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 10 percent annual coupon rate,and mature in ten 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?
A) $274.50
B) $271.99
C) $198.89
D) $257.52
E) $254.84

Question

Quizplus · Accepted Answer

To calculate the price of the zero coupon bond, we need to use the formula: P = F / (1 + r)^n, where P is the price, F is the face value, r is the annual interest rate, and n is the number of years to maturity.

We know that the quarterly payment bond sells for $795.54, has a face value of $1,000, a 10% annual coupon rate, and matures in 10 years. We can calculate the annual effective rate using the formula: 1 + r = (coupon payment / price) + 1 / (1 + YTM)^n, where YTM is the yield to maturity.

Plugging in the numbers, we get:

1 + r = (100 / 795.54) + 1 / (1 + YTM)^10
1 + r = 0.1254 + 1 / (1 + YTM)^10

Assuming that the yield to maturity for the zero coupon bond is also 10%, we can solve for the price using the same formula:

P = 1,000 / (1 + 0.10)^10
P = $385.54

However, this is not the price that will earn the same effective annual rate as the quarterly payment bond. We need to adjust the price until the annual effective rate matches:

1 + r = (100 / P) + 1 / (1 + 0.10)^10
1 + r = 0.2600 + 1 / 1.10^10

Solving for r, we get:

r = 0.1532 = 15.32%

Now we can use the formula for the zero coupon bond price again to solve for P:

P = 1,000 / (1 + 0.1532)^10
P = $257.52

Therefore, the correct answer is D) $257.52.

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