CP

return would be 15 percent. To see this, calculate the price of the bond with 13 years

left to maturity, assuming that interest rates remain at 15 percent. With a calculator,

enter N 
13, I 
15, PMT 
100, and FV 
1000, and then press PV to obtain the

bond’s value, $720.84.

Note that the capital gain for the year is the difference between the bond’s value at

Year 2 (with 13 years remaining) and the bond’s value at Year 1 (with 14 years remain-

ing), or $720.84 $713.78 
$7.06. The interest yield, capital gains yield, and total

yield are calculated as follows:

Interest, or current, yield 
 $100/$713.78 
 0.1401 
14.01%

Capital gains yield 
 $7.06/$713.78 
 0.0099 
 0.99%

Total rate of return, or yield 
 $107.06/$713.78 
 0.1500 
 15.00%

Figure 4-2 graphs the value of the bond over time, assuming that interest rates in

the economy (1) remain constant at 10 percent, (2) fall to 5 percent and then remain

constant at that level, or (3) rise to 15 percent and remain constant at that level. Of

course, if interest rates do notremain constant, then the price of the bond will fluctu-

ate. However, regardless of what future interest rates do, the bond’s price will ap-

proach $1,000 as it nears the maturity date (barring bankruptcy, in which case the

bond’s value might fall dramatically).

Bond Valuation 161

FIGURE 4-2 Time Path of the Value of a 10% Coupon, $1,000 Par Value

Bond When Interest Rates Are 5%, 10%, and 15%

0 123456789101112131415

M = 1,000

1,495

714

Years

M

Time Path of Bond Value When rd = Coupon Rate = 10%

(Par Bond)

Bond Value

($) Time Path of 10% Coupon Bond's Value When

rd Falls to 5% and Remains There

(Premium Bond)

Time Path of 10% Coupon Bond's Value When

rd Rises to 15% and Remains There

(Discount Bond)

Year rd
5% rd
10% rd
15%

0 — $1,000 —

1 $1,494.93 1,000 $713.78

....

....

....

15 1,000 1,000 1,000

Note: The curves for 5% and 15% have a slight bow.

SeeCh 04 Tool Kit.xls for
details.

Bonds and Their Valuation 157