Question

On January 1, 2005, Systil Corporation issues $50M 10 year bonds with a coupon rate of 10%. Interest is payable annually at the end of the year. If the required return on bonds of similar risk at January 1, 2006 is 8%, what will be the price of the bonds be at this date?

Answer 1

By January 1, 2006 the price of the bonds=$50.675 M

Step-by-step explanation:

The price of a bond at any given time can be expressed as;

Current price=(Annual coupon×((1-(1/(1+r)^i)/r)+ (face value/(1+r)^i)

where;

i-maturity period, from 2005-2006=1 year

r-nominal yield to maturity rate=8%

coupon rate=10%

face value=$50 M

Annual coupon=(10/100)×50 M=5 M

replacing;

Current price=Annual coupon×((1-(1/(1+r)^i)/r + face value/(1+r)^i

(5 M×((1-(1/(1+0.08)^1)/0.08)+50/(1+0.08)^1

(5 M×(1-0.93)/0.08)+46.3

(5×0.875)+46.3=4.375+46.3=50.675 M

By January 1, 2006 the price of the bonds=$50.675 M