The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

To be able to read this table, you need to be aware of certain assumptions. The coupon rate

and current yield are understood to be percents, even though they are often printed without

a % sign. The Volume column indicates the dollar amount of trading of this particular bond

that has taken place in the last day; this can be taken as an indication of how liquid this

bond is, or in other words how easy it would be to find a seller if you want to buy and a

buyer if you want to sell. The Last Price is also a percent; in this case it is a percent of the

par value that the bond is presently selling for.

Example 6.2.4 Based on the quote shown above, what is the current selling price

for one of Zarofi re’s May 25, 2019, 8% coupon bonds?

The bond is selling for 110.573% of par value. So the selling price is:

(110.573%)($1,000) 
 1.10573($1,000) 
 $1,105.73

Yield to Maturity

Based on the quote shown in the table, the current yield of this bond is 7.235%. Remember

that this means that if you buy this bond the semiannual interest payments that you will

receive work out to a 7.235% rate based on the amount you would currently pay for it. It

is easy to misunderstand this to mean that this means that you are earning a 7.235% rate

on your investment. That is not correct! The interest payments work out to 7.235% of the

price paid, but really we can’t entirely overlook the fact that you are paying more than the

par value. You pay $1,105.73 for the bond, but at maturity you will receive only $1,000

for it. We cannot overlook this when assessing the overall rate of return you are earning on

this investment.

The yield to maturity of a bond is a measurement of the actual interest rate that will

be earned, assuming that the bond is held to maturity. Unlike the current yield, the yield

to maturity takes into account the effect of any premium (or discount) to maturity value.

Calculating this by means of a formula is quite complicated, and falls outside the scope

of this book. It should be clear, though, that for the Zarofire Systems bond we have been

using as an example, the yield to maturity would be lower than the current yield. This is

because the current yield does not take into account the $105.73 “loss” between selling

price and par value. Likewise, it should be clear that a bond sold at a discount would have

a higher yield to maturity than current yield, because of the gain between purchase price

and par value.

For our purposes, the most efficient means to calculate the yield to maturity is using a

spreadsheet with guess and check. The following example is provided as an illustration of

how this can be done.

Example 6.2.5 Use a spreadsheet to determine the yield to maturity for the Zarofi re

Systems May 25, 1919, 8% coupon bond from the table given above.

The $1,105.73 selling price should be the present value of the payments that the seller will

receive. So we set up an amortization table. We will use the current yield of 7.235% as our

initial guess; even though we know it is not the yield to maturity, it is a good starting point

to work from. Since the remaining term is 12 years, the table should run to the 24th half

year.

Rows Omitted

26 24 $1,040.00 $40.00 $1,000.00 $105.73

25 23 $40.00 $40.00 $0.00 $1,105.73

1 Rate: 7.235% Initial Balance: $1,105.73

2

3

A B C D

Half Year Payment From Principal Ending Balance

1 $40.00 $0.00 $1,105.73

From Interest

$40.00

4 2 $40.00 $40.00 $0.00 $1,105.73

5 3$000$40 00 $40 00 $1 105 73

E

6.2 Bonds 265