19.c.

Hilary Spalding Econ101 Summer 03