U.S.Delay Corporation,a subsidiary of the Postal Service,must decide whether to issue zero coupon bonds or quarterly payment bonds to fund construction of new facilities.The $1,000.00 par value quarterly payment bonds would sell at $795.54,have a 4.50% coupon rate,and mature in 10 years.At what price would the zero coupon bonds with a maturity of 10 years have to sell to earn the same effective annual rate as the quarterly payment bonds? Do not round your intermediate calculations.

Question

Quizplus · Accepted Answer

The effective annual rate of the quarterly payment bond can be calculated using the following formula:
EAR = (1 + coupon rate/4)^4 - 1
EAR = (1 + 0.045/4)^4 - 1
EAR = 0.0455 or 4.55%

To find the price of the zero coupon bond, we can use the following formula:
Price = Face Value / (1 + r)^n
Where r is the annual interest rate and n is the number of years to maturity.

Since the effective annual rate is 4.55%, the annual interest rate would be slightly higher than this. Let's assume a rate of 4.60%.

Price = 1000 / (1 + 0.046)^10
Price = $479.72

Therefore, the price of the zero coupon bonds would have to be $479.72 to earn the same effective annual rate as the quarterly payment bonds. Thus, the best choice is to issue the zero coupon bonds.

USDelay Corporation,a Subsidiary of the Postal Service,must Decide Whether to Issue