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 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

First, we need to find the effective annual rate of the quarterly payment bonds:
N = 10 (since the bonds mature in 10 years)
I/Y = 4.5%/4 = 1.125% (since the coupon rate is quarterly)
PMT = $22.50 (= $1,000 x 4.5%/4)
FV = $1,000
Using the calculator, we solve for PV:
PV = $795.54

Next, we need to use the effective annual rate of the quarterly payment bonds to find the price of the zero coupon bonds. We can use the formula:
PV = FV / (1 + r)^N
where r is the annual effective rate, and N is the number of years to maturity.

We want to solve for PV, so:
FV = $1,000
N = 10
PV = ?
r = ?

To find r, we can use the formula:
r = (1 + i)^m - 1
where i is the quarterly rate (1.125%), and m is the number of quarters in a year (4).
r = (1 + 1.125%)^4 - 1
r = 4.57%

Now we can solve for PV:
PV = $1,000 / (1 + 4.57%)^10
PV = $479.72

Therefore, the zero coupon bonds would have to sell at $479.72 to earn the same effective annual rate as the quarterly payment bonds. Therefore, the best choice would be to issue zero coupon bonds, as they are cheaper for the same effective annual rate. Answer: C.

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