The Mathematics of Money

Bonds and Sinking Funds

When a company issues bonds, it takes on the obligation to make the promised pay-

ments. The ongoing interest payments are actually a comparatively small part of these

obligations. Looming ahead at the maturity date is the obligation to pay off the bond’s par

value.

Good planning requires the bond issuer to be preparing for the bond’s redemption over

the course of its term. As we discussed in Chapter 4, setting up a sinking fund is a reason-

able way to build up the funds needed. Sometimes the terms of a bond will require the

issuer to have a sinking fund in place, giving the buyers of the bonds greater confidence

that the redemption value will indeed be paid at maturity, and hopefully therefore allowing

the bonds to be sold at a better price for the issuer.

Example 6.2.9 The City of Summerfi eld issued seven thousand 10-year, $1,000 par

value bonds with a 4.7% semiannual coupon. The city set up a sinking fund into which

it will make semiannual payments to accumulate the bonds’ redemption value. The

sinking fund earns 4%. How much money does the city need semiannually to meet its

obligations under this bond issue?

Since the city issued 7,000 bonds, the total it will need for redemption is 7,000($1,000) 


$7,000,000. Calculating the sinking fund payment as we did in Chapter 4 gives:

FV = PMT s _n (^) | (^) i
$7, 000 , 000
PMT s__ 20 | (^). 02
$7, 000 , 000
PMT(24.2973698)
PMT
$288, 097
In addition, the city must pay the coupon on these bonds. The coupon payable for each
bond is:
I
PRT
I
($1,000)(0.047)(1/2)
I
$23. 50
The total of all the coupon payments will then be 7,000($23.50)
$164,500. In total, the
city will need $288,097  $164,500
$452,597 semiannually to service this debt.
The amount that an organization needs to pay periodically to cover its debts is sometimes
called its debt service.
EXERCISES 6.2
Copyright © 2008, The McGraw-Hill Companies, Inc.
A. The Language of Bonds

1. The coupon rate for a $1,000 par value bond is 7½%. Find the semiannual interest payment for this bond.


2. The coupon rate for a $5,000 par value bond is 4¾%. Find the semiannual interest payment.


3. An investor paid $9,467 for ten $1,000 par value bonds carrying a 5.25% coupon rate. How much will he receive in
   semiannual interest payments from this investment? How much will he receive at maturity?

Exercises 6.2 269