The Mathematics of Money

264 Chapter 6 Investments

Example 6.2.1 On May 25, 2007, Zarofi re Systems issued a $1,000 par value bond

with an 8% coupon rate and a May 25, 2019, maturity date. Interest will be paid

semiannually. What payments will the owner of this bond receive?

The owner of this bond will receive the par value, $1,000, on the maturity date of May 25,

2019. Interest payments will be made semiannually, on November 25 and May 25 of each
      year until maturity. The amount of the interest payments will be:

I 
 PRT

I 
 ($1,000)(0.08)(1/2)

I 
 $40

When a bond is issued, the par value and coupon rate are set in advance. The amount that the

issuer will receive for each bond is not. In an ideal situation (from a mathematical point of

view at least), each bond would sell for its par value, so that the coupon rate would be equal

to the actual interest rate. When this happens, we say that the bond is sold at par. This seldom

actually happens though. If the market decides that the bond’s issuer is a good credit risk (there

is not much concern that the issuer will be able to actually make the promised payments) and

the coupon rate is attractive, buyers may be willing to pay more than the par value for the bond.

We say then that the bond sells at a premium. On the other hand, if the issuer is not considered

quite so good a risk and the coupon rate is not so attractive, the issuer may not be able to sell

the bond for its full par value. In that case, we say that the bond sells at a discount.

Example 6.2.2 Suppose that Zarofi re Systems is fi nancially sound and the consensus

of the investment community is that the company’s prospects are excellent. Right

now, investors can earn around a 7% rate of return by buying bonds with similar

maturities issued by similarly sound companies. Would you expect Zarofi re’s bonds (from

Example 6.2.1) to sell at par, at a premium, or at a discount?

If you buy the bond at par, you will earn an 8% rate of return when comparable investments

pay only 7%. Since Zarofi re’s bonds offer a better deal, investors would be thrilled to be able

to buy these bonds at par, but in the open market they will almost certainly sell at a premium.

If you aren’t willing to pay more than par, someone else will, and for obvious reasons the

company will sell its bonds to whoever is willing to pay them the most.

Current Yield and Bond Tables

The current yield of a bond is the interest rate that the bond pays as a percent of the current

market price.

Example 6.2.3 Suppose that one of the May 25, 2019, 8% Zarofi re Systems bonds

sells for $1,094. What is the current yield?

We have already determined that the interest payments are $40 semiannually. Calculating

this as a rate based on the selling price gives:

I 
 PRT

$40 
 ($1,094)(R)(1/2)

R 
 7.31%

While the par value and the coupon rate are set when the bond is issued, the amount the

bond will sell for both initially and in any subsequent sales will be determined by the open

market. The selling price of a bond can change from day to day, or minute to minute, as

market conditions change. Suppose that some time goes by, and you want to know what

has happened to the price of your Zarofire Systems bond. The current market selling prices

of bonds can be found in some newspaper’s financial pages, on the Internet, and also from

a stockbroker (brokerage offices normally handle bond transactions as well as stocks). A

typical quote might look something like this:

CORPORATE BONDS

Company Coupon Maturity Current Yield $ Volume (000s) Last Price

Zarofi re Systems 8.000 5/25/19 7.235 25,073 110.573