When an individual buys a bond, he is lending his money to the issuer of the bond. The issuer of the bond, also known as the writer, borrows this money, with the promise to return it at the end of a specified time period. Additionally, interest payments are made to the lender, or purchaser of the bond, periodically over the time the bond is held. The amount of money that is lent, or the bond price, is equal to the present value of the lump sum that will be returned at the end of the bond’s holding period plus the present value of the annuity payments that the bond holder will receive as interest.
When bonds were first issued they were pieces of paper with a larger upper portion known by various names including, the “balloon payment”, “zero” and “face”.
For the purpose of this discussion, we will refer to the upper portion of the bond as the
“face”. In figure 19.c.1, the face is the orange portion of the bond. The lower portion of the bond, shown in figure 19.c.1 as the block of turquoise cells, represents the coupons that are redeemed, one per year, for an annuity payment in the dollar amount printed on the individual coupon.
IOU $100 in 10 years
Signed,
Borrower (writer)
$5 $5 $5 $5 $5 $5
Coupons- tear off one each year, take it to the borrower and redeem it to receive the annuity payment
Figure 19.c.1
The above illustration can help us to visualize how to calculate the price of a bond. The price of a bond consists of the present value of the lump sum, or orange “face” shown in the above diagram, added to the present value of the annuity payments, which represent bond interest and are shown as the turquoise coupons in illustration 19.c.1. For the purposes of our example, we assume an annual interest rate, R, of 5% and that there are
10 periods, N, over which interest payments are made. We calculate the bond price by

summing the present value of the lump sum, or “face” and the present value of the annuity payments.
The present value of the face is found using the formula for the present value of a lump sum, B, due at the end of N periods:
PV=B/(1+R)^N in this case PV=100/(1.05)^10
Note that the interest rate, R=5% is shown as a fraction of 100, expressed in decimal form, R=.05
The present value of the annuity payments, or coupons is found using the formula for the present value of an annuity payment:
PV=B/(1+R)+B/(1+R)^2+B/(1+R)^3+……B/(1+R)^N in this case
PV=5/(1.05)+5/(1.05)^2+5/(1.05)^3+…..+5/(1.05)^9+5/(1.05)^10
The number of terms in the above equation is equal to the number of periods, N, over which the annuity payment is made, thus the number of terms to be added together vary with each annuity payment depending on the number of periods of the annuity.
The face value of the bond is the sum of these two present value calculations,
1) The present value of the top, or lump sum, and
2) The present value of the coupons, or annuity payments, representing interest
Thus if you know the selling price of the bond, you can calculate the present value of the coupons, by subtracting the present value of the face, from the selling price of the bond.
For the bond in illustration 19.c.1, this is shown by the equation:
PV of coupons= $100-100/(1.05)^10
$100 is the selling price of the bond, and 100/(1.05)^10 is the present value of the bond’s face
Coupon Stripping
A bond can be broken up into its face and coupons and sold to separate individuals with different investment needs. This process is known as “slicing” bonds or “tranching”.
“Trance” is a French word that means, “trench” or “slice.” There are two types of investments that result from slicing bonds:
1) Zero Coupon Bond= This investment returns a lump sum plus interest at the end of a specified number of periods. This type of investment would appeal to a parent with a child that will attend college in the future.
2) Coupons= This investment pays a fixed annuity each year. This type of investment would appeal to a retiree who wants a steady income in the immediate future.

1)What is the formula for the present value of the face of a bond?
2)What is the formula for the present value of the coupons of a bond?
3) If you know the selling price of a bond, how can you determine the present value of the coupons without actually using the formula for the present value of an annuity?
4) What is coupon stripping?
5) What type of investor would benefit from the return received on a zero-coupon bond?
6) What type of investor would benefit from the return received on a coupons only bond?
Answers:
1) PV=B/(1+R)^N
2) PV=B/(1+R)+B/(1+R)^2+B/(1+R)^3+…..+B/(1+R)^N
3) You can subtract the present value of the face from the selling price of the bond
4) Coupon stripping is dividing the bond up into its face and coupon segments and selling each segment to different investors
5) An investor who wants to receive a large lump sum payment to help finance an expected future expense (ie. College)
6) An investor who wants a steady stream of income right now