Money, Banking, and International Finance
0. 1411
1
400 1,000
1
400
1
400
1,600 1 2 3
YTM=
+YTM
$ +$
+
+YTM
$
+
+YTM
$
$ =
( 6 )
As you can see, this calculation becomes very complicated. If you calculate the discount
rate manually, then you must calculate the PV 0 by selecting various discount rates, such as 0%,
5%, 10%, and 20%. Next, you insert your particular discount rate, r, into the Equation 7, and
select the discount rate that has a present value, PV 0 close to $1,600. Mathematicians wrote
programs that can solve for the discount rate. If you visit the author’s website, http://www.ken-
szulczyk.com, he has a JavaScript program that can solve for the discount rate.
^1 ^2 1 ^3
400 1,000
1
400
1
400
+r$ +$
+
+r$
+
+r$
PV 0 = ( 7 )
Yield to maturity generates two important rules on bonds, which are: Market interest rate (or yield to maturity) and the market price (or present value) of the
securities are inversely related. For example, if you examine the present value formula, the
interest rate, or yield to maturity is located in the denominators of the fractions. Thus, the
market price falls as the interest rate rises, and vice versa. If a bond has a shorter maturity, subsequently, its price will fluctuate less for a change in
the market interest rate. We show this by an example.For example, we have two bonds with a face value of $5,000 and a coupon interest rate of
10%, paid annually. In our case, both bonds pay $500 once a year. First bond matures in one
year while the other bond matures in 10 years. If the market interest rate rises to 16%, then the
one-year bond has a market price of $4,741.38 while the 10-year bond has a market value of
$3,550. Consequently, the interest rate change affected the 10-year bond more than the one-year
bond. We calculated the market value of the one-year bond in Equation 8 and the ten-year bond
in Equation 9. As this example illustrates, investors prefer money market securities because they
fluctuate less when the interest rate changes.
4,741.38
1 0.16
500 5,000
+^1 =$
$ +$
PV 0 = ( 8 )
3,550.03
1 0.16
500 5,000
1 0.16
500
1 0.16
500
(^12) + 10 =$