Money, Banking, and International Financegovernment or corporation could sell the bond for a greater market price, reducing the investor’s
return. Higher market price means the bond issuer sold the bond for a premium.
A corporation, for example, has a $1,000 bond that pays interest twice a year. Interest rate
on the bond is 8%, equaling $80 a year or $40 every six months. If the bond matures in two
years, then the present value formula has 4 periods.
Market interest rate currently is 4% a year, or 2% for a payment period. If the market
interest rate drops to 4%, the corporation would not sell this bond at face value because the
corporation would pay a higher interest rate than the market. Consequently, the corporation can
sell this bond for a greater price, reflecting the market interest rate. We calculate the bond
market price in Equation 3 , and it, PV 0 , equals $1,076.15. Therefore, a corporation pays 4%
interest on bonds with an 8% interest coupon rate.
1,076.15
1 0.02
40 1,000
1 0.02
40
1 0.02
40
1 0.02
40
1 2 3 4
PV =$
+
$ +$
+
+
$
+
+
$
+
+
$
PV =
0
0
( 3 )
Market interest rate could swing in the opposite direction. Consequently, the corporations
and governments could sell bonds at a discount if the market interest rate exceeds the bond’s
interest rate. For example, a corporation sells a $1,000 bond that pays 8% interest rate that pays
twice a year. Thus, the corporation pays $80 a year in interest, or $40 every six months.
Furthermore, the bond matures in two years, or 4 periods in the present value formula. If the
market interest rate rises to 12% a year (or 6% for a payment period), an investor would never
buy this bond at face value. They would earn 8% interest year. However, the corporation could
sell this bond for a lower price, compensating the investors for a greater market interest rate. We
calculate the bond market price in Equation 4 , and the bond’s market price, PV 0 , equals
$930.70. Consequently, investors would earn a 12% return on their 8% interest bonds.
930.70
1 0.06
40 1,000
1 0.06
40
1 0.06
40
1 0.06
40
1 2 3 4
PV =$
+
$ +$
+
+
$
+
+
$
+
+
$
PV =
0
0
( 4 )
A government or corporation could issue a bond that never matures, which we call a consul
or perpetuity. Consequently, the bond has no maturity date, but the bondholder receives interest
payments forever. A government or corporation rarely issues these bonds because most people
and government like end dates for loans. However, this bond possesses nice mathematical
properties.
A government, for example, sold a consul that pays $50 interest per year, and the bond
never matures. If the market interest rate equals 8%, then calculate the market price, PV 0 , of this
consul. Since all interest payments are equal, subsequently, all future values, FV, are the same in
the present value formula. Thus, the present value becomes an infinite series, which reduces to
FV ÷ i. Consequently, we calculate the market price of this consul as $625 in Equation 5.