Five years ago XYZ International issued some 29year zerocoup

Five years ago XYZ International issued some 29-year zero-coupon bonds that were priced with a market\'s required yield to maturity of 14 percent and a par value of $1,000. What did these bonds sell for when they were issued? Now that 5 years have passed and the market\'s required yeild to maturity on these bonds has climbed to 16 percent, what are they selling for? If the market\'s required yeild to maturity had fallen to 12 percent, what whould they have been selling for?

Solution

Given, Par value of bond = 1000$

Yield to maturity = (Par Value / PV) ^ (1/bond period) -1

or, 0.14 = (1000/PV)^(1/29) -1

or, 1.14^29 = 1000/PV

or, PV = 22.37$

Thus, the bonds were sell for 22.37$ when they were issued.

After 5 yeras, i.e. presnt year

for Yield to maturity = 16%

0.16 = (1000/PV)^(1/24) -1

or, 1.16^24 = 1000/PV

or, PV = 28.37$

Thus, the bonds are sold for 28.37$.

Now, for Yield to maturity = 12%

0.12 = (1000/PV)^(1/24) -1

or, 1.12^24 = 1000/PV

or, PV = 65.88$

Thus, the bonds are sold for 65.88$