Question

Atlantis Fisheries issues zero coupon bonds on the market at a price of $604 per bond. Each bond has a face value of $1,000 payable at maturity in 8 years. What is the percentage yield to maturity for these bonds? Note: Corporate bonds pay semi-annual coupons. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

Solution:

Given:

Market Price of Zero-Coupon Bonds or Present Value of Bonds = $ 604 per bond

Face Value of Bond = $ 1,000

Maturity Period = 8 years.

To Calculate:

The Percentage Yield to Maturity of Bonds

Formula:

Yield to Maturity of Zero-Coupon Bonds = ((Face Value / Present Value) ^ 1/ Years to Maturity) - 1

Here:

Face Value of Bond = $ 1,000

Present Value of Bond or Market Price of Bond = $ 604

Years to Maturity = 8 Years

On putting these values in the formula, we get,

Yield to Maturity of Zero-Coupon Bonds = (($ 1000 / $ 604) ^ 1/8) – 1

Yield to Maturity of Zero-Coupon Bonds = ((1.6556291391) ^ 1/8) – 1

Yield to Maturity of Zero-Coupon Bonds = ((1.6556291391) ^ 0.125) – 1

Yield to Maturity of Zero-Coupon Bonds = 1.0650509465 – 1

Yield to Maturity of Zero-Coupon Bonds = 0.0650509465 = 6.505 %

Yield to Maturity of Zero-Coupon Bonds = 6.505 % ≈ 6.51 % (rounded off to 2 decimal places)

Ans: Yield to Maturity of Zero-Coupon Bonds = 6.51 %